IFYPH003 Physics
THE NCUK INTERNATIONAL FOUNDATION YEAR
IFYPH003 Physics
Examination
Exemplar
Time Allowed
2 hours 40 minutes
1
1
INSTRUCTIONS TO STUDENTS
Questions
1-13
Answer ALL questions. These questions carry 40 marks in
total (40% of the exam marks).
Questions
14-18
Answer 3 questions ONLY. These questions carry 60 marks
in total (60% of the exam marks).
The marks for each question are indicated in square brackets [ ].

Formulae are included in the front of the examination booklet.

Graph paper will be provided.

An approved calculator may be used in the examination.

Show ALL workings in your answer booklet.

Examination materials must not be removed from the examination room.

State the units where necessary.

Where appropriate, working should be carried out to 4 significant figures and
answers given to 3 significant figures.
DO NOT OPEN THIS QUESTION PAPER UNTIL INSTRUCTED BY THE
INVIGILATOR
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Page 1 of 16
IFYPH003 Physics
Data, formulae and relationships
Data
Speed of light in a vacuum
Gravitational constant
Acceleration of free fall
Gravitational field strength
Electronic charge
Electronic mass
Proton rest mass
Electron-volt
Planck constant
Unified atomic mass unit
Molar gas constant
Boltzmann constant
Permittivity of free space
Coulomb Law constant
Avogadro Constant
Absolute temperature
c = 3.00  10 8 m s – 1
G = 6.67  10 – 11 N m 2 kg – 2
g = 9.81 m s – 2
(close to the Earth)
g = 9.81 N kg – 1
(close to the Earth)
e = – 1.60  10 – 19 C
me = 9.11  10 – 31 kg
mp = 1.67 x 10-27 kg
1 eV = 1.60  10 – 19 J
h = 6.63  10 – 34 J s
u = 1.66  10 – 27 kg
R = 8.31 J K – 1 mol – 1
k = 1.38  10 – 23 J K-1
o = 8.85  10 – 12 F m – 1
k = 1 / ( 4  o ) = 8.99  10 9 N m 2 C – 2
NA = 6.02  10 23 mol-1
T/K = θ/ºC+ 273.2
Rectilinear motion
For uniformly accelerated motion
=u+at
s=ut+½at2
2= u2+2as
s = [½(u + v)] t
Materials and Elasticity
Density
ρ = m/V
Young's modulus
E
For a spring
F = -kx
Energy
E = ½Fx = ½kx2
Pressure change
Δp = ρgΔh
FL
= σ/ε
Ae
Forces and moments
Moment of F about O = F  (Perpendicular distance from line of action of F to O)
Dynamics and Energy
Kinetic Energy
Ek = ½mv2
Gravitational Potential Energy
Ep = mgh
Exemplar
(near Earth’s surface)
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IFYPH003 Physics
Newton’s Law (for constant mass)
F mam
Impulse
F t = p
Power
P=F

p

t
t
Radioactive decay and the nuclear atom
Activity
A=N
Half-life
Radioactive decay
 t ½ = ln 2
A  A0 e   t
N  N 0e   t
Electric current and potential difference
Work
Q
t
V
R
I
W  QV  IVt
Electric power
P = I 2 R = V2/R = IV
Electric current
Resistance
I
Electrical circuits
RA
L
Resistivity

Resistors in series
R=R1+R2+R3
Resistors in parallel
Terminal potential difference
1
1
1
1



R R1 R2 R3
V=–Ir
Heat
Change of state:
Q = L m
Heating and cooling:
E  mc
Change of internal energy:
U = Q + W
Equation of State for ideal gas
pV  nRT
pV  NkT
Exemplar
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IFYPH003 Physics
Circular motion and oscillations
Angular speed
 

t r

Centripetal acceleration
a
Period
T 
2
r
= rω2
1 2

f

Simple Harmonic Motion
Displacement
x  A sin(t )
Acceleration
a = -ω2 x
Velocity
v  A cos(t ) = ± ω √( A 2 - x 2)
For a simple pendulum
T  2
l
g
For a mass on a spring
T  2
m
k
Waves, Wave Motion and Interference
Malus’ law
I = Iocos2ϴ
Wave speed
v = fλ
Young's slits
=
Diffraction grating
/
d sinθ = nλ
Gravitational fields
Mm
r2
Universal Law of Gravitation
F G
Gravitational field strength
g=F/m
Gravitational potential
V=W/m
Electric fields
F
Coulomb’s law
Q1Q2
4 0 r 2
Electrical potential
V = Q/(4πεor)
Electric field strength
E = F/Q
Exemplar
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IFYPH003 Physics
Q
4 0 r 2
1
For radial field
E
For uniform field
E=V/d
(in free space or in air)
Capacitance
Capacitance
C=Q/V
Energy stored
W = ½ C V 2 = ½ QV = ½ Q2/C
Capacitors in parallel
C=C1+C2+C3
Capacitors in series
1
1
1
1



