Practice questions
Subject
Grade
Points
Physics
IB-1
175
Section 1
Q1
A ball of mass 0.250 kg is released from rest at time t = 0 , from a height H above
[9]
a horizontal oor.
The graph shows the variation with time t of the velocity v of the ball. Air
resistance is negligible. Take g = −9.80 m s−2 . The ball reaches the
oor after
1.0 s .
(a)
Determine H .
[1]
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(b)
[3]
(i)
Label the time and velocity graph, using the letter M , the point where the ball
[1]
reaches the maximum rebound height.
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(ii)
State the acceleration of the ball at the maximum rebound height.
[1]
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(iii) Draw, on the axes, a graph to show the variation with time of the height of the
ball from the instant it rebounds from the
[1]
oor until the instant it reaches the
maximum rebound height. No numbers are required on the axes.
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(c)
Estimate the loss in the mechanical energy of the ball as a result of the collision
with the
[1]
oor.
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(d)
[4]
(i)
Determine the average force exerted on the
oor by the ball.
[3]
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(ii)
Suggest why the momentum of the ball was not conserved during the collision
with the
[1]
oor.
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Page 5 of 70
Q2
Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a
[10]
chamber and expelled from the spacecraft. The spacecraft is in outer space when
the propulsion system is turned on. The spacecraft starts from rest.
The mass of ions ejected each second is 6.6×10
−6
kg and the speed of each ion
is 5.2×104 m s−1 . The initial total mass of the spacecraft and its fuel is 740 kg .
Assume that the ions travel away from the spacecraft parallel to its direction of
motion.
(a)
Determine the initial acceleration of the spacecraft.
[2]
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An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half
(b)
[4]
of the fuel will be required to slow down the spacecraft before arrival at the
destination planet.
(i)
Estimate the maximum speed of the spacecraft.
[2]
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(ii)
Outline why the answer to (b)(i) is an estimate.
[1]
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(iii) Outline why scientists sometimes use estimates in making calculations.
[1]
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(c)
In practice, the ions leave the spacecraft at a range of angles as shown.
(i)
Outline why the ions are likely to spread out.
[4]
[2]
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(ii)
Explain what effect, if any, this spreading of the ions has on the acceleration of
[2]
the spacecraft.
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Q3
A xed mass of an ideal gas is contained in a cylinder closed with a frictionless
[6]
piston. The volume of the gas is 2.5×10−3 m3 when the temperature of the gas is
37° C and the pressure of the gas is 4.0×105 Pa .
(a)
Calculate the number of gas particles in the cylinder.
[2]
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(b)
Energy is now supplied to the gas and the piston moves to allow the gas to
[4]
expand. The temperature is held constant.
Discuss, for this process, the changes that occur in the
(i)
density of the gas.
[2]
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(ii)
internal energy of the gas.
[2]
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Q4
[6]
(a)
State what is meant by the internal energy of an ideal gas.
[1]
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Page 11 of 70
3
A quantity of 0.24 mol of an ideal gas of constant volume 0.20 m is kept at a
(b)
[3]
temperature of 300 K .
(i)
Calculate the pressure of the gas.
[1]
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(ii)
The temperature of the gas is increased to 500 K . Sketch, on the axes, a graph
[2]
to show the variation with temperature T of the pressure P of the gas during
this change.
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(c)
A container is lled with 1 mole of helium (molar mass 4 g mol−1 ) and 1 mole of
[2]
neon (molar mass 20 g mol−1 ). Compare the average kinetic energy of helium
atoms to that of neon atoms.
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Page 13 of 70
Q5
A planet is in a circular orbit around a star. The speed of the planet is constant.
(a)
[5]
[3]
(i)
Explain why a centripetal force is needed for the planet to be in a circular orbit.
[2]
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(ii)
State the nature of this centripetal force.
[1]
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(b)
Determine the gravitational eld of the planet.
