Grade 12
Work, Energy, Power and Momentum
PHYSICAL SCIENCE - WORKSHEET
INSTRUCTIONS FOR QUESTION 1
 Answer this question on the ANSWER SHEET provided. Write your NAME on the answer
sheet.
 Four possible answers, indicated by A, B, C and D, are supplied with each question. Each
question has only ONE correct answer. Choose only that answer, which in your opinion, is the
correct or best one and mark the appropriate block on the answer sheet with a cross (X).
 Do not make any other marks on the answer sheet. If more than one block is marked, no
marks will be awarded for that answer.
QUESTION 1
1.1
Consider the pendulum in the sketch. At a certain point A of its swing the ball has a
gravitational potential energy of 300 J with respect to its lowest point at B. At point B
the ball has a kinetic energy of 500 J.
The total mechanical energy of the system is ...
A
800 J
B
500 J
C
300 J
D
200 J
(4)
1.2
1.3
A body, mass m, falls freely from rest from a height h. It reaches a velocity of v after
falling a distance of x. If air resistance is negligible, its total mechanical energy at this
stage is …
A
mg(h – x)
B
½ mv2
C
mgh + ½ mv2
D
mgh
(4)
Two objects, R and P, of equal mass are at rest on top of a wall that has a vertical
height x. R falls straight down and hits the ground with a speed v. P slides down the
frictionless incline, length 2x, as shown in the sketch:
The speed of P at the bottom of the incline (point S) is …
A
½v
B
v
C
D
1.4
2v
2v
(4)
Which of the following graphs of the kinetic energy of an object against time suggests
that the object could not have accelerated uniformly?
(4)
2
1.5
1.6
A body slides down a frictionless, inclined plane of constant gradient. For which one of
the combinations given below, will both physical quantities experience a constant
increase in magnitude?
A
acceleration, velocity
B
momentum, kinetic energy
C
velocity, momentum
D
acceleration, displacement
(4)
A billiard ball B1, moving at 2 m.s-1, collides with two balls B2 and B3 at rest on a
horizontal, frictionless table (refer to the diagram given below). All three balls are
identical.
If both the total momentum and the total kinetic energy of the balls are conserved,
which one of the following sets of values gives the velocity, in m.s-1, of the three balls
after collision?
B1
B2
B3
A
–2
+2
+2
B
0
0
+2
C
0
+1
+1
D
–2
0
+4
(4)
1.7
A body is moved across a frictionless horizontal plane by a constant horizontal force.
Which one of the following physical quantities will NOT increase during the
displacement?
A
Momentum
B
Velocity
C
Acceleration
D
Kinetic energy
(4)
3
1.8
A railway truck moving at constant velocity collides with an identical truck, which is
stationary. The trucks become coupled and carry on moving in the original direction.
Which one of the following combinations will be TRUE for the collision?
Momentum
Kinetic energy
A
conserved
conserved
B
not conserved
conserved
C
not conserved
not conserved
D
conserved
not conserved
(4)
1.9
A body slides down a frictionless inclined plane.
Which one of the following physical quantities will remain constant throughout the
motion?
A
velocity
B
momentum
C
acceleration
D
kinetic energy
(4)
4
1.10
A solid rubber ball dropped from a certain height above a swimming pool, takes 0,3
seconds to reach the surface of the water (stage 1). The ball enters the water and
reaches its maximum depth after 0,2 seconds (stage 2). (Air resistance is negligible.)
Which one of the following statements is TRUE?
1.11
1.12
A
Both the mechanical energy and momentum of the ball are constant during
both stages (0,5 seconds).
B
Both the mechanical energy and momentum of the ball are constant during
stage 1 (first 0,3 seconds).
C
Only the mechanical energy of the ball remains constant during both stages
(0,5 seconds).
D
Only the mechanical energy of the ball remains constant during stage 1 (0,3
seconds), but changes during stage 2 (0,2 seconds).
(4)
A constant resultant force is applied to an object, which is able to move freely. Which
ONE of the following will ALWAYS remain constant while this force is applied?
A
Momentum
B
Acceleration
C
Kinetic energy
D
Gravitational potential energy
(4)
Two objects, moving towards each other, collide head-on and come to rest immediately
after the collision. This is only possible if, before the collision …
A
their masses are equal.
B
their kinetic energies are equal.
C
their speeds are equal.
D
the magnitudes of their momenta are equal.
5
(4)
1.13
1.14
1.15
A projectile is fired vertically upwards from the ground. At the highest point of its motion,
the projectile explodes and separates into two pieces of equal mass. If one of the
pieces is projected vertically upwards after the explosion, the second piece will …
A
drop to the ground at zero initial speed.
B
be projected downwards at the same initial speed as the first piece.
C
be projected upwards at the same initial speed as the first piece.
D
be projected downwards at twice the initial speed as the first piece.
(4)
Which one of the following physical quantities is the same as the rate of change of
momentum?
A
resultant force
B
work
C
power
D
impulse
(4)
Two trolleys, A (mass 2 kg) and B (mass 4 kg) which are attached to one another with
an elastic band, are pulled apart and then held at rest on a horizontal, frictionless
surface. After they are released, they move towards each other, collide and stick
together.