C C1 C 2 C3
Time constant
τ=RC
Capacitor discharge
Q = Qoe-t/ τ,
I = Io e-t/ τ,
V = Vo e-t/ τ
Magnetic fields
F  Bqv
Force on a wire
F  BIL sin 
Torque on a coil
T = BIAn
Magnetic flux linkage
NΦ = NBAcosθ
E.m.f. induced in a coil
= 
E.m.f. induced in a moving conductor
Φ
Force on moving charge
N
t
  BLv
Modern Physics
E  hf
Photoelectric effect
hf  Φ  E
De Broglie

Energy
E = mc2
Exemplar
k
Photon energy
max
h
mv
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IFYPH003 Physics
Mathematics
sin (90 o – ) = cos 
ln (x n) = n ln x
ln (e kx) = k x
Equation of a straight line
y = mx + c
Surface area of a cylinder
Surface area of a sphere
=2rh+2r2
=4r2
Volume of a cylinder
Volume of a sphere
=  r 2h
= 4  r 3/ 3
For small angles
sin   tan   
cos   1
Exemplar
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(in radians)
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IFYPH003 Physics
Questions 1-13
Answer ALL questions.
These questions carry 40 marks in total.
Question 1
[1]
When using the SI system, the units for velocity might be written as:
i)
mms-1
ii)
m ms-1
iii)
mm s-1
Select from the answers below which of these abbreviations for the units are
correct.
A
B
C
D
i) and ii) are correct
ii) and iii) are correct
i) and iii) are correct
All three are correct
Question 2
[1]
A nuclide decays by β+ emission. State which of the following statements,
A-D is correct:
A
B
C
D
The atomic number of the nuclide will increase by 1 and an antineutrino
will be emitted.
The atomic number of the nuclide will decrease by 1 and an antineutrino
will be emitted.
The atomic number of the nuclide will increase by 1 and a neutrino will
be emitted.
The atomic number of the nuclide will decrease by 1 and a neutrino will
be emitted.
Question 3
[1]
Photoelectrons are emitted from a metal surface when the energy of the
incident photons is greater than the work function of the metal. State which
of the following statements, A-D, is then correct:
A
B
C
D
The maximum kinetic energy of the photoelectrons decreases when the
intensity of the incident radiation is increased.
The maximum kinetic energy of the photoelectrons decreases when the
wavelength of the incident radiation is increased.
The maximum kinetic energy of the photoelectrons increases when the
wavelength of the incident radiation is increased.
The maximum kinetic energy of the photoelectrons increases when the
intensity of the incident radiation is increased.
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Page 7 of 16
IFYPH003 Physics
Question 4
[1]
State which of the following statements, A-D, is correct.
A
B
C
D
Both transverse and longitudinal waves can be polarized.
Electromagnetic waves travelling in free space all move at the same
speed.
The plane of the vibrations of an electromagnetic wave is parallel with
the direction of travel.
The plane of vibration of a longitudinal wave is perpendicular to the
direction of travel
Question 5
[1]
State which of the following statements, A-D, is correct:
A
B
C
D
The internal energy of a system is given by the total kinetic energy of
the molecules in the system.
Increasing the temperature of a body will lead to an increase in its
internal energy.
Thermal energy is transferred from a region of lower temperature to a
region of higher temperature.
Whilst a substance is changing state both its internal energy and its
temperature will remain constant.
Question 6
[1]
An electron has a de Broglie wavelength of 1.27 x 10-10 m. Its kinetic energy
in electron volts will be:
A
B
C
D
1.64 x 10-5 eV
3.27 x 10-5 eV
94.1 eV
188 eV
Question 7
[1]
A railway carriage of mass 4.50 x 104 kg, moving at 5.60 m s-1 collides with
an initially stationary wagon of mass 7.20 x 103 kg. The carriage and wagon
separate after the collision and the carriage moves at a speed of 4.40 m s-1
in the same direction as before the collision. The speed of the wagon after the
collision will be
A
B
C
D
5.60
6.25
7.50
62.5
m
m
m
m
s-1
s-1
s-1
s-1
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Page 8 of 16
IFYPH003 Physics
Question 8
[1]
A uniform brass wire of initial length 1.75 m is attached to a rigid support at
its top end and hangs vertically downwards. It is stretched elastically by a
force of 36.8 N and increases in length by 2.64 mm. Young’s modulus for
brass = 1.00 x 1011 Pa
The diameter of the wire must be:
A
B
C
D
5.57
2.79
3.11
1.56
x
x
x
x
10-4 m
10-4 m