[2]
The following data are given:
Mass of planet
= 8.0×1024 kg
Radius of the planet
= 9.1×106 m
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Q6
A mass of 1.0 kg of water is brought to its boiling point of 100° C using an electric
[12]
heater of power 1.6 kW .
(a)
[3]
(i)
The molar mass of water is 18 g mol−1 . Estimate the average speed of the
[2]
water molecules in the vapor produced. Assume the vapor behaves as an ideal
gas.
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(ii)
State one assumption of the kinetic model of an ideal gas.
[1]
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A mass of 0.86 kg of water remains after it has boiled for 200 s .
(b)
(i)
Estimate the speci c latent heat of vaporization of water. State an appropriate
[3]
[2]
unit for your answer.
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(ii)
Explain why the temperature of water remains at 100° C during this time.
[1]
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(c)
The heater is removed and a mass of 0.30 kg of pasta at −10° C is added to
[3]
the boiling water.
Determine the equilibrium temperature of the pasta and water after the pasta is
added. Other heat transfers are negligible.
Speci c heat capacity of pasta
= 1.8 kJ kg −1K −1
Speci c heat capacity of water
= 4.2 kJ kg −1K −1
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Page 17 of 70
(d)
The electric heater has two identical resistors connected in parallel.
[3]
The circuit transfers 1.6 kW when switch A only is closed. The external voltage
is 220 V .
(i)
Show that each resistor has a resistance of about 30 Ω .
[1]
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(ii)
Calculate the power transferred by the heater when both switches are closed.
[2]
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Page 18 of 70
Q7
Liquid oxygen at its boiling point is stored in an insulated tank. Gaseous oxygen is
[7]
produced from the tank when required using an electrical heater placed in the
liquid.
The following data are available.
(a)
Mass of 1.0 mol of oxygen
= 32 g
Speci c latent heat of vaporization of oxygen
= 2.1×105 J kg −1
Distinguish between the internal energy of the oxygen at the boiling point when
[2]
it is in its liquid phase and when it is in its gas phase.
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An oxygen ow rate of 0.25 mol s−1 is needed.
(b)
Calculate, in kW , the heater power required.
(i)
[4]
[2]
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(ii)
Calculate the volume of the oxygen produced in one second when it is allowed
[2]
to expand to a pressure of 0.11 MPa and to reach a temperature of −13° C .
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(c)
State one assumption of the kinetic model of an ideal gas that does not apply to
[1]
oxygen.
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Page 20 of 70
Q8
A glider is an aircraft with no engine. To be launched, a glider is uniformly
[10]
accelerated from rest by a cable pulled by a motor that exerts a horizontal force on
the glider throughout the launch.
(a)
The glider reaches its launch speed of 27.0 m s−1 after accelerating for 11.0 s .
[2]
Assume that the glider moves horizontally until it leaves the ground. Calculate
the total distance travelled by the glider before it leaves the ground.
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(b)
The glider and pilot have a total mass of 492 kg . During the acceleration the
[3]
glider is subject to an average resistive force of 160 N . Determine the average
tension in the cable as the glider accelerates.
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(c)
The cable is pulled by an electric motor. The motor has an overall ef ciency of
[3]
23% . Determine the average power input to the motor.
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(d)
After takeoff the cable is released and the unpowered glider moves horizontally
[2]
at constant speed. The wings of the glider provide a lift force. The diagram shows
the lift force acting on the glider and the direction of motion of the glider.
Draw the forces acting on the glider to complete the free-body diagram. The
dotted lines show the horizontal and vertical directions.
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Q9
[7]
−4 3
An ideal monatomic gas is kept in a container of volume 2.1×10 m ,
(a)
[4]
temperature 310 K and pressure 5.3×105 Pa .
(i)
State what is meant by an ideal gas.
[1]
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(ii)
Calculate the number of atoms in the gas.
[1]
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(iii) Calculate, in J , the internal energy of the gas.
