1.
When a voltage V of 12.2 V is applied to a DC motor, the current I in the motor is 0.20 A.
Which one of the following is the output power VI of the motor given to the correct appropriate
number of significant digits?
A.
2W
B.
2.4 W
C.
2.40 W
D.
2.44 W
(1)
2.
The diagram below shows a boat that is about to cross a river in a direction perpendicular to the
bank at a speed of 0.8 m s–1. The current flows at 0.6 m s–1 in the direction shown.
Bank
0.6 ms
–1
0.8 ms –1
Boat
Bank
The magnitude of the displacement of the boat 5 seconds after leaving the bank is
A.
3 m.
B.
4 m.
C.
5 m.
D.
7 m.
(1)
1
3.
Which one of the following units is a unit of energy?
A.
eV
B.
W s–1
C.
W m–1
D.
N m s–1
(1)
4.
Natalie measures the mass and speed of a glider. The percentage uncertainty in her
measurement of the mass is 3% and in the measurement of the speed is 10%. Her calculated
value of the kinetic energy of the glider will have an uncertainty of
A.
30%.
B.
23%.
C.
13%.
D.
10%.
(1)
5.
The ratio
diameter of a nucleus
is approximately equal to
diameter of an atom
A.
10–15.
B.
10–8.
C.
10–5.
D.
10–2.
(1)
2
6.
Which one of the following lists a fundamental unit and a derived unit?
A.
ampere
second
B.
coulomb
kilogram
C.
coulomb
newton
D.
metre
kilogram
(1)
7.
A student measures the current in a resistor as 677 mA for a potential difference of 3.6 V. A
calculator shows the resistance of the resistor to be 5.3175775 Ω. Which one of the following
gives the resistance to an appropriate number of significant figures?
A.
5.3 Ω
B.
5.32 Ω
C.
5.318 Ω
D.
5.31765775 Ω
(1)
8.
Two forces of magnitudes 7 N and 5 N act at a point. Which one of the following is not a
possible value for the magnitude of the resultant force?
A.
1N
B.
3N
C.
5N
D.
7N
(1)
3
9.
A student measures a distance several times. The readings lie between 49.8 cm and 50.2 cm.
This measurement is best recorded as
A.
49.8  0.2 cm.
B.
49.8  0.4 cm.
C.
50.0  0.2 cm.
D.
50.0  0.4 cm.
(1)
10.
The diameter of the nucleus of a hydrogen atom is of the order of
A.
10–8 m.
B.
10–15 m.
C.
10–23 m.
D.
10–30 m.
(1)
11.
The unit, the electron-volt is equivalent to
A.
1.6 × 1019 J.
B.
1.0 J.
C.
1.6 × 10–19 J.
D.
9.1 × 10–31 J.
(1)
4
12.
The time period T of oscillation of a mass m suspended from a vertical spring is given by the
expression
T = 2π
m
k
where k is a constant.
Which one of the following plots will give rise to a straight-line graph?
A.
T2 against m
B.
T against
C.
D.
m
T against m
T against m
(1)
13.
Which one of the following is a vector quantity?
A.
Electric power
B.
Electrical resistance
C.
Electric field strength
D.
Electric potential difference
(1)
5
14.
The power dissipated in a resistor of resistance R carrying a current I is equal to I2R. The value
of I has an uncertainty of ±2% and the value of R has an uncertainty of ±10%. The value of the
uncertainty in the calculated power dissipation is
A.
±8%.
B.
±12%.
C.
±14%.
D.
±20%.
(1)
15.
The number of heartbeats of a person at rest in one hour, to the nearest order of magnitude is
A.
101.
B.
102.
C.
103.
D.
105.
(1)
16.
The diameter of a proton is of the order of magnitude of
A.
10–12 m.
B.
10–15 m.
C.
10–18 m.
D.
10–21 m.
(1)
6
17.
An ammeter has a zero offset error. This fault will affect
A.
neither the precision nor the accuracy of the readings.
B.
only the precision of the readings.
C.
only the accuracy of the readings.
D.
both the precision and the accuracy of the readings.
(1)
18.
Which one of the following is a scalar quantity?
A.
Pressure
B.
Impulse
C.
Magnetic field strength
D.
Weight
(1)
19.
Which one of the following is a fundamental unit?
A.
Coulomb
B.
Ohm
C.
Volt
D.
Ampere
(1)
7
20.
When a force F of (10.0  0.2) N is applied to a mass m of (2.0 F 0.1) kg, the percentage
uncertainty attached to the value of the calculated acceleration m is
A.
2%.
B.
5%.
C.
7%.
D.
10%.
(1)
21.
Which one of the following is a fundamental unit?
A.
Coulomb
B.
Ohm
C.
Volt
D.
Ampere
(1)
22.
Which of the following gives the approximate ratio of the separation of the molecules in water
and in steam at atmospheric pressure?
Water : Steam
A.
1: 1
B.
1 : 10
C.
1 : 100
D.
1 : 1000
(1)
8
23.
The resistive force F acting on a sphere of radius r moving at speed v through a liquid is given
by
F = cvr
where c is a constant. Which of the following is a correct unit for c?
A.
N
B.
N s–1
C.
N m2 s–1
D.
N m–2 s
(1)
24.
Which of the following is the best estimate, to one significant digit, of the quantity shown
below?
π  8 .1
15.9
A.
1.5
B.
2.0
C.
5.8
D.
6.0
(1)
9
25.
Two objects X and Y are moving away from the point P. The diagram below shows the velocity
vectors of the two objects.
Velocity vector for object Y
P
Velocity vector for object X
Which of the following velocity vectors best represents the velocity of object X relative to
object Y?
A.
B.
C.
D.
(1)
10
26.
A student measures two lengths as follows:
T = 10.0  0.1 cm
S = 20.0  0.1 cm.
The student calculates:
FT, the fractional uncertainty in T
FS, the fractional uncertainty in S
FT–S, the fractional uncertainty in (T – S)
FT+S, the fractional uncertainty in (T + S).
Which of these uncertainties has the largest magnitude?
A.
FT
B.
FS
C.
FT–S
D.
FT+S
(1)
27.
A student moves between two points P and Q as shown below.
point P
x–direction
point Q
y–direction
The displacement from P in the x-direction is dX. The displacement from P in the y-direction is
dY. The resultant displacement from P is dR.
11
Which of the following diagrams shows the three displacements from point P?
A.
B.
P
P
dR
dY
dX
C.
dR
Q
P
dY
P
dY
dR
Q
Q
dX
D.
dX
dY
dX
dR
Q
(1)
28.
The order of magnitude of the weight of an apple is
A.
10–4 N.
B.
10–2 N.
C.
1 N.
D.
102 N.
(1)
12
29.
Which one of the following contains three fundamental units?
A.
Metre
Kilogram
Coulomb
B.
Second
Ampere
Newton
C.
Kilogram
Ampere
Kelvin
D.
Kelvin
Coulomb
Second
(1)
30.
The reading of a constant potential difference is made four times by a student. The readings are
1.176 V
1.178 V
1.177 V
1.176 V
The student averages these readings but does not take into account the zero error on the
voltmeter. The average measurement of the potential difference is
A.
precise and accurate.
B.
precise but not accurate.
C.
accurate but not precise.
D.
not accurate and not precise.
(1)
13
31.
The variation with time t of the speed v of an object is given by the expression
v = u + at
where u and a are constants.
A graph of the variation with time t of speed v is plotted. Which one of the following correctly
shows how the constants may be determined from this graph?
A.
B.
v
0
v
0
0
t
0
t
1
gradient =
a
gradient = a
–u
–u
C.
D.
v
0
v
0
u
t
gradient = a
0
0
u
t
1
gradient =
a
(1)
14
32.
An object of mass m is hung from a spring. When the object is pulled downwards and then
released, the frequency f of oscillation of the object is given by the expression
1
m
 2π
f
k
where k is a constant.
Which one of the following graphs would produce a straight-line for the variation with mass m
of frequency f?
x-axis
y-axis
A.
m
f
B.
m
1
f
C.
1
m2
1
f
D.
m
f2
(1)
15
33.
The volume V of a cylinder of height h and radius r is given by the expression
V = πr2h.
In a particular experiment, r is to be determined from measurements of V and h. The
uncertainties in V and in h are as shown below.
V
 7%
h
 3%
The approximate uncertainty in r is
A.
10%.
B.
5%.
C.
4%.
D.
2%.
(1)
34.
The ratio
diameter of hydrogen atom
to the nearest order of magnitude is
diameter of hydrogen nucleus
A.
102.
B.
105.
C.
1010.
D.
1015.
(1)
16
35.
The kWh is equal to
A.
1.0 × 103 J.
B.
3.6 × 103 J.
C.
6.0 × 104 J.
D.
3.6 × 106 J.
(1)
36.
The diagram below shows the position of the meniscus of the mercury in a mercury-in-glass
thermometer.
T / °C
2
4
6
8
10
Which of the following best expresses the indicated temperature with its uncertainty?
A.
(6.0 ± 0.5)°C
B.
(6.1 ± 0.1)°C
C.
(6.2 ± 0.2)°C
D.
(6.2 ± 0.5)°C
(1)
37.
Which of the following represents two vector quantities?
A.
distance, acceleration
B.
kinetic energy, work
C.
force, momentum
D.
electric field strength, electric potential
(1)
38.
The radius of a loop is measured to be (10.0 ± 0.5) cm. Which of the following is the best
estimate of the uncertainty in the calculated area of the loop?
17
A.
0.25%
B.
5%
C.
10%
D.
25%
(1)
39.
The mass of an atom of the isotope strontium-92 (92Sr) is of the order of
A.
