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IB Questions on Work, Energy, and Power
1.
2.
3.
An object of mass m1 has a kinetic energy K1. Another object of mass m2 has a kinetic energy
K
K2. If the momentum of both objects is the same, the ratio 1 is equal to
K2
A.
m2
.
m1
B.
m1
.
m2
C.
m2
.
m1
D.
m1
.
m2
A rocket is fired vertically. At its highest point, it explodes. Which one of the following
describes what happens to its total momentum and total kinetic energy as a result of the
explosion?
Total momentum
Total kinetic energy
A.
unchanged
increased
B.
unchanged
unchanged
C.
increased
increased
D.
increased
unchanged
The graph below shows the variation with displacement d of the force F applied by a spring on
a cart.
5
4
The work done by the force in moving the cart through a
distance of 2 cm is
A.
B.
C.
10 × 10–2J.
3
F/N
2
–2
7 × 10 J.
1
–2
5 × 10 J.
0
D.
–2
2.5 × 10 J.
0
1
2
–2
d / 10 m
3
1
4.
5.
An electric motor is used to raise a weight of 2.0 N. When connected to a 4.0 V supply, the
current in the motor is 1.5 A. Assuming no energy losses, the best estimate for the maximum
steady speed at which the weight can be raised is
A.
0.3 m s–1.
B.
3.0 m s–1.
C.
9.0 m s–1.
D.
12.0 m s–1.
The diagram below shows the variation with displacement x of the force F acting on an object in
the direction of the displacement.
F
R
Q
S
P
0 W
0
V
x1
T
x2
x
Which area represents the work done by the force when the displacement changes from x1 to x2?
6.
A.
QRS
B.
WPRT
C.
WPQV
D.
VQRT
An engine takes in an amount E of thermal energy and, as a result, does an amount W of useful
work. An amount H of thermal energy is ejected. The law of conservation of energy and the
efficiency of the engine are given by which of the following?
Law of conservation of energy
Efficiency
A.
E=W+H
W
B.
E=W+H
W
E
C.
E+H=W
W
H
D.
E+H=W
W
E–H
2
7.
8.
9.
10.
A machine lifts an object of weight 1.5 × 103 N to a height of 10 m. The machine has an overall
efficiency of 20%. The work done by the machine in raising the object is
A.
3.0 × 103 J.
B.
1.2 × 104 J.
C.
1.8 × 104 J.
D.
7.5 × 104 J.
An electric train develops a power of 1.0 MW when travelling at a constant speed of 50 ms–1.
The net resistive force acting on the train is
A.
50 MN.
B.
200 kN.
C.
20 kN.
D.
200 N.
A stone of mass m is attached to a string and moves round in a horizontal circle of radius R at
constant speed V. The work done by the pull of the string on the stone in one complete
revolution is
A.
zero.
B.
2πmV2.
C.
2 πmV 2
.
R
D.
2 πmV
.
R
An object of weight 50 N is dragged up an inclined plane at constant speed, through a vertical
height of 12 m. The total work done is 1500 J.
The work done against friction is
A.
2100 J.
B.
1500 J.
C.
900 J.
D.
50 J.
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11.
The variation with time of the vertical speed of a ball falling in air is shown below.
Speed
0
0
T
time
During the time from 0 to T, the ball gains kinetic energy and loses gravitational potential
energy ΔEp. Which of the following statements is true?
12.
A.
ΔEp is equal to the gain in kinetic energy.
B.
ΔEp is greater than the gain in kinetic energy.
C.
ΔEp is equal to the work done against air resistance.
D.
ΔEp is less than the work done against air resistance.
A spring is compressed by a force F.
F
For a compression e, the force F is given by F = ke. When the compression force is removed,
the spring returns to its original length in time t. The best estimate for the power developed by
the spring during its expansion is
A.
ke
.
2t
B.
ke
.
t
C.
ke 2
.
2t
D.
ke3
.
t
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13.
The output power of an electric motor is determined using the arrangement shown below.
motor
wheel
belt
W1
W2
The belt has weights W1 and W2 attached to its ends. The wheel has circumference S. When the
wheel is rotating at R revolutions per second, the belt is stationary.
Which one of the following is a correct expression for the output power of the motor?
A.
W1  SR
B.
W2  SR
C.
(W2 − W1)  SR
D.
(W2 + W1)  SR
(1)
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1.
This question is about the collision between two railway trucks (carts).
(a)
Define linear momentum.
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(1)
In the diagram below, railway truck A is moving along a horizontal track. It collides with a
stationary truck B and on collision, the two join together. Immediately before the collision,
truck A is moving with speed 5.0 ms–1. Immediately after collision, the speed of the trucks is v.
5.0 ms –1
B
A
Immediately before collision
v
A
B
Immediately after collision
The mass of truck A is 800 kg and the mass of truck B is 1200 kg.
(b)
(i)
Calculate the speed v immediately after the collision.
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(3)
(ii)
Calculate the total kinetic energy lost during the collision.
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(2)
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(c)
Suggest what has happened to the lost kinetic energy.
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(2)
(Total 8 marks)
2.
This question is about power output of an outboard motor.
A small boat is powered by an outboard motor of variable power P. The graph below shows the
variation with speed v of P when the boat is carrying different loads.
5.0
4.5
350 kg
4.0
3.5
3.0
300 kg
P / kW 2.5
2.0
1.5
250 kg
1.0
200 kg
0.5
0.0
0.0
0.5
1.0
1.5
2.0 2.5
v / ms–1
3.0 3.5
4.0
The masses shown are the total mass of the boat plus passengers,
(a)
For the boat having a steady speed of 2.0 m s–1 and with a total mass of 350 kg
(i)
use the graph to determine the power of the engine.