[2]
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The volume of the gas in (a) is increased to 6.8×10−4 m3 at constant
(b)
[3]
temperature.
(i)
Calculate, in Pa , the new pressure of the gas.
[1]
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(ii)
Explain, in terms of molecular motion, this change in pressure.
[2]
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Page 24 of 70
Q10 A chicken's egg of mass 58 g is dropped onto grass from a height of 1.1 m . The
[6]
egg comes to rest in a time of 55 ms . Assume that air resistance is negligible and
that the egg does not bounce or break.
(a)
Determine the magnitude of the average decelerating force that the ground
[4]
exerts on the egg.
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(b)
Explain why the egg is likely to break when dropped onto concrete from the same
[2]
height.
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Q11 To determine the acceleration due to gravity, a small metal sphere is dropped from
[6]
rest and the time it takes to fall through a known distance and open a trapdoor is
measured.
The following data are available.
= 12.0±0.1 mm
Distance between the point of release and the trapdoor = 654 ±2 mm
= 0.363 ±0.002 s
Measured time for fall
Diameter of metal sphere
(a)
Determine the distance fallen, in m , by the centre of mass of the sphere including
[2]
an estimate of the absolute uncertainty in your answer.
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(b)
Using the following equation
acceleration due to gravity =
[4]
2×distance fallen by centre of mass of sphere
(measured time to fall)2
calculate, for these data, the acceleration due to gravity including an estimate of
the absolute uncertainty in your answer.
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Page 27 of 70
Q12 A heat engine operates on the cycle shown in the pressure-volume diagram.
[10]
The cycle consists of an isothermal expansion AB , an isovolumetric change BC and
an adiabatic compression CA. The volume at B is double the volume at A . The gas
is an ideal monatomic gas.
At A the pressure of the gas is 4.00×106 Pa , the temperature is 612 K and the
volume is 1.50×10−4 m3 . The work done by the gas during the isothermal
expansion is 416 J .
(a)
[7]
(i)
Justify why the thermal energy supplied during the expansion AB is 416 J
[1]
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(ii)
Show that the temperature of the gas at C is 386 K .
[2]
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(iii) Show that the thermal energy removed from the gas for the change BC is
[2]
approximately 330 J .
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(iv) Determine the ef ciency of the heat engine.
[2]
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(b)
State and explain at which point in the cycle ABCA the entropy of the gas is the
[3]
largest.
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Page 29 of 70
Q13 A monatomic ideal gas is con ned to a cylinder with volume 2.0×10−3 m3 . The
[8]
initial pressure of the gas is 100 kPa . The gas undergoes a three-step cycle. First,
the gas pressure increases by a factor of ve under constant volume. Then, the gas
expands adiabatically to its initial pressure. Finally it is compressed at constant
pressure to its initial volume.
(a)
Show that the volume of the gas at the end of the adiabatic expansion is
[2]
approximately 5.3×10−3 m3
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(b)
Using the axes, sketch the three-step cycle.
[2]
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(c)
The initial temperature of the gas is 290 K . Calculate the temperature of the gas
[2]
at the start of the adiabatic expansion.
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(d)
Using your sketched graph in (b), identify the feature that shows that net work is
[2]
done by the gas in this three-step cycle.
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Page 31 of 70
Q14 The pV diagram of a heat engine using an ideal gas consists of an isothermal
[10]
expansion A → B , an isobaric compression B → C and an adiabatic compression
C → A.
The following data are available:
Temperature at A = 385 K
Pressure at A = 2.80×106 Pa
Volume at A
= 1.00×10−4 m3
Volume at B = 2.80×10−4 m3
Volume at C
Show that at C the
(a)
(i)
pressure is 1.00×106 Pa .
= 1.85×10−4 m3
[4]
[2]
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(ii)
temperature is 254 K .
[2]
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(b)
Show that the thermal energy transferred from the gas during the change B → C
[3]
is 238 J .