10–23 kg.
B.
10–25 kg.
C.
10–27 kg.
D.
10–29 kg.
(1)
40.
Which one of the following is a fundamental unit in the SI system?
A.
Ampere
B.
Volt
C.
Ohm
D.
Tesla
(1)
18
41.
Which one of the following measurements is stated correctly to two significant digits?
A.
0.006 m
B.
0.06 m
C.
600 m
D.
620 m
(1)
42.
The frequency f of an oscillating system is given by
f
1 g
2 l
where g and  are constants.
The frequency f is measured for different values of l and a graph is plotted.
Which one of the following will produce a straight-line graph?
x-axis
y-axis
A.
f
l
B.
f
l
C.
f2
1
l
D.
f2
l
(1)
19
43.
The mass of an atom of the isotope strontium-92 (92Sr) is of the order of
A.
10–23 kg.
B.
10–25 kg.
C.
10–27 kg.
D.
10–29 kg.
(1)
44.
The relationship between two measured quantities P and Q is of the form
P = kQn
where k and n are constants.
A plot of lg P (y-axis) against lg Q (x-axis) will enable the value of k to be determined by
measuring only
A.
the intercept on the lg P axis.
B.
the intercept on the lg Q axis.
C.
the slope of the graph.
D.
the reciprocal of the slope of the graph.
(1)
45.
An object has an acceleration of 2.0 m s−2. Which of the following gives the change in the speed
of the object after 7.00 s to the correct number of significant digits?
A.
14 m s−1
B.
14.0 m s−1
C.
14.00 m s−1
D.
14.000 m s−1
(1)
20
46.
A particle is moving in a circular path of radius r. The time taken for one complete revolution is
T. The acceleration a of the particle is given by the expression
a=
4 2 r
.
T2
Which of the following graphs would produce a straight-line?
A.
a against T
B.
a against T2
C.
a against
1
T
D.
a against
1
T2
(1)
47.
The diagram below shows two vectors, x and y.
y
x
Which of the vectors below best represents the vector c that would satisfy the relation
c = x + y?
A.
B.
C.
D.
(1)
21
48.
An object falls from rest with an acceleration g. The variation with time t of the displacement s
of the object is given by
1
s  gt 2 .
2
The uncertainty in the value of the time is  6 and the uncertainty in the value of g is  4.
The best estimate for the uncertainty of the position of the object is
A.
5.
B.
8.
C.
10.
D.
16.
(1)
49.
The mass of an electron is 9.1  10–31 kg and that of a proton is 1.7  10–27 kg. Which one of
the following is the difference in the order of magnitude of the masses of the electron and the
proton?
A.
10.8
B.
7.4
C.
5.4
D.
3
(1)
50.
Sub-multiples of units may be expressed using a prefix. Which one of the following lists the
prefixes in decreasing order of magnitude?
A.
centi-
micro-
milli-
nano-
B.
milli-
centi-
nano-
micro-
C.
centi-
milli-
micro-
nano-
D.
milli-
micro-
centi-
nano(1)
22
51.
Values of current I in an electrical component and of the corresponding potential difference V
across the component are plotted on a graph. Error bars for each point have been included.
Which one of the following shows the best-fit line for the plotted points?
A.
B.
I
I
V
V
C.
D.
I
V
I
V
(1)
23
52.
Which one of the following includes three vector quantities?
A.
velocity
weight
field strength
B.
weight
mass
field strength
C.
velocity
energy
weight
D.
mass
energy
field strength
(1)
53.
The length of a rod is measured using part of a metre rule that is graduated in millimetres, as
shown below.
cm
2
3
4
5
6
7
8
9
10
Which one of the following is the measurement, with its uncertainty, of the length of the rod?
A.
5  0.1 cm
B.
5  0.2 cm
C.
5.0  0.1 cm
D.
5.0  0.2 cm
(1)
24
54.
The graph below shows the variation with ln P of a quantity x. (ln P is the natural logarithm of
the quantity P.) The magnitude of the gradient of the line is g.
1nP
1nP0
0
0
x
Which one of the following is the correct expression for the variation of P with x?
A.
P = P0 e−gx
B.
P = P0 e+gx
C.
P = P0 + e−gx
D.
P = P0 − e+gx
(1)
25
55.
The graph below shows how a quantity y varies with time t for a falling object.
y
0
0
t
Which one of the following quantities could be represented by y?
A.
Speed when air resistance is negligible
B.
Speed when air resistance is not negligible
C.
Distance moved from rest when air resistance is negligible
D.
Distance moved from rest when air resistance is not negligible
(1)
56.
Which one of the following quantities is a vector?
A.
Work
B.
Temperature
C.
Electric field
D.
Pressure
(1)
26
57.
The volume of the Earth is approximately 1012 km3 and the volume of a grain of sand is
approximately 1 mm3. The order of magnitude of the number of grains of sand that can fit in the
volume of the Earth is
A.
1012.
B.
1018.
C.
1024.
D.
1030.
(1)
58.
The period T of oscillation of a mass m attached to the end of a spring is given by T  2 m ,
k
where k is an accurately known constant. The mass is measured as 0.500  0.045 kg.
What is the percentage uncertainty in the calculated value of the period?
A.
3.0
B.
4.5
C.
9.0
D.
18
(1)
59.
The time interval between human heartbeats is of the order of
A.
10–2 s.
B.
10–1 s.
C.
100 s.
D.
101 s.
(1)
27
60.
The kilowatt-hour is equivalent to approximately
A.
60 J.
B.
3.6  103 J.
C.
8.6  104 J.
D.
3.6  106 J.
(1)
61.
The speed of sound v in a gas is related to the pressure P of the gas by the expression
v  kP
where k is a constant.
Which variables should be plotted in order to produce a straight-line graph with the slope equal
to k?
A.
v2 against P2
B.
v2 against P
C.
v against P
D.
v against
P
(1)
62.
The sides of a cube are each of length 1.00 m. Each side is measured with an uncertainty of 2.
The absolute uncertainty in the volume of the cube is
A.
0.02 m3.
B.
0.06 m3.
C.
0.2 m3.
D.
0.6 m3.
(1)
63.
The length of a page of the examination paper is approximately 30 cm.
Which of the following gives the order of magnitude for the time taken for light to travel the
28
length of the page?
A.
10–7 s
B.
10–8 s
C.
10–9 s
D.
10–10 s
(1)
64.
The grid below shows one data point and its associated error bar on a graph. The x-axis is not
shown.
5.0
4.0
3.0
2.0
1.0
Which of the following is the correct statement of the y-value of the data point, with its
uncertainty?
A.
3  0.2
B.
3.0  0.2
C.
3.0  0.20
D.
3.00  0.20
(1)
29
65.
A resistor of resistance R is connected across the terminals of a battery of emf E and internal
resistance r. The current I in the circuit is measured using an ammeter.
r
E
I
A
R
Which of the following assumptions is made in order that E, R, r and I are related by the
equation below?
E = I(R + r)
A.
The resistor of resistance R obeys Ohm’s law.
B.
The resistance R is much greater than the internal resistance r.
C.
The resistance of the ammeter is much less than the internal resistance r.
D.
The resistance of the ammeter is much less than (R + r).
(1)
30
66.
The variation with speed v of the force F acting on an object is given by the expression
F = pv2 + qv,
where p and q are constants.
What quantity should be plotted on the y-axis of a graph and what should be plotted on the xaxis in order to give a straight-line graph?
y-axis
A.
B.
F
v
F
v
x-axis
v
v2
C.
F
v
D.
F
v2
(1)
31
67.
Quantity x varies with quantity y according to the expression
y = pxn,
where p and n are constants.
Values of lg x (log10 x) are plotted against the corresponding values of lg y as shown below.
1gy
I
0
1gx
0
The intercept on the lg y-axis is I. Which of the following gives the value of lg p?
A.
–I
B.
+I
C.
– lg I
D.
+ lg I
(1)
68.
Which of the following contains only fundamental SI units?
A.
ampere
newton
second
B.
volt
second
kelvin
C.
mole
ampere
kilogram
D.
kilogram
metre
tesla
(1)
32
69.
The mass of a body is measured to be 0.600 kg and its acceleration to be 3 m s–2. The net force
on the body, expressed to the correct number of significant figures is
A.
1.8 N.
B.
1.80 N.
C.
2 N.
D.
2.0 N.
(1)
70.
The molar mass of water is 18 g. The approximate number of water molecules in a glass of
water is
A.
1022.
B.
1025.
C.
1028.
D.
1031.
(1)
71.
Both random and systematic errors are present in the measurement of a particular quantity.
What changes, if any, would repeated measurements of this quantity have on the random and
systematic errors?
Random
Systematic
A.
reduced
reduced
B.
reduced
unchanged
C.
unchanged
reduced
D.
unchanged
unchanged
(1)
33
72.
The mass of a body is measured with an uncertainty of 2.0 and its volume with an uncertainty
of 10. What is the uncertainty in the density of the body?
A.
0.2
B.
5.0
C.
12
D.
20
(1)
73.
Which list gives the masses of the particles in ascending order of magnitude?
least → greatest
A.
α-particle
β-particle
proton
B.
proton
α-particle
β-particle
C.
proton
β-particle
α-particle
D.
β-particle
proton
α-particle
(1)
74.
The kilowatt-hour (kW h) is equivalent to
A.
6.0×104 J .
B.
6.0×104W .
C.
3.6×106 J .
D.
3.6×106W .
(1)
34
75.
Which of the following contains three scalar quantities?
A.
mass
charge
speed
B.
density
weight
mass
C.
speed
weight
charge
D.
charge
weight
density
(1)
35
76.
