Download Physics - Higher Level - Paper Two

– 14 –
M00/430/H(2)
B2. This question is about the motion of a firework rocket.
A firework rocket is fired vertically upwards from the ground. It accelerates uniformly from rest
with an acceleration of 8.0 m s !2 for 5.0 s after which time the fuel of the rocket has all been used.
(a)
(i)
Sketch below a graph to show how the velocity of the rocket changes with time from
the moment it leaves the ground until the moment that it returns to the ground. Mark
on your sketch the time t1 at which the fuel has run out, the time t2 at which the rocket
reaches its maximum height and the time t3 at which it reaches the ground.
[6]
(Note that you are not expected to give any quantitative values of velocity and time and
air resistance can be ignored.)
(ii)
Comment on the area(s) under the graph that you have drawn.
[2]
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(This question continues on the following page)
220-227
– 15 –
M00/430/H(2)
(Question B2 continued)
In the following calculations you may ignore any effects of air resistance and take the acceleration
due to gravity, g = 10 m s!2 .
(b)
Calculate the
(i)
[2]
speed of the rocket when the fuel runs out.
.....................................................................
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(ii)
height that the rocket reaches when the fuel has just run out.
[2]
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[3]
(iii) maximum height reached by the rocket.
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[2]
(iv) time it takes the rocket to reach its maximum height.
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(v)
time that it takes to fall from its maximum height to the ground.
[2]
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(This question continues on the following page)
220-227
Turn over
– 16 –
M00/430/H(2)
(Question B2 continued)
(c)
(i)
On the axes below sketch graphs to show how the gravitational potential energy and the
kinetic energy of the rocket varies as it moves from the ground to its maximum height.
[4]
(Note that this is only a sketch graph; you do not need to add any numerical values.)
(ii)
State one assumption, other than ignoring air resistance, that you have made in
sketching the above graph.
[1]
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(d)
The rocket plus fuel initially have a mass of 0.16 kg. If the initial mass of the fuel is 0.02 kg,
calculate the maximum kinetic energy of the rocket when all the fuel has been used.
[2]
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(e)
Calculate the power delivered to the rocket by the rocket fuel.
[2]
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(f)
Describe two consequences on the motion of the rocket as a result of air resistance acting on
the rocket.
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[2]
– 15 –
N00/430/H(2)
B2. This question is in three parts. Part 1 is about a collision, Part 2 is about molecular motion and
evaporation and Part 3 is about Huygen’s principle. Answer all three parts if you choose B2.
Part 1. Collision between car and truck
A car and a truck are both travelling at the speed limit of 60 km h !1 but in opposite directions as
shown. The truck has twice the mass of the car.
The vehicles collide head-on and become entangled together.
(a)
During the collision, how does the force exerted by the car on the truck compare with the
force exerted by the truck on the car? Explain.
[2]
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.........................................................................
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(b)
In what direction will the entangled vehicles move after collision or will they be stationary?
Support your answer, referring to a physics principle.
[2]
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(c)
Determine the speed (in km h !1 ) of the combined wreck immediately after the collision.
[3]
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(d)
How does the acceleration of the car compare with the acceleration of the truck during the
collision? Explain.
[2]
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(This question continues on the following page)
880-227
Turn over
– 16 –
N00/430/H(2)
(Question B2 continued)
(e)
Both the car and truck drivers are wearing seat belts. Which driver is likely to be the more
severely jolted in the collision? Explain.
[2]
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(f)
The total kinetic energy of the system decreases as a result of the collision. Is the principle of
conservation of energy violated? Explain.
[1]
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(This question continues on the following page)
880-227
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– 26 –
N04/4/PHYSI/HP2/ENG/TZ0/XX+
B3. This question is in two parts. Part 1 is about conservation of momentum and conservation of
energy. Part 2 is about electromagnetic induction.
Part 1 Conservation of momentum and energy
(a)
State Newton’s third law.
[1]
......................................................................
......................................................................
......................................................................
(b)
State the law of conservation of momentum.