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(c)
[3]
(i)
The work done by the gas from A → B is 288 J . Calculate the ef ciency of the
[2]
cycle.
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(ii)
State, without calculation, during which change (A → B,B → C or C → A) the
[1]
entropy of the gas decreases.
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Q15 The radius of a circle is measured to be (10.0±0.5) cm . What is the area of the
[1]
circle?
A (314.2±0.3) cm2
B (314 ±1) cm2
C (314 ±15) cm2
D (314 ±31) cm2
Page 34 of 70
Q16 Two different experiments, P and Q, generate two sets of data to con rm the
[1]
proportionality of variables x and y . The graphs for the data from P and Q are
shown. The maximum and minimum gradient lines are shown for both sets of data.
What is true about the systematic error and the uncertainty of the gradient when P
is compared to Q?
A A
B B
C C
D D
Page 35 of 70
Q17 The road from city X to city Y is 1000 km long. The displacement is 800 km from
[1]
X to Y .
What is the distance travelled from Y to X and the displacement from Y to X ?
A A
B B
C C
D D
Page 36 of 70
Q18 A car accelerates uniformly from rest to a velocity v during time t 1 . It then continues
at constant velocity v from t 1 to time t 2 .
[1]
What is the total distance covered by the car in t 2 ?
A vt 2
B
1
v t −t +vt1
2 ( 2 1)
C 1
2
D
v ( t2 +t1)
1
vt +v ( t2 −t1)
2 1
Q19 An object is sliding from rest down a frictionless inclined plane. The object slides
[1]
1.0 m during the rst second.
What distance will the object slide during the next second?
A 1.0 m
B 2.0 m
C 3.0 m
D 4.9 m
Page 37 of 70
Q20 A solid metal ball is dropped from a tower. The variation with time of the velocity of
[1]
the ball is plotted.
A hollow metal ball with the same size and shape is dropped from the same tower.
What graph will represent the variation with time of the velocity for the hollow
metal ball?
A A
B B
C C
D D
Page 38 of 70
Q21 An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a
[1]
straight line with a force of 10 N through a distance d .
The resultant force acting on the object throughout d is 6.0 N .
What is the value of the sliding coef cient of friction μ between the surface and
the object and what is the acceleration a of the object?
A A
B B
C C
D D
Page 39 of 70
Q22 A rocket has just been launched vertically from Earth. The image shows the free-
[1]
body diagram of the rocket. F 1 represents a larger force than F 2 .
Which force pairs with F 1 and which force pairs with F 2 , according to Newton's
third law?
A A
B B
C C
D D
Page 40 of 70
Q23 A ball rolls on the
oor towards a wall and rebounds with the same speed and at
[1]
the same angle to the wall.
What is the direction of the impulse applied to the ball by the wall?
A A
B B
C C
D D
Page 41 of 70
Q24 A book of mass m lies on top of a table of mass M that rolls freely along the
[1]
ground. The coef cient of friction between the book and the table is μ . A person is
pushing the rolling table.
What is the maximum acceleration of the table so that the book does not slide
backwards relative to the table?
A g
μ
B μg
C mg
Mμ
D
m
μg
M
Page 42 of 70
Q25 An object is pushed from rest by a constant net force of 100 N . When the object
[1]
−1
has travelled 2.0 m the object has reached a velocity of 10 m s .
What is the mass of the object?
A 2 kg
B 4 kg
C 40 kg
D 200 kg
Q26 Two blocks of different masses are released from identical springs of elastic
constant k= 100 N m
−1
[1]
, initially compressed a distance Δx = 0.1 m . Block X has
a mass of 1 kg and block Y has a mass of 0.25 kg .
What are the velocities of the blocks when they leave the springs?
A A
B B
C C
D D
Page 43 of 70
Q27 An insulated container of negligible mass contains a mass 2M of a liquid. A piece of
[1]
a metal of mass M is dropped into the liquid. The temperature of the liquid
increases by 10° C and the temperature of the metal decreases by 80° C in the
same time.