Immediately after the collision the trolleys will …
1.16
A
come to rest.
B
move to the left and then come to rest.
C
move to the left at a constant speed.
D
move to the right at a constant speed.
(4)
A ball with mass m strikes a wall perpendicularly with a speed v. If it rebounds in the
opposite direction with the same speed v, the magnitude of the change in momentum
will be …
A
2 mv
B
mv
C
½ mv
D
0 mv
(4)
6
1.17
A constant resultant force acts on a body moving from rest in a straight line. Which one
of the following graphs best represents the work done on the body as a function of the
displacement of the body?
(4)
[68]
QUESTION 2
Themba is designing a toy roller coaster using 3 m of track and a car of mass 0,5 kg. The
average frictional force between the car and the track is 1,2 N per metre length of the track.
2.1
2.2
Themba releases the car from rest at point A so that it rolls down the track to reach
point C, 0,6 m above the ground, with a speed of 0,8 m.s-1. The length of the track
ABC is 3 m. Calculate the height of the track above the ground at point A.
(9)
Name the law used to solve question 2.1 above.
(1)
[10]
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QUESTION 3
An iron ball, mass 0,6 kg, suspended from an inelastic rope, is released from point A, which is
3,45 m above its lowest position (point C). It strikes a glass plate, GP, which is placed 1 m
vertically above the level of point C. It breaks the glass plate and continues to swing, passing
point C at a velocity of 6,51 m.s-1. Ignore the thickness of the glass and the effect of air friction
when answering the following questions:
3.1
What is gravitational potential energy?
(2)
3.2
Calculate the decrease in gravitational potential energy of the iron ball between point A
and point B. (Point B is the point at which the iron ball makes contact with the glass
plate.)
(5)
Calculate the work done by the iron ball in breaking the glass plate.
(7)
3.3
[14]
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QUESTION 4
A trolley of mass 3 kg collides with a compressed spring device (attached to a wall) while moving
at a speed of 4 m.s-1 (figure 1). At the instant the spring is completely released, the trolley
rebounds with a speed of 6 m.s-1 (figure 2).
4.1
Calculate the change in kinetic energy of the trolley.
(5)
4.2
State whether the kinetic energy of the trolley increased or decreased.
(2)
4.3
Explain what caused the change in the kinetic energy of the trolley.
(2)
After colliding with the spring device, the trolley rolls back to the left (figure 2) and
comes to rest after 10 m.
4.4
Calculate the magnitude of the acceleration of the trolley while coming to rest.
(4)
4.5
Calculate the time taken for the trolley to come to rest.
(4)
4.6
Calculate the frictional force acting on the trolley to come to rest.
(4)
[21]
QUESTION 5
The operation manual of a car, mass 760 kg, claims that the car, starting from rest, can reach a
speed of 54 km.h-1 (15 m.s-1) in first gear in 3 seconds. The acceleration of the car is constant
and friction can be ignored.
If the car operates under these conditions, calculate:
5.1
The power output in first gear
(6)
5.2
The maximum distance covered in 3 seconds
(5)
[11]
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QUESTION 6
An experiment is conducted to calculate the velocity at which a cricketer can throw a ball. A
cricket ball, mass 0,4 kg, is thrown horizontally at a ball of clay suspended by a string (point X).
The ball of clay has a mass of 5 kg.
When the cricket ball hits the clay at X, it sticks (becomes embedded) in the clay. The
combination of the clay and cricket ball rises 0,45 m to point Y. Ignore air friction.
6.1
Explain, in words, the principle of conservation of mechanical energy.
(3)
6.2
Show by calculation that the magnitude of the velocity of the combination at point X is
equal to 3 m.s-1.
(3)
Calculate the magnitude of the velocity with which the cricket ball is thrown.
(6)
6.3
[12]
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QUESTION 7
The track consists of a curved section AB and a horizontal section BC. The track is frictionless.
Body Q, mass 0,9 kg, is stationary on section BC. A second body P, mass 0,6 kg, is placed at
point A, which is 3,2 m vertically above the horizontal section. It is released and slides down
section AB.
7.1
Show that P moves at a velocity of 8 m.s-1 when it reaches body Q.
(3)
P collides with Q. Q then moves towards C at a velocity of 4,4 m.s-1.
7.2
Calculate the velocity of P immediately after the collision.
(7)
7.3
Calculate the average force that Q exerts on P if the two bodies remain in contact for
0,8 seconds.
(5)
[15]
QUESTION 8
A paratrooper in full kit, total mass 120 kg, jumps at a height of 450 m from a stationary
helicopter. The paratrooper’s parachute does not open and he reaches a terminal velocity of 30
m.s-1 before luckily landing on a snow bank. The snow bank gives way, creating a crater of 1,5 m
deep. The paratrooper comes to rest at the bottom of the crater with minor injuries.
8.1
Under what conditions will a falling body reach terminal velocity?
(2)
8.2
Calculate the initial gravitational potential energy of the paratrooper, relative to the
ground.
(4)
8.3
Calculate the paratrooper's kinetic energy just before he lands on the snow.