A student uses a metre rule and a set-square to measure a series of vertical heights, as shown.
set-square
metre rule
height to
be measured
The metre rule is not vertical.
What type of error is reduced by using a set-square and what type of error is caused because the
metre rule is not vertical?
error reduced by use of
set-square
error caused by
non-vertical ruler
A.
random
random
B.
random
systematic
C.
systematic
random
D.
systematic
systematic
(1)
36
77.
The electrical resistance R of a component varies with temperature T according to the
expression
R = R0ek/T
where R0 and k are constants.
A graph of the variation with
on the
1
of lnR is drawn and a straight line is obtained. The intercept
T
1
axis is equal to
T
A.
–lnR0
B.

C.
lnR0
D.
ln R 0
k
ln R0
k
(1)
78.
An elephant has a life expectancy of 60 years. Which of the following gives the order of
magnitude of this lifetime?
A.
1011s
B.
109s
C.
107s
D.
105s
(1)
37
79.
The frequency f of waves of wavelength λ travelling on the surface of deep water is given by
g
f=
2
where g is the acceleration of free fall.
Which of the following will yield a straight-line graph?
y-axis
x-axis
1
A.
f2
B.
f2

C.
f

D.
f

1

(1)
80.
The diagram below shows two vectors X and Y.
X
Y
Which of the following best represents the vector Z = X – Y.
A.
Z
C.
B.
Z
D.
Z
Z
(1)
38
81.
Which of the following graphs shows the best-fit line for the plotted points?
A.
B.
y
0
C.
0
0
x
D.
y
0
0
x
y
0
x
0
x
y
0
(1)
82.
The period T of oscillation of a mass m on a spring, having spring constant k is T = 2π
m
.
k
The uncertainty in k is 11% and the uncertainty in m is 5%. The approximate uncertainty in T is
A.
4%.
B.
6%.
C.
8%.
D.
16%.
(1)
39
83.
The order of magnitude of the weight of an apple is
A.
10–4 N.
B.
10–2 N.
C.
1 N.
D.
102 N.
(1)
84.
The density of a metal cube is given by the expression ρ 
M
where M is the mass and V is the
V
volume of the cube. The percentage uncertainties in M and V are as shown below.
M
12
V
4.0
The percentage uncertainty in the calculated value of the density is
A.
3.0.
B.
8.0.
C.
16.
D.
48.
(1)
40
85.
The volume V of a cylinder of height h and radius r is given by the expression
V = r2h.
In a particular experiment, r is to be determined from measurements of V and h. The
uncertainties in V and in h are as shown below.
V
7
h
3
The approximate uncertainty in r is
A.
10.
B.
5.
C.
4.
D.
2.
(1)
86.
This question is about units and momentum.
(a)
Distinguish between fundamental units and derived units.
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
The rate of change of momentum R of an object moving at speed v in a stationary fluid of
constant density is given by the expression
R = kv2
where k is a constant.
(i)
State the derived units of speed v.
...........................................................................................................................
(1)
(ii)
Determine the derived units of R.
41
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Use the expression and your answers in (b)(i) and (b)(ii) to determine the derived
units of k.
...........................................................................................................................
...........................................................................................................................
(1)
(c)
Define
(i)
linear momentum.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
impulse.
...........................................................................................................................
...........................................................................................................................
(1)
(d)
In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed
of 18 m s–1. It passes through a shallow tank containing stationary water. The tank is of
length 9.3 m. The carriage leaves the tank at a speed of 13 m s–1.
18 m s–1
water-tank
13 m s –1
carriage, mass 450 kg
9.3m
As the carriage passes through the tank, the carriage loses momentum and causes some
water to be pushed forwards with a speed of 19 m s–1 in the direction of motion of the
carriage.
(i)
For the carriage passing through the water-tank, deduce that the magnitude of its
total change in momentum is 2250N s.
...........................................................................................................................
42
...........................................................................................................................
(1)
(ii)
Use the answer in (d)(i) to deduce that the mass of water moved in the direction of
motion of the carriage is approximately 120 kg.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Calculate the mean value of the magnitude of the acceleration of the carriage in the
water.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(e)
For the carriage in (d) passing through the water-tank, determine
(i)
its total loss in kinetic energy.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
43
(ii)
the gain in kinetic energy of the water that is moved in the direction of motion of
the carriage.
...........................................................................................................................
...........................................................................................................................
(1)
(f)
By reference to the principles of conservation of momentum and of energy, explain your
answers in (e).
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 20 marks)
87.
This question is about an experiment designed to investigate Newton’s second law.
In order to investigate Newton’s second law, David arranged for a heavy trolley to be
accelerated by small weights, as shown below. The acceleration of the trolley was recorded
electronically. David recorded the acceleration for different weights up to a maximum of 3.0 N.
He plotted a graph of his results.
heavy trolley
acceleration
pulley
weight
44
(a)
Describe the graph that would be expected if two quantities are proportional to one
another.
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
David’s data are shown below, with uncertainty limits included for the value of the
weights. Draw the best-fit line for these data.
1.40
acceleration
/ ms–2
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
weight / N
(2)
45
(c)
Use the graph to
(i)
explain what is meant by a systematic error.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
estimate the value of the frictional force that is acting on the trolley.
...........................................................................................................................
(1)
(iii)
estimate the mass of the trolley.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 9 marks)
88.
Data based question. This question is about change of electrical resistance with temperature.
The table below gives values of the resistance R of an electrical component for different values
of its temperature T. (Uncertainties in measurement are not shown.)
T/°C
1.2
2.0
3.5
5.2
6.8
8.1
9.6
R/Ω
3590
3480
3250
3060
2880
2770
2650
46
(a)
On the grid below, plot a graph to show the variation with temperature T of the resistance
R. Show values on the temperature axis from T = 0°C to T = 10°C.
(3)
(b)
(i)
Draw a curve that best fits the points you have plotted. Extend your curve to cover
the temperature range from 0°C to 10°C.
(1)
(ii)
Use your graph to determine the resistance at 0°C and at 10°C.
Resistance at 0°C = ...............................................Ω
Resistance at 10°C = .............................................Ω
(2)
(c)
On your graph, draw a straight-line between the resistance values at 0°C and at 10°C.
This line shows the variation with temperature (between 0°C and 10°C) of the resistance,
47
assuming a linear change.
(1)
(d)
(i)
Assuming a linear change of resistance with temperature, use your graph to
determine the temperature at which the resistance is 3060 Ω.
Temperature = .........................................................°C
(1)
(ii)
Use your answer in (d)(i) to calculate the percentage difference in the temperature
for a resistance of 3060 Ω that results from assuming a linear change rather than
the non-linear change.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(Total 11 marks)
89.
This question is about measuring the permittivity of free space ε0.
The diagram below shows two parallel conducting plates connected to a variable voltage
supply. The plates are of equal areas and are a distance d apart.
variable voltage supply
+
d
V
–
48
The charge Q on one of the plates is measured for different values of the potential difference V
applied between the plates. The values obtained are shown in the table below. Uncertainties in
the data are not included.
(a)
V/V
Q / nC
10.0
30
20.0
80
30.0
100
40.0
160
50.0
180
Plot a graph of V (x-axis) against Q (y-axis).
(4)
(b)
Draw the line of best fit for the data points.
(1)
49
(c)
Determine the gradient of your best-fit line.
(2)
.....................................................................................................................................
.....................................................................................................................................
(d)
The gradient of the graph is a property of the two plates and is known as capacitance.
Deduce the units of capacitance.
.....................................................................................................................................
(1)
The relationship between Q and V for this arrangement is given by the expression
Q=
ε0 A
d
V
where A is the area of one of the plates.
In this particular experiment A = 0.20 m2 and d = 0.50 mm.
(e)
Use your answer to (c) to determine a value for ε0.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 11 marks)
50
90.
This question is about measuring the permittivity of free space ε0.
The diagram below shows two parallel conducting plates connected to a variable voltage
supply. The plates are of equal areas and are a distance d apart.
variable voltage supply
+
d
V
–
The charge Q on one of the plates is measured for different values of the potential difference V
applied between the plates. The values obtained are shown in the table below. The uncertainty
in the value of V is not significant but the uncertainty in Q is 10%.
V/V
Q / nC  10%
10.0
30
20.0
80
30.0
100
40.0
160
50.0
180
51
(a)
Plot the data points opposite on a graph of V (x-axis) against Q (y-axis).
(4)
(b)
By calculating the relevant uncertainty in Q, add error bars to the data points (10.0, 30)
and (50.0, 180).
(3)
(c)
On the graph above, draw the line that best fits the data points and has the maximum
permissible gradient. Determine the gradient of the line that you have drawn.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
52
(d)
The gradient of the graph is a property of the two plates and is known as capacitance.
Deduce the units of capacitance.
.....................................................................................................................................
(1)
The relationship between Q and V for this arrangement is given by the expression
Q=
ε0 A
d
V
where A is the area of one of the plates.
In this particular experiment A = 0.20  0.05 m2 and d = 0.50  0.01 mm.
(e)
Use your answer to (c) to determine the maximum value of ε0 that this experiment yields.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(Total 15 marks)
53
91.
This question is about power output of an outboard motor.
A small boat is powered by an outboard motor of variable power P. The graph below shows the
variation with speed v of P when the boat is carrying different loads.
5.0
4.5
350 kg
4.0
3.5
3.0
300 kg
P / kW 2.5
2.0
1.5
250 kg
1.0
200 kg
0.5
0.0
0.0
0.5
1.0
1.5
2.0 2.5
v / ms–1
3.0 3.5
4.0
The masses shown are the total mass of the boat plus passengers,
(a)
For the boat having a steady speed of 2.0 m s–1 and with a total mass of 350 kg
(i)
use the graph to determine the power of the engine.