What is
specific heat capacity of the liquid
?
specific heat capacity of the metal
A 2
B 4
C 8
D 16
Page 44 of 70
Q28 A quantity of an ideal gas is at a temperature T in a cylinder with a movable piston
[1]
that traps a length L of the gas. The piston is moved so that the length of the
trapped gas is reduced to
5L
and the pressure of the gas doubles.
6
What is the temperature of the gas at the end of the change?
A
5
T
12
B
3
T
5
C 5
3
D
T
12
T
5
Page 45 of 70
Q29 The molar mass of an ideal gas is M . A xed mass m of the gas expands at a
[1]
constant pressure p . The graph shows the variation with temperature T of the gas
volume V .
What is the gradient of the graph?
A
Mp
mR
B
MR
mp
C
mp
MR
D
mR
Mp
Q30 What is true for an ideal gas?
[1]
A nRT = Nk BT
B nRT = k BT
C RT = Nk BT
D RT = k BT
Page 46 of 70
Q31 Which assumption is part of the molecular kinetic model of ideal gases?
[1]
A The work done on a system equals the change in kinetic energy of
the system.
B The volume of a gas results from adding the volume of the individual
molecules.
C A gas is made up of tiny identical particles in constant random motion.
D All particles in a gas have kinetic and potential energy.
Page 47 of 70
Q32 Water at room temperature is placed in a freezer. The speci c heat capacity of
[1]
water is twice the speci c heat capacity of ice. Assume that thermal energy is
transferred from the water at a constant rate.
Which graph shows the variation with time of the temperature of the water?
A A
B B
C C
D D
Page 48 of 70
Q33 System X is at a temperature of 40 °C . Thermal energy is provided to system X
[1]
until it reaches a temperature of 50 °C . System Y is at a temperature of 283 K .
Thermal energy is provided to system Y until it reaches a temperature of 293 K .
What is the difference in the thermal energy provided to both systems?
A Zero
B Larger for X
C Larger for Y
D Cannot be determined with the data given
Q34 A mass at the end of a string is moving in a horizontal circle at constant speed. The
[1]
string makes an angle θ to the vertical.
What is the magnitude of the acceleration of the mass?
A g
B gsinθ
C gcosθ
D gtanθ
Page 49 of 70
Q35 A satellite is orbiting Earth in a circular path at constant speed. Three statements
[1]
about the resultant force on the satellite are:
I. It is equal to the gravitational force of attraction on the satellite.
II. It is equal to the mass of the satellite multiplied by its acceleration.
III. It is equal to the centripetal force on the satellite.
Which combination of statements is correct?
A I and II only
B
I and III only
C II and III only
D I, II and III
Q36 Three statements about Newton's law of gravitation are:
[1]
I. It can be used to predict the motion of a satellite.
II. It explains why gravity exists.
III. It is used to derive the expression for gravitational potential energy.
Which combination of statements is correct?
A I and II only
B
I and III only
C II and III only
D
I, II and III
Page 50 of 70
Q37 A ball of mass (50±1) g is moving with a speed of (25±1) m s−1 . What is the
[1]
fractional uncertainty in the momentum of the ball?
A 0.02
B 0.04
C 0.06
D 0.08
Page 51 of 70
Q38 Two sets of data, shown below with circles and squares, are obtained in two
[1]
experiments. The size of the error bars is the same for all points.
What is correct about the absolute uncertainty and the fractional uncertainty of the
y intercept of the two lines of best t?
A A.
B B.
C C.
D D.
Page 52 of 70
Q39 The graph shows the variation with time t of the velocity of an object.
[1]
What is the variation with time t of the acceleration of the object?
A A
B B
C C
D D
Page 53 of 70
Q40 X and Y are two objects on a frictionless table connected by a string. The mass of
[1]
X is 2 kg and the mass of Y is 4 kg . The mass of the string is negligible. A constant
horizontal force of 12 N acts on Y .