[2]
......................................................................
......................................................................
The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest
and ball A is moving with speed V along a line joining the centres of the balls. The mass of each
ball is M.
Before collision
During the collision of the balls, the magnitude of the force that ball A exerts on ball B is FAB
and the magnitude of the force that ball B exerts on ball A is FBA .
(c)
On the diagram below, add labelled arrows to represent the magnitude and direction of
the forces FAB and FBA .
[3]
During the collision
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(Question B3, part 1 continued)
The balls are in contact for a time $t. After the collision, the speed of ball A is vA and the
speed of ball B is vB in the directions shown.
vA
vB
After the collision
As a result of the collision there is a change in momentum of ball A and of ball B.
(d)
Use Newton’s second law of motion to deduce an expression relating the forces acting
during the collision to the change in momentum of
(i)
ball B.
[2]
.................................................................
.................................................................
(ii)
ball A.
[2]
.................................................................
.................................................................
(e)
Apply Newton’s third law and your answers to (d), to deduce that the change in momentum
of the system (ball A and ball B) as a result of this collision, is zero.
[4]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
(f)
Deduce, that if kinetic energy is conserved in the collision, then after the collison, ball A
will come to rest and ball B will move with speed V.
[3]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
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A3. This question is about estimating the energy changes for an escalator (moving staircase).
The diagram below represents an escalator. People step on to it at point A and step off at
point B.
40!
(a)
The escalator is 30 m long and makes an angle of 40! with the horizontal. At full capacity,
48 people step on at point A and step off at point B every minute.
(i)
Calculate the potential energy gained by a person of weight 700 N in moving from
A to B.
[2]
.................................................................
.................................................................
.................................................................
(ii)
Estimate the energy supplied by the escalator motor to the people every minute
when the escalator is working at full capacity.
[1]
.................................................................
.................................................................
(iii) State one assumption that you have made to obtain your answer to (ii).
[1]
.................................................................
.................................................................
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(Question A3 continued)
The escalator is driven by an electric motor that has an efficiency of 70 %.
(b)
(i)
Using your answer to (a) (ii), calculate the minimum input power required by the
motor to drive the escalator.
[3]
.................................................................
.................................................................
.................................................................
.................................................................
(ii)
Explain why it is not necessary to take into account the weight of the escalator
when calculating the input power.
[1]
.................................................................
.................................................................
(c)
Explain why in practice, the power of the motor will need to be greater than that calculated
in (b) (i).
[1]
......................................................................
......................................................................
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N04/4/PHYSI/HP2/ENG/TZ0/XX+
SECTION A
Answer all the questions in the spaces provided.
A1. 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.
P / kW
2.00
v / ms 1
The masses shown are the total mass of the boat plus passengers.
(a)
For the boat having a steady speed of2.00
2.0 ms 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]
.................................................................
.................................................................
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(Question A1 continued)
Consider the case of the boat moving with a speed of2.50
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
(ii)
250
300
350
400
[6]
450
W / kg
Use data from the graph that you have drawn to determine the power of the motor
for a total mass of 330 kg.
[1]
.................................................................
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(Question A1 continued)
The relationship between power P and speed v is of the form
P kv n
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.
lg (P / kW)
lg (v / m s 1)
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(Question A1 continued)
(c)
Use the graph to deduce the value of n and explain how you obtained your answer.
[3]
......................................................................
......................................................................
......................................................................
......................................................................
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is in two parts. Part 1 is about momentum and the kinematics of a proposed
journey to Jupiter. Part 2 is about radioactive decay.
Part 1 Momentum and kinematics
(a)
State the law of conservation of momentum.
[2]
......................................................................
......................................................................
......................................................................
A solar propulsion engine uses solar power to ionise atoms of xenon and to accelerate them.
As a result of the acceleration process, the ions are ejected from the spaceship with a speed of
3.0 s104 m s 1.
xenon ions
speed 3.0 s104 m s 1
(b)
spaceship
mass 35.4
.0 s1042 kg
m s 1
The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of
.0 s10
s 1
xenon is 32.2
104–25mkg.