...........................................................................................................................
(1)
(ii)
calculate the frictional (resistive) force acting on the boat.
...........................................................................................................................
...........................................................................................................................
(2)
54
Consider the case of the boat moving with a speed of 2.5 m s–1.
(b)
(i)
Use the axes below to construct a graph to show the variation of power P with the
total mass W.
200
250
300
350
400
450
W / kg
(6)
(ii)
Use data from the graph that you have drawn to determine the output power of the
motor for a total mass of 330 kg.
...........................................................................................................................
(1)
(Total 10 marks)
55
92.
This question is about power output of an outboard motor.
A small boat is powered by an outboard motor of variable power P. The graph below shows the
variation with speed v of P when the boat is carrying different loads.
5.0
4.5
350 kg
4.0
3.5
3.0
300 kg
P / kW 2.5
2.0
1.5
250 kg
1.0
200 kg
0.5
0.0
0.0
0.5
1.0
1.5
2.0 2.5
v / ms–1
3.0 3.5
4.0
The masses shown are the total mass of the boat plus passengers,
(a)
For the boat having a steady speed of 2.0 m s–1 and with a total mass of 350 kg
(i)
use the graph to determine the power of the engine.
...........................................................................................................................
(1)
(ii)
calculate the frictional (resistive) force acting on the boat.
...........................................................................................................................
...........................................................................................................................
(2)
56
Consider the case of the boat moving with a speed of 2.5 ms–1.
(b)
(i)
Use the axes below to construct a graph to show the variation of power P with the
total mass W.
200
250
300
350
400
450
W / kg
(6)
(ii)
Use data from the graph that you have drawn to determine the power of the motor
for a total mass of 330 kg.
...........................................................................................................................
(1)
57
The relationship between power P and speed v is of the form
P = kvn
where n is an integer and k is a constant.
The graph below shows the variation of lg v (log10 v) with lg P (log10 P) for the situation when
the total mass is 350 kg. P is measured in kW and v is measured in m s–1.
0.7
1g (P / kW)
0.6
0.5
0.4
0.3
0.2
0.1
–0.4
0.0
–0.3 –0.2 –0.1 0.0
–0.1
0.1
0.2
0.3
0.4
0.5
0.6
1g (v / ms –1)
–0.2
–0.3
–0.4
–0.5
–0.6
–0.7
–0.8
–0.9
–1.0
58
(c)
Use the graph to deduce the value of n and explain how you obtained your answer.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 13 marks)
93.
This question is about trajectory motion.
Antonia stands at the edge of a vertical cliff and throws a stone upwards at an angle of 60° to
the horizontal.
v = 8.0ms –1
60°
Sea
59
The stone leaves Antonia’s hand with a speed v = 8.0 m s–1. The time between the stone leaving
Antonia’s hand and hitting the sea is 3.0 s.
The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the
point where the stone leaves Antonia’s hand.
Ignoring air resistance calculate
(a)
the maximum height reached by the stone.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(b)
the horizontal distance travelled by the stone.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 5 marks)
94.
The resistive force F that acts on an object moving at speed v in a stationary fluid of constant
density is given by the expression
F = kv2
where k is a constant.
60
(a)
State the derived units of
(i)
force F.
...........................................................................................................................
(1)
(ii)
speed v.
...........................................................................................................................
(1)
(b)
Use your answers in (a) to determine the derived units of k.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 3 marks)
95.
This question is about radioactive decay.
A nucleus of the isotope xenon, Xe-131, is produced when a nucleus of the radioactive isotope
iodine I-131 decays.
(a)
Explain the term isotopes.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
Fill in the boxes below in order to complete the nuclear reaction equation for this decay.
131
I
131
Xe + – +
54
(2)
61
(c)
The activity A of a freshly prepared sample of the iodine isotope is 3.2 × 105 Bq. The
variation of the activity A with time t is shown below.
3.5
3.0
2.5
2.0
5
A /10 Bq
1.5
1.0
0.5
0
0
5.0
10
15
20
25
30
35
40
45
t / days
Draw a best-fit line for the data points.
(1)
(d)
Use the graph to estimate the half-life of I-131.
.....................................................................................................................................
(1)
(Total 6 marks)
62
96.
Data analysis question
At high pressures, a real gas does not behave as an ideal gas. For a certain range of pressures, it
is suggested that the relation between the pressure P and volume V of one mole of the gas at
constant temperature is given by the equation
PV = A + BP
where A and B are constants.
In an experiment to measure the deviation of nitrogen gas from ideal gas behaviour, 1 mole of
nitrogen gas was compressed at a constant temperature of 150 K. The volume V of the gas was
measured for different values of the pressure P. A graph of the product PV of pressure and
volume was plotted against the pressure P and is shown below. (Error bars showing the
uncertainties in measurements are not shown).
13
12
PV / ×10 2 N m
11
10
0
5.0
10
15
20
P / ×106 Pa
(a)
Draw a line of best fit for the data points.
(1)
63
(b)
Use the graph to determine the values of the constants A and B in the equation
PV = A + BP.
Constant A ……………………………….................................................................
……………………………….................................................................
……………………………….................................................................
Constant B ……………………………….................................................................
……………………………….................................................................
……………………………….................................................................
……………………………….................................................................
……………………………….................................................................
(5)
(c)
State the value of the constant B for an ideal gas.
.....................................................................................................................................
(1)
(d)
The equation PV = A + BP is valid for pressures up to 6.0 × 107 Pa.
(i)
Determine the value of PV for nitrogen gas at a pressure of 6.0 × 107 Pa.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Calculate the difference between the value of PV for an ideal gas and nitrogen gas
when both are at a pressure of 6.0 × 107 Pa.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(e)
In the original experiment, the pressure P was measured to an accuracy of 5% and the
volume V was measured to an accuracy of 2%. Determine the absolute error in the value
of the constant A.
64
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 14 marks)
97.
The Geiger-Nuttall theory of α-particle emission relates the half-life of the α-particle emitter to
the energy E of the α-particle. One form of this relationship is
L=
166
1
E2
– 53.5.
L is a number calculated from the half-life of the α-particle emitting nuclide and E is measured
in MeV.
Values of E and L for different nuclides are given below. (Uncertainties in the values are not
shown.)

1
Nuclide
238
236
234
228
208
212
(a)
E / MeV
L
1
/ Me V
1
2
E2
U
4.20
17.15
0.488
U
4.49
14.87
0.472
U
4.82
12.89
0.455
Th
5.42
7.78
…………..
Rn
6.14
3.16
0.404
Po
7.39
–2.75
0.368
Complete the table above by calculating, using the value of E provided, the value of
1
1
E2
for the nuclide
228
Th . Give your answer to three significant digits.
(1)
The graph below shows the variation with
1
E
1
2
of the quantity L. Error bars have not been
added.
65
L
20
16
12
8
4
0
0.2
0.3
0.4
0.5
1
11
–2
E 2 / MeV
–4
(b)
(i)
Identify the data point for the nuclide
208
Rn . Label this point R.
(1)
(ii)
On the graph, mark the point for the nuclide
228
Th . Label this point T.
(1)
(iii)
Draw the best-fit straight-line for all the data points.
(1)
66
(c)
(i)
Determine the gradient of the line you have drawn in (b)(iii).
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Without taking into consideration any uncertainty in the values for the gradient and
for the intercept on the x-axis, suggest why the graph does not agree with the stated
relationship for the Geiger-Nuttall theory.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(d)
On the graph above, draw the line that would be expected if the relationship for the
Geiger-Nuttall theory were correct. No further calculation is required.
(2)
(Total 10 marks)
98.
This question is about collisions and radioactive decay.
(a)
(i)
Define linear momentum and impulse.
Linear momentum: ..........................................................................................
..........................................................................................
Impulse:
..........................................................................................
..........................................................................................
(2)
67
(ii)
State the law of conservation of momentum.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Using your definitions in (a)(i), deduce that linear momentum is constant for an
object in equilibrium.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
A stationary radon-220 ( 220
86 Rn ) nucleus undergoes α-decay to form a nucleus of polonium (Po).
The α-particle has kinetic energy of 6.29 MeV.
(b)
(i)
Complete the nuclear equation for this decay.
220
86 Rn

Po
+
(2)
(ii)
Calculate the kinetic energy, in joules, of the α-particle.
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Deduce that the speed of the α-particle is 1.74 × 107 m s–1.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
The diagram below shows the α-particle and the polonium nucleus immediately after the decay.
The direction of the velocity of the α-particle is indicated.
68
-particle
polonium nucleus
(c)
(i)
On the diagram above, draw an arrow to show the initial direction of motion of the
polonium nucleus immediately after the decay.
(1)
(ii)
Determine the speed of the polonium nucleus immediately after the decay.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(iii)
In the decay of another radon nucleus, the nucleus is moving before the decay.
Without any further calculation, suggest the effect, if any, of this initial speed on
the paths shown in (c)(i).
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
The half-life of the decay of radon-220 is 55 s.
(d)
(i)
Explain why it is not possible to state a time for the life of a radon-220 nucleus.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
69
(ii)
Define half-life.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
A sample of radon-220 has an initial activity A0.
(iii)
On the axes below, draw a graph to show the variation with time t of the activity A
for time t = 0 to time t = 180 s.
A0
A
0
0
40
80
120
160
200
t/s
(2)
70
(iv)
Use your graph to determine the activity, in terms of A0, of the sample of radon at
time t = 120 s. Also, estimate the activity, in terms of A0, at time t = 330 s.