What are the acceleration of Y and the magnitude of the tension in the string?
A A
B B
C C
D D
Page 54 of 70
Q41 The graph shows how the position of an object varies with time in the interval from
[1]
0 to 3 s .
At which point does the instantaneous speed of the object equal its average speed
over the interval from 0 to 3 s ?
A A.
B B.
C C.
D D.
Q42 A cyclist rides up a hill of vertical height 100 m in 500 s at a constant speed. The
[1]
combined mass of the cyclist and the bicycle is 80 kg . The power developed by the
cyclist is 200 W . What is the ef ciency of the energy transfer in this system?
A 8%
B 20%
C 60%
D 80%
Page 55 of 70
Q43 A block rests on a frictionless horizontal surface. An air ri e pellet is red
[1]
horizontally into the block and remains embedded in the block.
What happens to the total kinetic energy and to the total momentum of the block
and pellet system as a result of the collision?
A A
B B
C C
D D
Page 56 of 70
Q44 Masses X and Y rest on a smooth horizontal surface and are connected by a
[1]
massless spring. The mass of X is 3.0 kg and the mass of Y is 6.0 kg . The masses
are pushed toward each other until the elastic potential energy stored in the spring
is 1.0 J .
The masses are released. What is the maximum speed reached by mass Y ?
A 0.11 m s−1
B 0.33 m s−1
C 0.45 m s−1
D 0.66 m s−1
Q45 A xed mass of an ideal gas has a volume of V , a pressure of p and a temperature
of 30° C . The gas is compressed to the volume of
[1]
V
and its pressure increases to
6
12p . What is the new temperature of the gas?
A 15° C
B 60° C
C 333° C
D 606° C
Page 57 of 70
Q46 A sunbather is supported in water by a
oating sun bed. Which diagram represents
[1]
the magnitudes of the forces acting on the sun bed?
A A.
B B.
C C.
D D.
Q47 What is the unit of power expressed in fundamental SI units?
[1]
A kg m s−2
B kg m2 s−2
C kg m s−3
D kg m2 s−3
Page 58 of 70
Q48 Which aspect of thermal physics is best explained by the molecular kinetic model?
[1]
A The equation of state of ideal gases
B The difference between Celsius and Kelvin temperature
C The value of the Avogadro constant
D The existence of gaseous isotopes
Q49 What does the constant n represent in the equation of state for an ideal gas
[1]
pV = nRT ?
A The number of atoms in the gas
B The number of moles of the gas
C The number of molecules of the gas
D The number of particles in the gas
Page 59 of 70
Q50 A liquid is vaporized to a gas at a constant temperature.
[1]
Three quantities of the substance are the
I. total intermolecular potential energy
II. root mean square speed of the molecules
III. average distance between the molecules.
Which quantities are greater for the substance in the gas phase compared to the
liquid phase?
A I and II only
B I and III only
C II and III only
D I, II and III
Q51 A mass m of a liquid of speci c heat capacity c
ows every second through a
[1]
heater of power P . What is the difference in temperature between the liquid
entering and leaving the heater?
A mc
P
B
C
D
273+
mc
P
P
mc
273+
P
mc
Page 60 of 70
Q52 Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the
[1]
ideal gas. Y has four times the volume of X . The pressure in X is twice that in Y .
What is
temperature of gas in X
?
temperature of gas in Y
A 1
4
B
1
2
C 1
D 2
Q53 A satellite X of mass m orbits the Earth with a period T . What will be the orbital
[1]
period of satellite Y of mass 2m occupying the same orbit as X ?
A
T
2
B T
C
2T
D 2T
Page 61 of 70
Q54 A child stands on a horizontal rotating platform that is moving at constant angular
[1]
speed. The centripetal force on the child is provided by
A the gravitational force on the child.