10-4 m
10-4 m
Question 9
[1]
A rectangular coil of wire measuring 30 mm x 20 mm and consisting of 50
turns is placed in a uniform magnetic field of 3.69 x 10-3 T. The torque on
the coil when the plane of the coil is at an angle of 20° to the direction of the
magnetic field and a current of 250 mA is flowing through the coil will be:
A
B
C
D
2.60
9.47
5.20
1.89
x
x
x
x
10-5
10-6
10-7
10-7
N
N
N
N
m
m
m
m
Question 10
[1]
An electron in the 5.70 eV excited state of a mercury atom falls to the
4.90 eV excited state of the atom. Determine the wavelength of the
photon that will be emitted.
A
B
C
D
1.55
2.86
1.55
2.86
x
x
x
x
10-7
10-7
10-6
10-6
m
m
m
m
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Page 9 of 16
IFYPH003 Physics
Question 11
(a)
Determine the magnitude of the electric field strength at a distance of
50.0 mm from a small negatively charged, 20 μC point charge, placed
in a vacuum.
(b)
Point charges of +2 μC, +5 μC, +7μC and -6 μC are placed at the corners
of a square of side length 0.50 m. A point charge Q, of -4 μC is placed
at the centre of the square. Assume ε = εo.
[2]
i.
Determine the magnitude of the resultant force on charge Q.
[6]
ii.
Determine the direction of the resultant force on charge Q.
[2]
Question 12
A narrow beam of purple light contains two colours, red light of wavelength
6.00 x 10-7 m and violet light of an unknown wavelength. The same light
source is used in two separate experiments as described below.
(a)
(b)
The narrow beam of purple light is incident normally on a plane
diffraction grating.
i.
Determine the spacing between the lines on the grating if the 2nd
order red line has a diffraction angle of 47°.
[2]
ii.
The 3rd order violet line is also at this same diffraction angle.
Determine the wavelength of the violet light.
[2]
iii.
Determine the maximum diffraction order visible for the violet light.
[2]
The purple light is then used in a Young’s double slit experiment. The
slit spacing is 0.25 mm and the distance between the fourth red fringe
on one side of the centre to that of the fourth red fringe on the other
side of the centre is 24.0 mm.
i.
Determine the distance between the double slits and the screen.
[2]
ii.
Determine the spacing between the violet fringes.
wavelength you obtained in part a)).
[2]
(Use the
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IFYPH003 Physics
Question 13
(a)
Define electromotive force (e.m.f.) of a power supply.
[2]
(b)
Cell A has an e.m.f. ε and internal resistance, r. It is connected in a
circuit as shown below. With switch S open, a current of 0.250 A is
recorded. With switch S closed, the current increases to 0.410 A.
i.
Determine the internal resistance, r, of the cell.
[6]
ii.
Determine the e.m.f., ε, of the cell.
[2]
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IFYPH003 Physics
Questions 14 - 18
Answer 3 questions ONLY
These questions carry 60 marks in total.
Question 14
(a)
i.
Define gravitational field strength.
[2]
ii.
Assuming the Earth is a sphere of radius 6.37 x 103 km and that
the acceleration due to gravity at the Earth’s surface is 9.81 m s-2,
show that the mass of the Earth is 5.97 x 1024 kg.
(You will need to use this value for the mass of the Earth in other
parts of this question).
[2]
iii.
Determine the average density of the Earth.
[2]
(b)
The International Space Station (ISS) orbits the Earth at a height of
412 km above its surface. Determine the time taken in minutes for the
ISS to complete one circular orbit of the Earth.
(c)
A communication satellite is in a synchronous orbit of the Earth.
[5]
i.
What is the satellite’s period of rotation.
[1]
ii.
Determine the satellite’s angular velocity.
[2]
iii.
Determine the radius of the satellite’s orbit around the Earth.
[3]
iv.
Determine the linear velocity of the satellite in km h-1.
[3]
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IFYPH003 Physics
Question 15
Radium-223 (Ra-223) is an isotope used in the treatment of bone cancer. It
decays by α-particle emission to radon-219 (Rn-219).
(a)
(b)
Measurements of the activity of a sample of Ra-223 gave the following
results:
Time/days 0
5
10
15
20
25
30
Activity/
kBq
442
329
245
182
135
101
595
i.
Plot a graph of activity (y axis) against time (x axis).
[4]
ii.
Use the graph to determine the half life of Ra-223.
[2]
iii.
Determine the decay constant of Ra-223.
[2]
iv.
How could the results in the table be used to obtain a straight line