[2]
......................................................................
......................................................................
......................................................................
......................................................................
(c)
The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 7.7 s1018 xenon
ions every second, the fuel will last for 1.5 years. (1
(1year
year=3.2 s107s))
[2]
......................................................................
......................................................................
......................................................................
......................................................................
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(Question B1, part 1 continued)
(d)
The mass of the spaceship is 5.4 s102 kg. Deduce that the initial acceleration of the
spaceship is 8.2 s105 m s 2 .
[5]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
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(Question B1, part 1 continued)
The graph below shows the variation with time t of the acceleration a of the spaceship. The solar
propulsion engine is switched on at time t 0 when the speed of the spaceship is 1.2 s103 m s 1.
10.0
9.5
aa//s105 m s 2
9.0
8.5
8.0
(e)
0.0
1.0
2.0
3.0
tt//s107 s
4.0
5.0
6.0
Explain why the acceleration of the spaceship is increasing with time.
[2]
......................................................................
......................................................................
......................................................................
......................................................................
(f)
Using data from the graph, calculate the speed of the spaceship at the time when the
xenon fuel has all been used.
[4]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
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(Question B1, part 1 continued)
(g)
The distance of the spaceship from Earth when the solar propulsion engine is switched on
is very small compared to the distance from Earth to Jupiter. The fuel runs out when the
spaceship is a distance of 4.7 s1011 m from Jupiter. Estimate the total time that it would
take the spaceship to travel from Earth to Jupiter.
[2]
......................................................................
......................................................................
......................................................................
......................................................................
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B4. This question is in two parts. Part 1 is about driving a metal bar into the ground and the engine
used in the process. Part 2 is about the force between current-carrying wires.
Part 1 The metal bar
Large metal bars can be driven into the ground using a heavy falling object.
object mass = 2.0 s103 kg
bar mass = 400 kg
In the situation shown, the object has a mass 2.0 s103 kg and the metal bar has a mass of 400 kg.
The object strikes the bar at a speed of 6.0 m s 1. It comes to rest on the bar without bouncing.
As a result of the collision, the bar is driven into the ground to a depth of 0.75 m.
(a)
Determine the speed of the bar immediately after the object strikes it.
[4]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
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(Question B4, part 1 continued)
(b)
Determine the average frictional force exerted by the ground on the bar.
[3]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
(c)
The object is raised by a diesel engine that has a useful power output of 7.2 kW.
In order that the falling object strikes the bar at a speed of 6.0 m s 1, it must be raised to
a certain height above the bar. Assuming that there are no energy losses due to friction,
calculate how long it takes the engine to raise the object to this height.
[4]
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
......................................................................
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B4. This question is in two parts. Part 1 is about momentum. Part 2 is about the quantum nature of
radiation.
Part 1 Momentum
(a)
State the law of conservation of momentum.
[2]
.......................................................................
.......................................................................
.......................................................................
(b)
An ice hockey puck collides with the wall of an ice rink. The puck is sliding along a line
that makes an angle of 45! to the wall.
wall
45!
45!
ice rink
direction of puck
before collision
direction of puck
after collision
The collision between the wall and the puck is perfectly elastic.
(i)
State what is meant by an elastic collision.
[1]
..................................................................
..................................................................
(ii)
Discuss how the law of conservation of momentum applies to this situation.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
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(Question B4, part 1 continued)
(c)
The diagram below is a scale diagram that shows the vector representing the momentum
of the puck before collision.
Scale: 1.0 cm = 0.10 N s
By adding appropriate vectors to the diagram, deduce that the magnitude of the change in
momentum of the puck as a result of the collision is 0.71 N s.
[4]
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(Question B4, part 1 continued)
(d)
The sketch-graph below shows the variation with time t of the force F exerted by the wall
on the puck.
F
0
0
t
The total contact time is 12 ms. Estimate, explaining your reasoning, the magnitude of
the maximum force exerted by the wall on the puck.
[3]
.......................................................................