B the friction on the child's feet.
C the tension in the child's muscles.
D the normal reaction of the platform on the child.
Q55 Which lists one scalar and two vector quantities?
[1]
A Mass, momentum, potential difference
B Mass, power, velocity
C Power, intensity, velocity
D Power, momentum, velocity
Q56 How many signi cant gures are there in the number 0.0450 ?
[1]
A 2
B 3
C 4
D 5
Page 62 of 70
Q57 A mass m attached to a string of length R moves in a vertical circle with a constant
[1]
speed. The tension in the string at the top of the circle is T . What is the kinetic
energy of the mass at the top of the circle?
A
R (T +mg)
2
B
R (T −mg)
2
C
Rmg
2
D
R (2T +mg)
2
Q58 A 1.0 kW heater supplies energy to a liquid of mass 0.50 kg . The temperature of
[1]
the liquid changes by 80 K in a time of 200 s . The speci c heat capacity of the
liquid is 4.0 kJ kg −1 K −1 . What is the average power lost by the liquid?
A 0
B 200 W
C 800 W
D 1600 W
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Q59 The fraction of the internal energy that is due to molecular vibration varies in the
[1]
different states of matter. What gives the order from highest fraction to lowest
fraction of internal energy due to molecular vibration?
A liquid > gas > solid
B solid > liquid > gas
C solid > gas > liquid
D gas > liquid > solid
Q60 A container is lled with a mixture of helium and oxygen at the same temperature.
The molar mass of helium is 4 g mol
What is the ratio
−1
and that of oxygen is 32 g mol
−1
[1]
.
average speed of helium molecules
?
average speed of oxygen molecules
A 1
8
B
1
8
C
8
D 8
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Q61 A stationary nucleus of polonium-210 undergoes alpha decay to form lead-206. The
[1]
initial speed of the alpha particle is v . What is the speed of the lead-206 nucleus?
A 206
4
v
B v
C 206
210
D
v
4
v
206
Q62 A 700 W electric heater is used to heat 1 kg of water without energy losses. The
[1]
−1 −1
K . What is the time taken to heat
speci c heat capacity of water is 4.2 kJ kg
the water from 25° C to 95° C ?
A 7s
B 30 s
C 7 minutes
D 420 minutes
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Q63 A quantity of 2.00 mol of an ideal gas is maintained at a temperature of 127° C in
[1]
a container of volume 0.083 m3 . What is the pressure of the gas?
A 8 kPa
B 25 kPa
C 40 kPa
D 80 kPa
Q64 A small ball of weight W is attached to a string and moves in a vertical circle of
[1]
radius R .
What is the smallest kinetic energy of the ball at position X for the ball to maintain
the circular motion with radius R ?
A W R
2
B W R
C 2W R
D
5W R
2
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Q65 Airboats are used for transport across a river. To move the boat forward, air is
[13]
propelled from the back of the boat by a fan blade.
An airboat has a fan blade of radius 1.8 m . This fan can propel air with a maximum
speed relative to the boat of 20 m s−1 . The density of air is 1.2 kg m−3 .
(a)
Outline why a force acts on the airboat due to the fan blade.
[3]
Words: 0
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(b)
In a test the airboat is tied to the river bank with a rope normal to the bank. The
[3]
fan propels the air at its maximum speed. There is no wind.
(i)
Show that a mass of about 240 kg of air moves through the fan every second.
[2]
Words: 0
(ii)
Show that the tension in the rope is about 5 kN .
[1]
Words: 0
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(c)
The rope is untied and the airboat moves away from the bank. The variation with
[7]
time t of the speed v of the airboat is shown for the motion.
(i)
Explain why the airboat has a maximum speed under these conditions.
[2]
Words: 0
(ii)
Estimate the distance the airboat travels to reach its maximum speed.
[2]
Words: 0
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(iii) Deduce the mass of the airboat.
[3]
Words: 0
Page 70 of 70