Activity at time t = 120 s : ……………………................................................
Activity at time t = 330 s : ………………………............................................
(2)
(Total 25 marks)
99.
The Geiger-Nuttall theory of α-particle emission relates the half-life of the α-particle emitter to
the energy E of the α-particle. One form of this relationship is
L=
166
1
E
– 53.5.
2
L is a number calculated from the half-life of the α-particle emitting nuclide and E is measured
in MeV.
Values of E and L for different nuclides are given below. (Uncertainties in the values are not
shown.)
1
Nuclide
238
236
234
228
208
212
(a)
E / MeV
L
1
E

/ MeV
1
2
2
U
4.20
17.15
0.488
U
4.49
14.87
0.472
U
4.82
12.89
0.455
Th
5.42
7.78
…………..
Rn
6.14
3.16
0.404
Po
7.39
–2.75
0.368
Complete the table above by calculating, using the value of E provided, the value of
1
1
E2
for the nuclide
228
Th . Give your answer to three significant digits.
(1)
The graph below shows the variation with
1
1
of the quantity L. Error bars have not been
E2
added.
71
L
20
16
12
8
4
0
0.2
0.3
0.4
0.5
1
11
–2
E 2 / MeV
–4
(b)
(i)
Identify the data point for the nuclide
208
Rn . Label this point R.
(1)
(ii)
On the graph, mark the point for the nuclide
228
Th . Label this point T.
(1)
(iii)
Draw the best-fit straight-line for all the data points.
(1)
72
(c)
(i)
Determine the gradient of the line you have drawn in (b)(iii).
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
Without taking into consideration any uncertainty in the values for the gradient and
for the intercept on the x-axis, suggest why the graph does not agree with the stated
relationship for the Geiger-Nuttall theory.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(d)
On the graph above, draw the line that would be expected if the relationship for the
Geiger-Nuttall theory were correct. No further calculation is required.
(2)
(e)
238
U is ± 0.03 MeV. Deduce that this
1
uncertainty is consistent with quoting the value of
to three significant digits.
1
The uncertainty in the measurement of E for
E2
(3)
(Total 13 marks)
73
100. This question is about collisions and radioactive decay.
(a)
(i)
Define linear momentum and impulse.
Linear momentum: ..........................................................................................
..........................................................................................
Impulse:
..........................................................................................
..........................................................................................
(2)
(ii)
State the law of conservation of momentum.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Using your definitions in (a)(i), deduce that linear momentum is constant for an
object in equilibrium.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
A stationary radon-220 ( 220
86 Rn ) nucleus undergoes α-decay to form a nucleus of polonium (Po).
The α-particle has kinetic energy of 6.29 MeV.
(b)
(i)
Complete the nuclear equation for this decay.
220
86 Rn

Po
+
(2)
74
(ii)
Calculate the kinetic energy, in joules, of the α-particle.
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
Deduce that the speed of the α-particle is 1.74 × 107 m s–1.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
The diagram below shows the α-particle and the polonium nucleus immediately after the decay.
The direction of the velocity of the α-particle is indicated.
-particle
polonium nucleus
(c)
(i)
On the diagram above, draw an arrow to show the initial direction of motion of the
polonium nucleus immediately after the decay.
(1)
(ii)
Determine the speed of the polonium nucleus immediately after the decay.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
75
(iii)
In the decay of another radon nucleus, the nucleus is moving before the decay.
Without any further calculation, suggest the effect, if any, of this initial speed on
the paths shown in (c)(i).
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
The half-life of the decay of radon-222 is 3.8 days and radon-220 has a half-life of 55 s.
(d)
(i)
Suggest three ways in which nuclei of radon-222 differ from those of radon-220.
1.
.................................................................................................................
.................................................................................................................
2.
.................................................................................................................
.................................................................................................................
3.
.................................................................................................................
.................................................................................................................
(3)
(ii)
Define half-life.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
76
(iii)
State the expression that relates the activity At at time t of a sample of a radioactive
material to its initial activity A0 at time t = 0 and to the decay constant λ. Use this
expression
to derive the relationship between the decay constant λ and the half-life
T1
2 .
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(iv)
Radon-222 emits α-particles. The activity of radon gas in a sample of 1.0 m3 of air
is 4.6 Bq. Given that 1.0 m3 of the air contains 2.6 × 1025 molecules, determine the
ratio
number of radon - 222 atoms in 1.0 m 3 of air
number of molecules in 1.0 m 3 of air
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(e)
Suggest whether radon-222 or radon-220 presents the greater hazard to people over a long
period of time.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 30 marks)
77
101. This question is about an electrostatics experiment to investigate how the force between two
charges varies with the distance between them.
A small charged sphere S hangs vertically from an insulating thread as shown below.
S
A second identically charged sphere P is brought close to S. S is repelled as shown below.
P
S
force F
r
The magnitude of the electrostatic force on sphere S is F. The separation between the two
spheres is r.
78
(a)
On the axes below draw a sketch
1 graph to show how, based on Coulomb’s law, you
2
would expect F to vary with r
.
F
0
0
1
2
r
(2)
79
Values of F are determined for different values of r. The variation with
1
of these values is
r2
shown below. The estimated uncertainties in these values are negligible.
F / 10 - 3 N
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0
(b)
(i)
2.0
4.0
6.0
8.0
10.0
12.0
1
/10 3 m- 2
r2
Draw the best-fit line for these data points.
(2)
(ii)
Use the graph to explain whether, in the experiment, there are random errors,
systematic errors or both.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
80
(iii)
Calculate the gradient of the line drawn in (b) (i).
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(iv)
The magnitude of the charge on each sphere is the same. Use your answer to (b)
(iii) to calculate this magnitude.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
(Total 13 marks)
81
102. This question is about an electrostatics experiment to investigate how the force between two
charges varies with the distance between them.
A small charged sphere S hangs vertically from an insulating thread as shown below.
S
A second identically charged sphere P is brought close to S. S is repelled as shown below
P
S
force F
r
82
The magnitude of the electrostatic force on sphere S is F. The separation between the two
spheres is r.
(a)
On the axes below draw a sketch graph to show how, based on Coulomb’s law, you
would expect F to vary with
1
.
r2
F
0
0
1
2
r
(2)
83
Values of F are determined for different values of r. The variation with
1
of these values is
r2
shown below. The estimated uncertainties in these values are negligible.
F / 10 - 3 N
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0
(b)
(i)
2.0
4.0
6.0
8.0
10.0
12.0
1
/10 3 m- 2
r2
Draw the best-fit line for these data points.
(2)
(ii)
Use the graph to explain whether, in the experiment, there are random errors,
systematic errors or both.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
84
(iii)
Calculate the gradient of the line drawn in (b) (i).
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(iv)
The magnitude of the charge on each sphere is the same. Use your answer to (b)
(iii) to calculate this magnitude.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
(c)
Explain how a graph showing the variation with lg r of lg F can be used to verify the
relation between r and F.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 16 marks)
85
103. This question is about the rise of water in a capillary tube.
A capillary tube is a tube that is open at both ends and has a very narrow bore. A capillary tube
is supported vertically with one end immersed in water. Water rises up the tube due to a
phenomenon called capillary action. The water in the bore of the tube forms a column of height
h as shown below.
narrow bore
glass wall
glass wall
h
water
86
(a)
The height h, for a particular capillary tube was measured for different temperatures of
the water. The variation with temperature  of the height h is shown below. Uncertainties
in the measurements are not shown.
17
16
15
14
13
h / cm
12
11
10
9.0
8.0
0
(i)
10
20
30
40
50
C
60
70
80
90
On the graph above, draw a best-fit line for the data points.
(1)
(ii)
Determine the height h0 of the water column at temperature = 0C.
.........................................................................................................................
.........................................................................................................................
(1)
87
(b)
Explain why the results of this experiment suggest that the relationship between the
height h and temperature  is of the form
h = h0(1 − k)
where k is constant.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(4)
(c)
Deduce that the value of k is approximately 4.8  10−3 deg C−1.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
88
(d)
The experiment is repeated using tubes with bores of different radii r but1 keeping the
water temperature constant. The graph below shows the variation with r of the height h
for capillary tubes of different radii r for a water temperature of 20C.
0.35
0.30
0.25
0.20
h/m
0.15
0.10
0.05
0
0
5.0
10.0
15.0
1
– / 10 3 m–1
r
20.0
25.0
It is suggested that capillary action is one of the means by which water moves from the
roots of a tree to the leaves. A particular tree has a height of 25 m.
Use the graph to estimate the radius of the bore of the tubes that would enable water to be
raised by capillary action from ground level to the top of the tree. Comment on your
answer.
Estimate: .................................................................................................................
.................................................................................................................
.................................................................................................................
Comment: .................................................................................................................
.................................................................................................................
.................................................................................................................
(4)
(Total 13 marks)
89
104. This question is about a spider’s web.
An experiment was carried out to measure the extension x of a thread of a spider’s web when a
load F is applied to it. The results of the experiment are shown plotted below. Uncertainties in
the measurements are not shown.
9.0
thread
breaks at
this point
8.0
7.0
6.0
5.0
F / 10 –2 N
4.0
3.0
2.0
1.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
x / 10 –2 m
(a)
Draw a best-fit line for the data points.
(1)
90
(b)
When a load is applied to a material, it is said to be under “stress”. The magnitude P of
the stress is given by
P
F
A
where, A is the area of cross-section of the sample of the material.
Use the graph and the data below to deduce that the thread used in the experiment has a
greater breaking stress than steel.