.......................................................................
.......................................................................
.......................................................................
.......................................................................
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is about mechanical power and heat engines.
Mechanical power
(a)
Define power.
[1]
.......................................................................
.......................................................................
(b)
A car is travelling with constant speed v along a horizontal straight road. There is a total
resistive force F acting on the car.
Deduce that the power P to overcome the force F is
P = Fv.
[2]
.......................................................................
.......................................................................
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(Question B1 continued)
(c)
A car drives up a straight incline that is 4.80 km long. The total height of the incline is
0.30 km.
4.80 km
0.30 km
The car moves up the incline at a steady speed of 16 m s!1. During the climb, the average
resistive force acting on the car is 5.0 % 102 N. The total weight of the car and the driver
is 1.2 % 104 N.
(i)
Determine the time it takes the car to travel from the bottom to the top of the incline.
[2]
..................................................................
..................................................................
..................................................................
(ii)
Determine the work done against the gravitational force in travelling from the bottom
to the top of the incline.
[1]
..................................................................
(iii) Using your answers to (i) and (ii), calculate a value for the minimum power output
of the car engine needed to move the car from the bottom to the top of the incline.
[4]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
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(Question B1 continued)
(d)
From the top of the incline, the road continues downwards in a straight-line. At the point
where the incline starts to go downwards, the driver of the car in (c) stops the car to look
at the view. In continuing his journey, the driver decides to save fuel. He switches off the
engine and allows the car to move freely down the incline. The car descends a height of
0.30 km in a distance of 6.40 km before levelling out.
6.40 km
0.30 km
The average resistive force acting on the car is 5.0 % 102 N.
Estimate
(i)
the acceleration of the car down the incline.
[5]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
the speed of the car at the bottom of the incline.
[2]
..................................................................
..................................................................
(e)
In fact, for the last few hundred metres of its journey down the incline, the car travels at
constant speed. State the value of the frictional force acting on the car whilst it is moving
at constant speed.
[1]
.......................................................................
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(Question B1 continued)
Part 2
Collisions
A large metal ball is hung from a crane by means of a cable of length 5.8 m as shown below.
cable
crane
5.8 m
wall
metal ball
In order to knock down a wall, the metal ball of mass 350 kg is pulled away from the wall and
then released. The crane does not move. The graph below shows the variation with time t of
the speed v of the ball after release.
3.0
2.0
v / m s–1
1.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
t/s
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(Question B1, part 2 continued)
The ball makes contact with the wall when the cable from the crane is vertical.
(a)
For the ball just before it hits the wall,
(i)
state why the tension in the cable is not equal to the weight of the ball.
[1]
..................................................................
..................................................................
(ii)
by reference to the graph, estimate the tension in the cable. The acceleration of
free fall is 9.8 m s–2.
[3]
..................................................................
..................................................................
..................................................................
..................................................................
(b)
Use the graph to determine the distance moved by the ball after coming into contact with
the wall.
[2]
.......................................................................
.......................................................................
.......................................................................
.......................................................................
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(Question B1, part 2 continued)
(c)
For the collision between the ball and the wall, calculate
(i)
the total change in momentum of the ball.
[2]
..................................................................
..................................................................
..................................................................
(ii)
the average force exerted by the ball on the wall.
[2]
..................................................................
..................................................................
..................................................................
(d)
(i)
State the law of conservation of momentum.
[2]
..................................................................
..................................................................
..................................................................
(ii)
The metal ball has lost momentum. Discuss whether the law applies to this situation.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
(e)
During the impact of the ball with the wall, 12 % of the total kinetic energy of the ball is
converted into thermal energy in the ball. The metal of the ball has specific heat capacity
450 J kg–1 K–1. Determine the average rise in temperature of the ball as a result of colliding
with the wall.
.......................................................................
.......................................................................
.......................................................................
.......................................................................
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is in two parts. Part 1 is about the motion of a ball in the presence of
air resistance. Part 2 is about the emission of electrons from a surface.