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(1)
(ii)
calculate the frictional (resistive) force acting on the boat.
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(2)
Consider the case of the boat moving with a speed of 2.5 m s–1.
(b)
(i)
Use the axes below to construct a graph to show the variation of power P with the
total mass W.
200
250
300
350
400
450
W / kg
(6)
(ii)
Use data from the graph that you have drawn to determine the output power of the
motor for a total mass of 330 kg.
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(1)
(Total 10 marks)
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3.
This question is about estimating 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.
B
30m
A
(a)
40°
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 7.0 × 102 N in moving
from A to B.
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(2)
(ii)
Estimate the energy supplied by the escalator motor to the people every minute
when the escalator is working at full capacity.
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(1)
(iii)
State one assumption that you have made to obtain your answer to (ii).
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(1)
The escalator is driven by an electric motor that has an efficiency of 70%.
(b)
Using your answer to (a) (ii), calculate the minimum input power required by the motor
to drive the escalator.
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(3)
(Total 7 marks)
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4.
This question is about driving a metal bar into the ground.
Large metal bars can be driven into the ground using a heavy falling object.
object
mass = 2.0×103 kg
bar
mass = 400 kg
In the situation shown, the object has a mass 2.0 × 103 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.
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(4)
(b)
Determine the average frictional force exerted by the ground on the bar.
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(3)
(Total 7 marks)
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5.
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.
6.0m s–1
train carriage A
500kg
train carriage B
700kg
The graph below shows the variation with time t of the velocities of the two train carriages
before, during and after the collision.
v / ms–1
6.0
train carriage B
5.0
4.0
3.0
2.0
1.0
0.0
1.0
2.0
3.0
–1.0
4.0
5.0
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;
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(2)
(ii)
the collision is elastic.
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(2)
(b)
Calculate the magnitude of the average force experienced by train carriage B.
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(3)
(Total 7 marks)
6.
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 / ms–1
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0.0
(a)
0.5
1.0
1.5
2.0
2.5
3.0
t/s
State what the area under the graph represents.
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(1)
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(b)
Estimate the maximum height reached by the ball.
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(1)
(c)
Determine, for the ball at t = 1.0 s,
(i)
the acceleration;
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(3)
(ii)
the magnitude of the force of air resistance.
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(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.
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(2)
(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 / ms–1 30
20
10
0.0
0.0
2.0
4.0
t/s
–10
–20
–30
(2)
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(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.
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(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.
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(2)
(Total 15 marks)
7.
Block on an inclined plane
A block is held stationary on a frictionless inclined plane by means of a string as shown below.
string
block
inclined plane
(a)
(i)
On the diagram draw arrows to represent the three forces acting on the block.
(3)
(ii)
The angle  of inclination of the plane is 25. The block has mass 2.6 kg. Calculate
the force in the string. You may assume that g = 9.8 m s–2.
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(2)
(b)
The string is pulled so that the block is now moving at a constant speed of 0.85 m s–1 up
the inclined plane.
(i)
Explain why the magnitude of the force in the string is the same as that found in
(a)(ii).
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(2)
(ii)
Calculate the power required to move the block at this speed.
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(2)
(iii) State the rate of change of the gravitational potential energy of the block. Explain
your answer.
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(2)
(Total 11 marks)
8.
This question is about power.
(a)
Define power.
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(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
P = Fv
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(2)
(c)
Sand falls vertically on to a horizontal conveyor belt at a rate of 60 kg s–1.
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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.
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(2)
(iii) Calculate the power P required to move the conveyor belt at constant speed.
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(1)
(iv)
Determine the rate of change of kinetic energy K of the sand.
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(2)
(v)
Explain why P and K are not equal.
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(2)
(d)
The engine that drives the conveyor belt has an efficiency of 40%. Calculate the input
power to the engine.
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(2)
(Total 13 marks)
9.
This question is about the kinematics of an elevator (lift).
(a)
Explain the difference between the gravitational mass and the inertial mass of an object.
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(3)
An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its
motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s
velocity with time is shown below.
velocity / m s –1
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(b)
The mass of the elevator is 250 kg. Use this information to calculate
(i)
the acceleration of the elevator during the first 0.50 s.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
17
(2)
(ii)
the total distance travelled by the elevator.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iii)
the minimum work required to raise the elevator to the higher floor.
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(2)
(iv) the minimum average power required to raise the elevator to the higher floor.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(v)
the efficiency of the electric motor that lifts the elevator, given that the input power
to the motor is 5.0 kW.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(c)
On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain
your reasoning. (The simplified version is shown as a dotted line)
velocity / m s –1
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(2)
18
The elevator is supported by a cable. The diagram below is a free-body force diagram for when
the elevator is moving upwards during the first 0.50 s.
tension
weight
(d)
In the space below, draw free-body force diagrams for the elevator during the following
time intervals.
(i)
0.5 to 11.50 s
(ii)
11.50 to 12.00 s
(3)
A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on
the scales is W.
(e)
On the axes below, sketch a graph to show how the reading on the scales varies during
the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you
do not need to add any values.)
19
reading on scales
W
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(3)
(f)
The elevator now returns to the ground floor where it comes to rest. Describe and explain
the energy changes that take place during the whole up and down journey.
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.....................................................................................................................................
(4)
(Total 25 marks)
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