Breaking stress of steel = 1.0  109 N m−2
Radius of spider web thread = 4.5  10−6 m
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
91
(c)
In a particular web, one thread has the same original length as the thread used in the
experiment. In the making of this web, the original length of the thread is extended by 2.4
 10−2 m.
(i)
Use the graph to deduce that the amount of work required to further extend the
thread to the length at which it just breaks, is about 1.6  10−3 J. Explain your
working.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
If the thread is not to break due to the impact of a flying insect, then the thread
must be capable of absorbing all the kinetic energy of the insect as it is brought to
rest by the impact. Determine the impact speed that an insect of mass 0.15 g must
have in order that it just breaks the thread.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(Total 10 marks)
92
105. This question is about a spider’s web.
An experiment was carried out to measure the extension x of a thread of a spider’s web when a
load F is applied to it. The results of the experiment are shown plotted below. Uncertainties in
the measurements are not shown.
9.0
thread
breaks at
this point
8.0
7.0
6.0
5.0
F / 10 –2 N
4.0
3.0
2.0
1.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
x / 10 –2 m
(a)
Draw a best-fit line for the data points.
(1)
(b)
The relationship between F and x is of the form F = kxn.
State and explain the graph you would plot in order to determine the value n.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
93
(c)
When a load is applied to a material, it is said to be under “stress”. The magnitude P of
the stress is given by
P
F
A
where, A is the area of cross-section of the sample of the material.
Use the graph and the data below to deduce that the thread used in the experiment has a
greater breaking stress than steel.
Breaking stress of steel = 1.0  109 N m−2
Radius of spider web thread = 4.5  10−6 m
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(d)
The uncertainty in the measurement of the radius of the thread is  0.1  10−6 m.
Determine the percentage uncertainty in the value of the area of the thread.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
94
(e)
In a particular web, one thread has the same original length as the thread used in the
experiment. In the making of this web, the original length of the thread is extended by 2.4
 10−2 m.
(i)
Use the graph to deduce that the amount of work required to further extend the
thread to the length at which it just breaks, is about 1.6  10−3 J. Explain your
working.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
If the thread is not to break due to the impact of a flying insect, then the thread
must be capable of absorbing all the kinetic energy of the insect as it is brought to
rest by the impact. Determine the impact speed that an insect of mass 0.15 g must
have in order that it just breaks the thread.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(Total 15 marks)
95
106. A hot object may be cooled by blowing air past it. This cooling process is known as forced
convection. In order to investigate forced convection, hot oil was placed in a metal can. The can
was placed on an insulating block and air was blown past the can, as shown below.
stirrer
thermometer
lid
hot oil
current of air
metal can
insulating block
96
The hot oil was stirred continuously and its temperature was taken every minute as it cooled.
The graph below shows the variation with time of the temperature of the cooling oil.
120
100
temperature /  C
80
60
40
20
0
0
2
4
6
8
time / minutes
10
12
14
97
It is thought that the rate R of decrease of temperature depends on the temperature difference
between the oil and its surroundings (the excess temperature θE). The temperature of the
surroundings was 26C.
(a)
On the graph above,
(i)
draw a straight-line parallel to the time axis to represent the temperature of the
surroundings;
(1)
(ii)
by drawing a suitable tangent, calculate the rate of decrease of temperature, in C
s–1, for an excess temperature of 50 Celsius degrees (C).
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
98
(b)
In order to investigate the variation with R of E, a graph of R against E is plotted. The
graph below shows four plotted data points. Uncertainties in the points are not included.
0.24
0.20
0.16
R /  C s–1
0.12
0.08
0.04
0.00
0
20
40
60
E
(i)
80
100
/ C
Using your answer to (a)(ii), plot the data point corresponding toE = 50C.
(1)
(ii)
The uncertainty in the measurement of R at each excess temperature is 10. On
the graph, draw error bars to represent the uncertainties in R at excess temperatures
of 20C and 81C.
(2)
99
(c)
Explain why the graph in (b) supports the conclusion that the excess temperature E is
related to the rate of cooling R by the expression
R = k E ,
where k is a constant.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 11 marks)
107. A hot object may be cooled by blowing air past it. This cooling process is known as forced
convection. In order to investigate forced convection, hot oil was placed in a metal can. The can
was placed on an insulating block and air was blown past the can, as shown below.
stirrer
thermometer
lid
hot oil
current of air
metal can
insulating block
100
The hot oil was stirred continuously and its temperature was taken every minute as it cooled.
The graph below shows the variation with time of the temperature of the cooling oil.
120
100
temperature /  C
80
60
40
20
0
0
2
4
6
8
time / minutes
10
12
14
It is thought that the rate R of decrease of temperature depends on the temperature difference
between the oil and its surroundings (the excess temperature E). The temperature of the
surroundings was 26C.
(a)
On the graph above,
(i)
draw a straight-line parallel to the time axis to represent the temperature of the
surroundings.
(1)
101
(ii)
by drawing a suitable tangent, calculate the rate of decrease of temperature, in C
s–1, for an excess temperature of 50 Celsius degrees (C).
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
(b)
In order to investigate the variation with R of E, a graph of R against E is plotted. The
graph below shows four plotted data points. Uncertainties in the points are not included.
0.24
0.20
0.16
R /  C s–1
0.12
0.08
0.04
0.00
0
20
40
60
E
80
100
/ C
102
(i)
Using your answer to (a)(ii), plot the data point corresponding toE = 50C.
(1)
(ii)
The uncertainty in the measurement of R at each excess temperature is 10. On
the graph, draw error bars to represent the uncertainties in R at excess temperatures
of 20C and 81C.
(2)
(c)
(i)
Explain why the graph in (b) supports the conclusion that the excess temperature
E is related to the rate of cooling R by the expression
R = k E,
where k is a constant.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
At high excess temperatures, the equation in (i) is thought to become invalid.
Discuss whether the graph in (b) provides any evidence for this suggestion.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
103
(d)
In a second experiment, the data is analysed by plotting a graph of lgR against lgE. (lg is
the logarithm to the base 10.)
(i)
On the axes below, draw a sketch graph to show the line that would be obtained.
(Note that this is a sketch graph. No data points or values on the axes are
required.)
1gR
1g
E
(1)
(ii)
Assuming the expression in (c)(i) is correct, state the gradient of the line of the
graph. Also, explain how the value of k is obtained.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(Total 16 marks)
104
108. This question is about thermal energy transfer through a rod.
A student designed an experiment to investigate the variation of temperature along a copper rod
when each end is kept at a different temperature. In the experiment, one end of the rod is placed
in a container of boiling water at 100C and the other end is placed in contact with a block of
ice at 0.0C as shown in the diagram.
temperature sensors
boiling water
100 C
ice
0 C
copper rod
not to scale
105
Temperature sensors are placed at 10 cm intervals along the rod. The final steady state
temperature  of each sensor is recorded, together with the corresponding distance x of each
sensor from the hot end of the rod.
The data points are shown plotted on the axes below.
/C
110
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
x / cm
The uncertainty in the measurement of  is 2C. The uncertainty in the measurement of x is
negligible.
(a)
On the graph above, draw the uncertainty in the data points for x = 10 cm, x = 40 cm and
x = 70 cm.
(2)
(b)
On the graph above, draw the line of best-fit for the data.
(1)
106
(c)
Explain, by reference to the uncertainties you have indicated, the shape of the line you
have drawn.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(d)
(i)
Use your graph to estimate the temperature of the rod at x = 55 cm.
.........................................................................................................................
(1)
(ii)
Determine the magnitude of the gradient of the line (the temperature gradient) at
x = 50 cm.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
107
(e)
The rate of transfer of thermal energy R through
the cross-sectional area of the rod is
θ
proportional to the temperture gradient  x along the rod. At x = 10 cm, R = 43W and
θ
the magnitude of the temperature gradient is  x =1.81C cm−1. At x = 50 cm the value
of R is 25 W.
Use these data and your answer to d(ii) to suggest whether the rate R of thermal energy
transfer is in fact proportional to the temperature gradient.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 12 marks)
109. This question is about thermal energy transfer through a rod.
A student designed an experiment to investigate the variation of temperature along a copper rod
when each end is kept at a different temperature. In the experiment, one end of the rod is placed
in a container of boiling water at 100C and the other end is placed in contact with a block of
ice at 0.0C as shown in the diagram.
temperature sensors
boiling water
100 C
ice
0 C
copper rod
not to scale
108
Temperature sensors are placed at 10 cm intervals along the rod. The final steady state
temperature  of each sensor is recorded, together with the corresponding distance x of each
sensor from the hot end of the rod.
The data points are shown plotted on the axes below.
/ C
110
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
90
80
x / cm
The uncertainty in the measurement of  is 2C. The uncertainty in the measurement of x is
negligible.
(a)
On the graph above, draw the uncertainty in the data points for x = 10 cm, x = 40 cm and
x = 70 cm.
(2)
(b)
On the graph above, draw the line of best-fit for the data.
(1)
109
(c)
Explain, by reference to the uncertainties you have indicated, the shape of the line you
have drawn.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(d)
(i)
Use your graph to estimate the temperature of the rod at x =55 cm.
.........................................................................................................................
(1)
(ii)
Determine the magnitude of the gradient of the line (the temperature gradient) at
x = 50 cm.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(e)
The rate of transfer of thermal energy R through the cross-sectional area of the rod is
θ
along the rod. At x = 10 cm, R = 43 W and
x
θ
the magnitude of the temperature gradient is
= 1.81C cm–1. At x = 50 cm the value
x
proportional to the temperature gradient
of R is 25 W.
Use these data and your answer to d(ii) to suggest whether the rate R of thermal energy
transfer is in fact proportional to the temperature gradient.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
110
(f)
It is suggested that the variation with x of the temperature  is of the form
θ  θ 0 e  kx
where 0 and k are constants.