Part 1
Motion of a ball
A ball of mass 0.25 kg is projected vertically upwards from the ground with an initial velocity
of 30 m s–1. The acceleration of free fall is 10 m s–2, but air resistance cannot be neglected.
The graph below shows the variation with time t of the velocity v of this ball for the
upward part of the motion.
v / m s–1
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
t/s
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(Question B1, part 1 continued)
(a)
State what the area under the graph represents.
[1]
.......................................................................
(b)
Estimate the maximum height reached by the ball.
[1]
.......................................................................
.......................................................................
(c)
Determine, for the ball at t 1.0 s,
(i)
the acceleration.
[3]
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
the magnitude of the force of air resistance.
[2]
..................................................................
..................................................................
..................................................................
(d)
Use the graph to explain, without any further calculations, that the force of air resistance
is decreasing in magnitude as the ball moves upward.
[2]
.......................................................................
.......................................................................
.......................................................................
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(Question B1, part 1 continued)
(e)
The diagram below is a sketch graph of the upward motion of the ball.
Draw a line to indicate the downward motion of the ball. The line should indicate the
motion from the maximum height of the ball until just before it hits the ground.
v / m s–1
[2]
30
20
10
0.0
0.0
2.0
4.0
t/s
–10
–20
–30
(f)
State and explain, by reference to energy transformations, whether the speed with which
the ball hits the ground is equal to 30 m s–1.
[2]
.......................................................................
.......................................................................
.......................................................................
(g)
Use your answer in (f) to state and explain whether the ball takes 2.0 s to move from its
maximum height to the ground.
[2]
.......................................................................
.......................................................................
.......................................................................
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A2. This question is about energy and momentum.
A train carriage A of mass 500 kg is moving horizontally at 6.0 m s–1. It collides with another
train carriage B of mass 700 kg that is initially at rest, as shown in the diagram below.
6.0 m s–1
train carriage A
500 kg
train carriage B
700 kg
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(Question A2 continued)
The graph below shows the variation with time t of the velocities of the two train carriages
before, during and after the collision.
v / m s–1
6.0
train carriage B
5.0
4.0
3.0
2.0
1.0
0.0
1.0
2.0
3.0
4.0
5.0
–1.0
6.0
7.0
8.0
9.0
10.0
t/s
train carriage A
–2.0
(a)
Use the graph to deduce that
(i)
the total momentum of the system is conserved in the collision.
[2]
..................................................................
..................................................................
..................................................................
(ii)
the collision is elastic.
[2]
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..................................................................
..................................................................
(b)
Calculate the magnitude of the average force experienced by train carriage B.
[3]
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B2. This question is in two parts. Part 1 is about momentum and Part 2 is about thermal physics.
Part 1
(a)
Momentum
State the law of conservation of linear momentum.
[2]
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(Question B2, part 1 continued)
(b)
A toy rocket of mass 0.12 kg contains 0.59 kg of water as shown in the diagram below.
high-pressure air
water
nozzle, radius 1.4 mm
The space above the water contains high-pressure air. The nozzle of the rocket has
a circular cross-section of radius 1.4 mm. When the nozzle is opened, water emerges
from the nozzle at a constant speed of 18 m s–1. The density of water is 1000 kg m–3.
(i)
Deduce that the volume of water ejected per second through the nozzle
is 1.1 s 10–4 m3.
[2]
..................................................................
..................................................................
..................................................................
(ii)
Deduce that the upward force that the ejected water exerts on the
rocket is approximately 2.0 N.
Explain your working by reference to
Newton’s laws of motion.
[4]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(iii) State why the rocket does not lift off at the instant that the nozzle is opened.
[1]
..................................................................
..................................................................
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is in two parts. Part 1 is about linear motion and Part 2 is about nuclear
reactions.
Part 1
Linear motion
At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope
and dip are shown in the diagram below. The vertical height of the slope is 41 m.
A
(not to scale)
slope
41 m
B
C D
1.8 m
dip
12 m
The graph below shows the variation with time t of the speed v down the slope of
the skier.