graph?
[2]
v.
Describe how the decay constant would be obtained from this
straight line graph.
Determine the energy, Q, in joules, released when an atom of
Ra-223 undergoes α-decay.
The atomic masses are as follows:
Ra-223
223.0185u
Rn-219
219.0095u
α particle 4.0015u
Use all of the significant figures shown in your calculations.
[2]
If all the energy released becomes the combined kinetic energy of
the radon atom and α-particle, determine the recoil velocity of the
radon atom.
[4]
i.
ii.
[4]
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Page 13 of 16
IFYPH003 Physics
Question 16
A child is playing with a ball of mass 0.850 kg on a cliff top. The child kicks
the ball and it leaves the ground at an angle of 15° above the horizontal, at
a speed of 17.5 m s-1. Unfortunately, the ball goes over the cliff edge and
straight into the calm sea, 30.3 m below the top of the cliff.
Ignoring air resistance:
(a)
Determine the maximum height above the sea reached by the ball.
[4]
(b)
Determine the time taken for the ball to reach its maximum height.
[2]
(c)
Determine the time taken for the ball to reach the sea.
[5]
(d)
What happens to the horizontal component of the ball’s velocity during
this motion?
Determine the horizontal distance travelled by the ball before it lands
in the sea.
[1]
(f)
Determine the vertical component of velocity of the ball as it enters the
sea.
[3]
(g)
Determine the total kinetic energy of the ball as it enters the sea.
[3]
(e)
[2]
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IFYPH003 Physics
Question 17
(a)
A block of ice of mass 0.850 kg at -5 °C is melted by a 2 kW heater and
the resulting water continues to be heated. Determine the time taken,
in minutes, to melt the ice and increase the water temperature to 35 °C,
if the process is 75% efficient.
Specific heat capacity of ice , cice
= 2100 J kg-1 K-1
Specific heat capacity of water, cw
= 4180 J kg-1 K-1
[4]
Specific latent heat of fusion of ice, Li = 3.34 x 105 J kg-1
(b)
(c)
A cylinder of volume 3.00 x 10-3 m3 contains helium gas at a temperature
of 200 K and a pressure of 4.35 x 104 Pa.
i.
Determine the number of moles of helium inside the cylinder.
[2]
ii.
Determine the number of atoms of helium in the cylinder.
[2]
iii.
The molar mass of helium is 4.00 x 10-3 kg. Determine the mass
of 1 atom of helium.
[2]
iv.
Determine the volume that the helium would occupy at s.t.p. (0
°C and 1.01 x 105 Pa).
[3]
v.
Determine the density of helium at s.t.p.
[3]
A glass container, initially at a temperature of 20 °C is placed in liquid
nitrogen. 0.250 kg of liquid nitrogen is boiled off in cooling down the
glass to the liquid nitrogen temperature of -196 °C.
i.
Determine the mass of the glass container, ignoring all other
sources of heat gain or loss.
[2]
Specific heat capacity of glass = 0.750 kJ kg-1 K-1
Specific latent heat of vaporisation of nitrogen = 209 kJ K-1
ii.
Liquid helium at its boiling temperature of -269 °C is then poured
into the glass container. Determine the mass of helium that will be
boiled off when the container is cooled down to the temperature of
the liquid helium, assuming all other sources of heat gain or loss
are ignored.
[2]
Specific latent heat of vaporisation of helium = 25.0 kJ kg-1
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Page 15 of 16
IFYPH003 Physics
Question 18
(a)
Define simple harmonic motion (SHM).
[2]
(b)
The upper end of a vertical spring of original length 0.120 m is attached
to a clamp stand. A mass of 0.250 kg is fastened to the lower end of the
spring. The spring constant is 30.5 N m-1.
i.
Determine the stretched length of the spring.
[3]
ii.
The mass is then pulled down a further 28.0 mm and released so
that it vibrates with SHM. Determine the time period of this
vibration.
[2]
iii.
Determine the frequency of the vibration.
[1]
iv.
Determine the magnitude of the acceleration of the mass at the
instant it was released.
[3]
v.
Determine the maximum kinetic energy of the mass.
[3]
vi.
Sketch a graph to show how the kinetic energy of the mass (y axis)
varies with time (x axis) over one full cycle of the vibration, starting
with the mass at its lowest point.
[2]
vii.
Determine the time taken for the mass to move directly from a
position 15.0 mm below the equilibrium position to 15.0 mm above
the equilibrium position.
[4]
-
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