State how the value of k may be determined from a suitable graph.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 14 marks)
111
110. The question is about investigating a fireball caused by an explosion.
When a fire burns within a confined space, the fire can sometimes spread very rapidly in the
form of a circular fireball. Knowing the speed with which these fireballs can spread is of great
importance to fire-fighters. In order to be able to predict this speed, a series of controlled
experiments was carried out in which a known amount of petroleum (petrol) stored in a can was
ignited.
The radius R of the resulting fireball produced by the explosion of some petrol in a can was
measured as a function of time t. The results of the experiment for five different volumes of
petroleum are shown plotted below. (Uncertainties in the data are not shown.)
Key:
25
30 10–3 m3
20
25 10–3 m3
15
15 10–3 m3
10
5.0 10 –3 m3
10 10–3 m3
R/m
5
0
0
10
20
30
40
50
60
70
t / ms
(a)
The original hypothesis was that, for a given volume of petrol, the radius R of the fireball
would be directly proportional to the time t after the explosion. State two reasons why the
plotted data do not support this hypothesis.
1.
.........................................................................................................................
.........................................................................................................................
2.
.........................................................................................................................
.........................................................................................................................
(2)
112
(b)
The uncertainty in the radius is 0.5 m. The addition of error bars to the data points
would show that there is in fact a systematic error in the plotted data. Suggest one reason
for this systematic error.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
113
(c)
It is known that the energy released in the explosion is proportional to the initial volume
of petrol. A hypothesis made by the experimenters is that, at a given time, the radius of
the fireball is proportional to the energy E released by the explosion. In order to test this
hypothesis, the radius R of the fireball 20 ms after the explosion was plotted against the
initial volume V of petrol causing the fireball. The resulting graph is shown below.
15
10
R/m
5
0
0
5
10
15
20
–3
V / 10 m
25
30
35
3
The uncertainties in R have been included. The uncertainty in the volume of petrol is
negligible.
(i)
Describe how the data for the above graph are obtained from the graph in (a).
.........................................................................................................................
.........................................................................................................................
(1)
(ii)
Draw the line of best-fit for the data points.
(2)
(iii)
Explain whether the plotted data together with the error bars support the hypothesis
that R is proportional to V.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
114
(d)
Analysis shows that the relation between the radius R, energy E released and time t is in
fact given by
R5 = Et2.
Use data from the graph in (c) to deduce that the energy liberated by the combustion of
1.0  10–3 m3 of petrol is about 30 MJ.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(4)
(Total 13 marks)
115
111. The question is about investigating a fireball caused by an explosion.
When a fire burns within a confined space, the fire can sometimes spread very rapidly in the
form of a circular fireball. Knowing the speed with which these fireballs can spread is of great
importance to fire-fighters. In order to be able to predict this speed, a series of controlled
experiments was carried out in which a known amount of petroleum (petrol) stored in a can was
ignited.
The radius R of the resulting fireball produced by the explosion of some petrol in a can was
measured as a function of time t. The results of the experiment for five different volumes of
petroleum are shown plotted below. (Uncertainties in the data are not shown.)
Key:
25
30 10–3 m3
20
25 10–3 m3
15
15 10–3 m3
10
5.0 10 –3 m3
10 10–3 m3
R/m
5
0
0
10
20
30
40
50
60
70
t / ms
(a)
The original hypothesis was that, for a given volume of petrol, the radius R of the fireball
would be directly proportional to the time t after the explosion. State two reasons why the
plotted data do not support this hypothesis.
1.
.........................................................................................................................
.........................................................................................................................
2.
.........................................................................................................................
.........................................................................................................................
(2)
116
(b)
The uncertainty in the radius is  0.5 m. The addition of error bars to the data points
would show that there is in fact a systematic error in the plotted data. Suggest one reason
for this systematic error.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(c)
Since the data do not support direct proportionality between the radius R of the fireball
and time t, a relation of the form
R = ktn
is proposed, where k and n are constants.
In order to find the value of k and of n, lg(R) is plotted against lg(t). The resulting graph,
for a particular volume of petrol, is shown below. (Uncertainties in the data are not
shown.)
1.3
1.2
1.1
1g(R)
1.0
0.9
0.8
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1g(t)
117
Use this graph to deduce that the radius R is proportional to t0.4. Explain your reasoning.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(4)
118
(d)
It is known that the energy released in the explosion is proportional to the initial volume
of petrol. A hypothesis made by the experimenters is that, at a given time, the radius of
the fireball is proportional to the energy E released by the explosion. In order to test this
hypothesis, the radius R of the fireball 20 ms after the explosion was plotted against the
initial volume V of petrol causing the fireball. The resulting graph is shown below.
15
10
R/m
5
0
0
5
10
15
20
–3
V / 10 m
25
30
35
3
The uncertainties in R have been included. The uncertainty in the volume of petrol is
negligible.
(i)
Describe how the data for the above graph are obtained from the graph in (a).
.........................................................................................................................
.........................................................................................................................
(1)
(ii)
Draw the line of best-fit for the data points.
(2)
(iii)
Explain whether the plotted data together with the error bars support the hypothesis
that R is proportional to V.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
119
(e)
Analysis shows that the relation between the radius R, energy E released and time t is in
fact given by
R5 = Et2.
Use data from the graph in (d) to deduce that the energy liberated by the combustion of
1.0  10–3 m3 of petrol is about 30 MJ.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(4)
(Total 17 marks)
120
112. As part of a road-safety campaign, the braking distances of a car were measured.
A driver in a particular car was instructed to travel along a straight road at a constant speed v. A
signal was given to the driver to stop and he applied the brakes to bring the car to rest in as short
a distance as possible. The total distance D travelled by the car after the signal was given was
measured for corresponding values of v. A sketch-graph of the results is shown below.
v
0
D
0
(a)
State why the sketch graph suggests that D and v are not related by an expression of the
form
D =mv + c,
where m and c are constants.
...................................................................................................................................
...................................................................................................................................
(1)
121
(b)
It is suggested that D and v may be related by an expression of the form
D = av + bv2,
where a and b are constants.
In order to test this suggestion, the data shown below are used. The uncertainties in the
measurements of D and v are not shown.
(i)
v / m s–1
D/m
D
/ ........
v
10.0
14.0
1.40
13.5
22.7
1.68
18.0
36.9
2.05
22.5
52.9
27.0
74.0
2.74
31.5
97.7
3.10
In the table above, state the unit of
D
.
v
(1)
(ii)
Calculate the magnitude of
D
, to an appropriate number of significant digits, for
v
v = 22.5 m s–1.
.........................................................................................................................
.........................................................................................................................
(1)
122
(c)
Data from the table are used to plot a graph of
D
(y-axis) against v (x-axis). Some of the
v
data points are shown plotted below.
3.50
3.00
2.50
D
(S.I. units)
v
2.00
1.50
1.00
0.50
0.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
–1
v/ms
On the graph above,
(i)
plot the data points for speeds corresponding to 22.5 m s–1 and to 31.5 m s–1.
(2)
(ii)
draw the best-fit line for all the data points.
(1)
123
(d)
Use your graph in (c) to determine
(i)
the total stopping distance D for a speed of 35 m s–1.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
the intercept on the
D
axis.
v
.........................................................................................................................
(1)
(iii)
the gradient of the best-fit line.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(e)
Using your answers to (d)(ii) and (d)(iii), deduce the equation for D in terms of v.
D = .........................................................................................................................
(1)
(f)
(i)
Use your answer to (e) to calculate the distance D for a speed v of 35.0 m s–1.
.........................................................................................................................
.........................................................................................................................
(1)
(ii)
Briefly discuss your answers to (d)(i) and (f)(i).
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
(Total 14 marks)
113. As part of a road-safety campaign, the braking distances of a car were measured.
124
A driver in a particular car was instructed to travel along a straight road at a constant speed v. A
signal was given to the driver to stop and he applied the brakes to bring the car to rest in as short
a distance as possible. The total distance D travelled by the car after the signal was given was
measured for corresponding values of v. A sketch-graph of the results is shown below.
v
0
D
0
(a)
State why the sketch graph suggests that D and v are not related by an expression of the
form
D = mv + c,
where m and c are constants.
...................................................................................................................................
...................................................................................................................................
(1)
125
(b)
It is suggested that D and v may be related by an expression of the form
D = av + bv2,
where a and b are constants.
In order to test this suggestion, the data shown below are used. The uncertainties in the
measurements of D and v are not shown.
(i)
v / m s–1
D/m
D
/ ........
v
10.0
14.0
1.40
13.5
22.7
1.68
18.0
36.9
2.05
22.5
52.9
27.0
74.0
2.74
31.5
97.7
3.10
In the table above, state the unit of
D
.
v
(1)
(ii)
Calculate the magnitude of
D
, to an appropriate number of significant digits, for v
v
= 22.5 m s–1.
.........................................................................................................................
.........................................................................................................................
(1)
126
(c)
Data from the table are used to plot a graph of
D
(y-axis) against v (x-axis). Some of the
v
data points are shown plotted below.
3.50
3.00
2.50
D
(S.I. units)
v
2.00
1.50
1.00
0.50
0.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
–1
v/ms
On the graph above,
(i)
plot the data points for speeds corresponding to 22.5 m s–1 and to 31.5 m s–1.
(2)
(ii)
draw the best-fit line for all the data points.
(1)
127
(d)
Use your graph in (c) to determine
(i)
the total stopping distance D for a speed of 35 m s–1.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
the intercept on the
D
axis.
v
.........................................................................................................................