25.0
20.0
15.0
v / ms
–1
10.0
5.0
0.0
0.0
1.0
2.0
3.0
4.0
t/s
5.0
6.0
7.0
8.0
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(Question B1 part 1 continued)
The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.
(a)
Use the graph to
(i)
calculate the kinetic energy EK of the skier at point B.
[2]
..................................................................
..................................................................
..................................................................
(ii)
determine the length of the slope.
[4]
..................................................................
..................................................................
..................................................................
..................................................................
..................................................................
(b)
(i)
Calculate the change $EP in the gravitational potential energy of the skier between
point A and point B.
[2]
..................................................................
..................................................................
..................................................................
(ii)
Use your answers to (a) and (b)(i) to determine the average retarding force on the
skier between point A and point B.
[3]
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..................................................................
..................................................................
..................................................................
(iii) Suggest two causes of the retarding force calculated in (ii).
[2]
1.
.............................................................
2.
.............................................................
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(Question B1 part 1 continued)
(c)
At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on
the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.
Determine the distance CD of the point D from the edge C of the dip. Air resistance may
be assumed to be negligible.
[4]
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.......................................................................
.......................................................................
.......................................................................
.......................................................................
(d)
The lower side of the dip is altered so that it is inclined to the horizontal,
as shown below.
B
C
slope
D
1.8 m
dip
12 m
(i)
State the effect of this change on the landing position D.
[1]
..................................................................
..................................................................
(ii)
Suggest the effect of this change on the impact felt by the skier on landing.
[2]
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is in two parts. Part 1 is about momentum and energy and Part 2 is about
gravitation.
Part 1
(a)
Momentum and energy
Define impulse of a force and state the relation between impulse and momentum.
[2]
definition
.......................................................................
.......................................................................
relation
.......................................................................
.......................................................................
(b)
By applying Newton’s laws of motion to the collision of two particles, deduce that
momentum is conserved in the collision.
[5]
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(Question B1 part 1 continued)
(c)
In an experiment to measure the speed of a bullet, the bullet is fired into a piece of plasticine
suspended from a rigid support by a light thread.
bullet
24 cm
speed V
plasticine
The speed of the bullet on impact with the plasticine is V. As a result of the impact,
the bullet embeds itself in the plasticine and the plasticine is displaced vertically through
a height of 24 cm. The mass of the bullet is 5.2 "10!3 kg and the mass of the plasticine
is 0.38 kg.
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(Question B1 part 1 continued)
(i)
Ignoring the mass of the bullet, calculate the speed of the plasticine immediately
after the impact.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
Deduce that the speed V with which the bullet strikes the plasticine is about
160 m s !1 .
[2]
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..................................................................
..................................................................
(iii) Estimate the kinetic energy lost in the impact.
[3]
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(Question B1 part 1 continued)
(d)
Another bullet is fired from a different gun into a large block of wood. The block remains
stationary after impact and the bullet melts completely. The temperature rise of the block
is negligible. Use the data to estimate the minimum impact speed of the bullet.
[5]
mass of bullet
specific heat capacity of the material of the bullet
latent heat of fusion of the material of the bullet
melting point of the material of the bullet
initial temperature of bullet
= 5.2"10!3 kg
= 130 J kg !1K !1
= 870 J kg !1
= 330 oC
= 30 oC
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B4. This question is in two parts. Part 1 is about power and an ideal gas and Part 2 is about
photoelectric effect.
Part 1
(a)
Power and an ideal gas
Define power.
[1]
.......................................................................
.......................................................................
(b)
A constant force of magnitude F moves an object at constant speed v in the direction
of the force. Deduce that the power P required to maintain constant speed is given by
the expression
[2]
P = Fv
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(Question B4 part 1 continued)
(c)
Sand falls vertically on to a horizontal conveyor belt at a rate of 60 kg s–1.
sand
60 kg s–1
2.0 m s–1
The conveyor belt that is driven by an engine, moves with speed 2.0 m s–1.
When the sand hits the conveyor belt, its horizontal speed is zero.