(3)
8.4
Calculate the total work done by air resistance on the paratrooper while he falls.
(3)
8.5
Calculate the average force exerted by the snow in stopping him.
(5)
[17]
11
QUESTION 9
A sandbag on a trolley moves down a frictionless inclined plane. When it reaches the bottom of
the incline at point B, it continues towards C at a constant speed of 2 m.s-1 in the direction as
indicated in the diagram. The sandbag and trolley have a combined mass of 4 kg. A bullet of
mass 0,15 kg is fired as shown and gets embedded in the sandbag. Immediately after the
collision the trolley-sandbag-bullet combination travels backwards towards B, at 5,3 m.s-1.
9.1
State the principle of the conservation of linear momentum.
(3)
9.2
Calculate the magnitude of the velocity of the bullet just before it hits the sandbag.
(6)
9.3
Show that the kinetic energy of the trolley-sandbag-bullet combination as it moves
backwards along CB towards the slope is 58,3 J.
(4)
The trolley-sandbag-bullet combination now moves up the inclined plane.
9.4
Determine the vertical height of the incline h, if the trolley-sandbag-bullet combination
only just reaches the top of the incline at point A, in other words, it has zero kinetic
energy. Ignore friction.
(4)
[17]
12
QUESTION 10
The Table Mountain cable car has a total mass of 3 000 kg when fully laden. The motor used for
hoisting the cable car to the top of the mountain is labelled as follows:
Voltage:
440 V d.c.
Max. Power output:
10.1
10.2
10.3
88 kW
If the motor operates at maximum power output, calculate the electrical energy used by
the motor in hoisting the cable car to the top of the mountain in 7 minutes.
(5)
Calculate the gain in gravitational potential energy of the car when it moves fully laden
from the lower to the upper station. Compare your answer with the value calculated in
question 10.1 and give a possible explanation for the difference.
(6)
Should the fully laden car's braking mechanism fail while at the upper station, with what
6
speed will the car strike the lower station if during its descent the car loses 6 x 10 J of
mechanical energy in doing work against friction?
(8)
[19]
13
QUESTION 11
An unpowered, empty rail truck with a mass of 10 000 kg rolls with an initial constant velocity of
5 m.s-1 under an elevator where 30 000 kg of maize is dropped into the truck at a constant rate
while the truck is moving. The maize falls freely into the truck. Assume that air friction and the
frictional forces between the wheels of the truck and the rails are negligible.
11.1
Describe the motion of the rail truck from the moment that the empty truck approaches
the elevator until it moves away from it fully loaded. (No explanation is required.)
(2)
11.2
Calculate the magnitude of the velocity of the rail truck after it is fully loaded.
(6)
11.3
Calculate the difference between the kinetic energy of the empty rail truck approaching
the elevator and the kinetic energy of the rail truck (including its load) as it moves away.
(6)
11.4
What happened to the “lost” kinetic energy in 11.3?
(2)
11.5
Explain the origin of the force that led to the change in velocity of the rail truck.
(5)
[21]
14
QUESTION 12
A rubber ball, with a mass of 80 g, is thrown horizontally and collides perpendicularly with a wall
at a velocity of 7 m.s-1. The ball rebounds in the opposite direction at 6 m.s-1.
12.1
12.2
Calculate the magnitude and state the direction, of the change in momentum of the ball
during the collision.
(6)
If the collision lasts for 0,02 s, calculate the magnitude of the force the ball experiences
during the collision.
(4)
[10]
15
QUESTION 13
In a railway shunting yard, a locomotive of mass 4 000 kg, travelling due east with a velocity of
1,5 m.s-1, collides with a stationary goods wagon of mass 3 000 kg in an attempt to couple with
it. The coupling fails and instead the goods wagon moves due east with a velocity of 2,8 m.s-1.
13.1
13.2
Calculate the magnitude and direction of the velocity of the locomotive immediately after
collision.
(6)
Name and state in words the law you used to answer question 13.1.
(4)
[10]
16
QUESTION 14
The sketch below shows three toy cars on a smooth horizontal surface. The green car of mass
5 kg moves to the right at 5 m.s-1, the blue car of mass 2 kg is stationary, while the red car of
mass 10 kg moves to the left at 2 m.s-1. The green and red cars collide simultaneously with the
blue car. After the collision, the red car and the blue car move away together to the right at 3
m.s-1.
BEFORE COLLISION
AFTER COLLISION
14.1
State the law of conservation of momentum.
(3)
14.2
Calculate the total momentum of the system before the collision.
(4)
14.3
Calculate the velocity of the green car after the collision.
(4)
[11]
17
QUESTION 15
A tennis ball with mass 100 g is hit and collides perpendicularly with a wall. The initial velocity of
the ball was 10 m.s-1. The collision is considered to be completely elastic and the ball therefore
rebounds with the same speed.
15.1
State the Principle of Conservation of Momentum.
(3)
15.2
Calculate the magnitude and state the direction of the change in momentum of the ball
during the collision.
(6)
If the collision lasts 0,01 s, calculate the magnitude and direction of the force the ball
experiences during the collision.
(5)
15.3
[14]
[TOTAL: 270]
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