(1)
(iii)
the gradient of the best-fit line.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(e)
Using your answers to (d)(ii) and (d)(iii), deduce the equation for D in terms of v.
D = .........................................................................................................................
(1)
128
(f)
The uncertainty in the measurement of the distance D is 0.3 m and the uncertainty in the
measurement of the speed v is 0.5 m s–1.
(i)
For the date point corresponding to v = 27.0 m s–1, calculate the absolute
D
.
uncertainty in the value of
v
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
Each of the data points in (b) was obtained by taking the average of several values
of D for each value of v. Suggest what effect, if any, the taking of averages will
have on the uncertainties in the data points.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(Total 16 marks)
129
114. This question is about data analysis.
Data for the refractive index n of a type of glass and wavelength λ of the light transmitted
through the glass are shown below.
Only the uncertainties in the values of n are significant and these uncertainties are shown by
error bars.
1.6065
1.6060
1.6055
1.6050
1.6045
n
1.6040
1.6035
1.6030
1.6025
1.6020
1.6015
300
350
400
450
500
550
600
650
/nm
(a)
State why the data do not support the hypothesis that there is a linear relationship between
refractive index and wavelength.
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
Draw a best-fit line for the data points.
(2)
130
(c)
The rate of change of refractive index D with wavelength is referred to as the dispersion.
At any particular value of wavelength, D is defined by
D =
n

Use the graph to determine the value of D at a wavelength of 380 nm.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
131
(d)
Based on the plotted data, it is suggested that the relationship between n and λ is of the
form
n=A+
B
2
where A and B are constants.
To test this suggestion, values of n are plotted against values of
1
2
. The resulting graph
with the line of best fit is shown below.
1.6065
1.6060
1.6055
1.6050
1.6045
n
1.6040
1.6035
1.6030
1.6025
1.6020
1.6015
1.6010
0
0.1
0.2
0.3
0.4
0.5
1
2
0.6
0.7
0.8
0.9
1.0
1.1
1.2
/ 10 -15 m-2
132
(i)
Use the graph to determine the value of the constant A.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
State the significance of the constant A.
...........................................................................................................................
...........................................................................................................................
(1)
(Total 11 marks)
133
115. This question is about data analysis.
Data for the refractive index n of a type of glass and wavelength λ of the light transmitted
through the glass are shown below.
Only the uncertainties in the values of n are significant and these uncertainties are shown by
error bars.
1.6065
1.6060
1.6055
1.6050
1.6045
n
1.6040
1.6035
1.6030
1.6025
1.6020
1.6015
300
350
400
450
500
550
600
650
/nm
(a)
State why the data do not support the hypothesis that there is a linear relationship between
refractive index and wavelength.
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
Draw a best-fit line for the data points.
(2)
134
(c)
The rate of change of refractive index D with wavelength is referred to as the dispersion.
At any particular value of wavelength, D is defined by
D =
n

Use the graph to determine the value of D at a wavelength of 380 nm.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(d)
It is suggested that the relationship between n and  is of the form
n = kp
where k and p are constants.
State and explain the graph that you would plot in order to determine the value of p.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
135
(e)
A second suggestion is that the relationship between n and  is of the form
n=A+
B
2
where A and B are constants.
To test this suggestion, values of n are plotted against values of
1
2
. The resulting graph
with the line of best fit is shown below.
1.6065
1.6060
1.6055
1.6050
1.6045
n
1.6040
1.6035
1.6030
1.6025
1.6020
1.6015
1.6010
0
0.1
0.2
0.3
0.4
0.5
1
2
0.6
0.7
0.8
0.9
1.0
1.1
1.2
/ 10 -15 m-2
136
(i)
Use the graph to determine the value of the constant A.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
State the significance of the constant A.
...........................................................................................................................
...........................................................................................................................
(1)
(Total 14 marks)
137
116. Some data for the resistance R of an electrical component at different temperatures are shown
below.
t /°C
R/Ω
10.0
15.0
25.0
30.0
35.0
40.0
2600
2150
1510
1280
1080
925
A graph of the variation with temperature t of the resistance R of the component is shown
below. Error bars have been included.
3400
3200
3000
2800
2600
2400
2200
R/
2000
1800
1600
1400
1200
1000
800
0
5
10
15
20
t/
25
30
35
40
45
C
138
(a)
Estimate the uncertainty range in the temperature measurements.
.....................................................................................................................................
(1)
(b)
Use the graph to determine the
(i)
most probable resistance of the component at 20.0°C and at 5.0°C.
Resistance at 20.0°C ........................................................................................
(1)
Resistance at 5.0°C ..........................................................................................
(2)
(ii)
rate of change of resistance with temperature at 20.0°C.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(c)
The relationship between resistance and temperature is not linear. Describe, and explain,
the evidence for a non-linear relationship that is provided by the graph.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
139
(d)
A student suggests that the relationship between the resistance R and temperature is of the
form
R=
c
T
where c is a constant and T is the thermodynamic (absolute) temperature.
Use data from the table to determine, without drawing a graph, whether this suggestion is
correct.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 12 marks)
140
117. Some data for the resistance R of an electrical component at different temperatures are shown
below.
t /°C
R/Ω
10.0
15.0
25.0
30.0
35.0
40.0
2600
2150
1510
1280
1080
925
A graph of the variation with temperature t of the resistance R of the component is shown
below. Error bars have been included.
3400
3200
3000
2800
2600
2400
2200
R/
2000
1800
1600
1400
1200
1000
800
0
5
10
15
20
t/
25
30
35
40
45
C
141
(a)
Estimate the
(i)
uncertainty range in the temperature measurements.
...........................................................................................................................
(1)
(ii)
percentage uncertainty in the resistance at 10.0°C.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(b)
Use the graph to determine the
(i)
most probable resistance of the component at 20.0°C and at 5.0°C.
Resistance at 20.0°C ........................................................................................
(1)
Resistance at 5.0°C ..........................................................................................
(2)
(ii)
rate of change of resistance with temperature at 20.0°C.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(c)
The relationship between resistance and temperature is not linear. Describe, and explain,
the evidence for a non-linear relationship that is provided by the graph.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
142
(d)
A student suggests that the relationship between the resistance R and temperature is of the
form
R=
c
T
where c is a constant and T is the thermodynamic (absolute) temperature.
Use data from the table to determine, without drawing a graph, whether this suggestion is
correct.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 14 marks)
143
118. This question is about the electrical power available from a wind turbine.
The maximum electrical power generated by a wind turbine, Pout , was measured over a range of
incident wind speeds, vin.
The graph below shows the variation with vin of Pout. Uncertainties for the data are not shown.
(a)
It is suggested that Pout is proportional to
(i)
v in .
Draw the line of best-fit for the data points.
(1)
(ii)
State one reason why the line you have drawn does not support this hypothesis.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
(iii)
The uncertainty in the power at 15 m s–1 is 5. Draw an error bar on the graph to
represent this uncertainty.
(2)
144
(b)
The theoretical relationship between the available power in the wind, Pin, and incident
wind speed is shown in the graph below.
4000
3500
3000
2500
Pm / kW
2000
1500
1000
500
0
0
5
10
15
20
25
Vm / ms–1
Using both graphs,
(i)
determine the efficiency of the turbine for an incident wind speed of 14 m s–1.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
145
(ii)
suggest, without calculation, how the efficiency of the turbine changes with
increasing wind speed.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(c)
Outline one advantage and one disadvantage of using wind turbines to generate electrical
energy.
Advantage:
...................................................................................................
...................................................................................................
...................................................................................................
...................................................................................................
Disadvantage: ...................................................................................................
...................................................................................................
...................................................................................................
...................................................................................................
(2)
(Total 12 marks)
146
119. This question is about the electrical power available from a wind turbine.
The maximum electrical power generated by a wind turbine, Pout , was measured over a range of
incident wind speeds, vin.
The graph below shows the variation with vin of Pout. Uncertainties for the data are not shown.
(a)
It is suggested that Pout is proportional to
(i)
v in .
Draw the line of best-fit for the data points.
(1)
(ii)
State one reason why the line you have drawn does not support this hypothesis.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
(iii)
The uncertainty in the power at 15 m s–1 is 5. Draw an error bar on the graph to
represent this uncertainty.
(2)
147
(b)
The theoretical relationship between the available power in the wind, Pin, and incident
wind speed is shown in the graph below.
Using both graphs,
(i)
determine the efficiency of the turbine for an incident wind speed of 14 m s–1.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
148
(ii)
suggest, without calculation, how the efficiency of the turbine changes with
increasing wind speed.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(c)
Outline one advantage and one disadvantage of using wind turbines to generate electrical
energy.
Advantage:
...................................................................................................
...................................................................................................
...................................................................................................
...................................................................................................
Disadvantage: ...................................................................................................
...................................................................................................
...................................................................................................
...................................................................................................
(2)
(Total 12 marks)
149
120. This question is about the photoelectric effect.
Light is incident on a clean metal surface in a vacuum. The maximum kinetic energy KEmax of
the electrons ejected from the surface is measured for different values of the frequency f of the
incident light.
The measurements are shown plotted below.
2.0
1.5
KEmax / × 10–19 J 1.0
0.5
0.0
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
14
f / × 10 Hz
(a)
Draw a line of best fit for the plotted data points.
(1)
(b)
Use the graph to determine
(i)
the Planck constant;
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(2)
(ii)
the minimum energy required to eject an electron from the surface of the metal (the
work function).
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(3)
150
(c)
Explain briefly how Einstein’s photoelectric theory accounts for the fact that no electrons
are emitted from the surface of this metal if the frequency of the incident light is less than
a certain value.
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(3)
(Total 9 marks)
151