(i)
Identify the force F that accelerates the sand to the speed of the conveyor belt.
[1]
..................................................................
(ii)
Determine the magnitude of the force F.
[2]
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..................................................................
..................................................................
..................................................................
(iii) Calculate the power P required to move the conveyor belt at constant speed.
[1]
..................................................................
..................................................................
(iv) Determine the rate of change of kinetic energy K of the sand.
[2]
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..................................................................
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(v)
Explain why P and K are not equal.
[2]
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SECTION B
This section consists of four questions: B1, B2, B3 and B4. Answer two questions.
B1. This question is in two parts. Part 1 is about units and momentum and Part 2 is about X-rays.
Part 1
(a)
Units and momentum
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.
[2]
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(iii) Use the expression and your answers in (b)(i) and (b)(ii) to determine the derived
units of k.
[1]
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(Question B1, part 1 continued)
(c)
Define
(i)
linear momentum.
[1]
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..................................................................
(ii)
impulse.
[1]
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(Question B1, part 1 continued)
(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
9.3 m
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 2250 N s.
[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]
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(Question B1, part 1 continued)
(e)
For the carriage in (d) passing through the water-tank, determine
(i)
its total loss in kinetic energy.
[3]
..................................................................
..................................................................
..................................................................
..................................................................
(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]
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A2. This question is about momentum.
(a)
A rocket in outer space far from any other masses is used to propel a satellite. At t 0
the engines are turned on and gases leave the rear of the rocket with speed v relative to
the rocket.
satellite
v
fuel
rocket
(i)
Explain, in terms of Newton’s laws of motion, why the rocket will accelerate.
[2]
..................................................................
..................................................................
..................................................................
..................................................................
(ii)
Outline how the law of conservation of momentum applies to the motion of
the rocket.
[2]
..................................................................
..................................................................
..................................................................
(iii) The gases leave the rear of the rocket at a constant rate of R kg per second. The mass
of the rocket (including fuel) at t 0 is M.
Deduce that the initial acceleration, a, of the rocket is given by the expression
a
Rv .
M
[3]
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(Question A2 continued)
(b)
The diagram below shows a two-stage rocket that is used to accelerate a satellite that
has the same mass as in (a). The rocket has the same mass as the single stage rocket and
carries the same mass of fuel as in (a).
satellite
v
fuel
fuel
first stage
second stage
Each stage is discarded after all its fuel has been used. Explain, using the answer in
(a)(iii), whether the final speed of the satellite will be larger, equal or smaller than
that of the satellite accelerated by the single stage rocket.
[2]
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.......................................................................
.......................................................................
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B3. This question is in two parts. Part 1 is about mechanics. Part 2 is about wave-particle duality.
Part 1
(a)
Mechanics
A girl falls from rest on to the horizontal surface of a trampoline.
The graph below shows the variation with time t of the net force F exerted on the girl
before, during and after contact with the trampoline.
F / N 1500
1250
1000
750
500
250
0
0.0
0.2
D 0.6
0.4
0.8
1.0
1.2 t / s
–250
C
–500
The girl first makes contact with the trampoline at point C.
Use data from the graph to calculate the
(i)
mass of the girl.
[1]
..................................................................
..................................................................
(ii)
speed of the girl just before she lands on the trampoline.
[2]
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..................................................................
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(Question B3, part 1 continued)
(iii) initial height above the surface of the trampoline from which the girl falls.
[2]
..................................................................
..................................................................
..................................................................
(iv) magnitude of the maximum acceleration of the girl for the time she is in contact
with the trampoline.
[2]
..................................................................
..................................................................
..................................................................
(b)
The girl has a maximum speed at point D as shown on the graph.
For the time between point C and point D
(i)
explain why the speed of the girl is increasing.
[2]
..................................................................
..................................................................
..................................................................
(ii)
deduce that the change in momentum of the girl is approximately 5 N s.
[2]
..................................................................
..................................................................
..................................................................
(iii) estimate the maximum speed of the girl.
[2]
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