SPH4U - Practice Test Unit 4: Work, Energy, and Collisions
True/False
____
1. Work is done when the force and the displacement are in the same direction.
____
2. The maximum work a force can do on an object occurs when the force is parallel to the direction of motion.
____
3. Kinetic energy is a vector quantity.
____
4. To raise a 2.3-kg mass from its resting place on a table, more work is done by lifting it diagonally than lifting
it straight up.
____
5. The impulse is always in the same direction as the net force.
____
6. When you triple the velocity of an object of constant mass, you also triple the momentum.
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
7. A net force of 12 N changes the momentum of a 250-g ball by 3.7 kgm/s. The force acts for
a. 0.31 s
d. 3.2 s
b. 0.81 s
e. 44 s
c. 1.2 s
____
8. A 1.5-kg bird is flying at a velocity of 18 m/s [22º above the horizontal]. The vertical component of its
momentum is
a. 10 m/s [up] (2 significant digits)
d. 17 m/s [up]
b. 6.7 kgm/s [up]
e. none of the above
c. 25 kgm/s [up]
____
9. Two objects of equal mass with the speeds indicated by the vectors below, collide and stick together.
Which vector below best represents the velocity of the combined objects after the collision?
a. A
b. B
c. C
d. D
e. E
____ 10. When you catch a fast-moving baseball, your hand hurts less if you move it in the direction of the ball
because
a. the ball changes momentum more slowly
b. the force applied is smaller
c. you decrease the impulse required to stop the ball
d. two of A, B, and C
e. all of A, B, and C
____ 11. To maximize the gravitational potential energy of an object, you should
a. raise it as quickly as possible
d. get it as high as possible
b. maximize the total distance travelled
e. lower it in the vertical direction
c. avoid acceleration during lifting
____ 12. Rubbing your hands together can quickly produce 45 J of thermal energy. If it is done with an average
frictional force of 8.4 N, the distance your hands have slid past each other is
a. 49 m
d. 3.7 m
b. 5.4 m
e. 1.2 m
c. 4.5 m
____ 13. A rocket triples its height but looses half its mass in fuel. The gravitational potential energy of the rocket has
changed by a factor of
a. 0.33
d. 1.5
b. 0.5
e. 3
c. 1
____ 14. Which of the following is not a unit of energy?
a. J
d. Ws
b.
e.
c. Nm
____ 15. A student in a lab exerts a 25 N force to pull a block a distance of 48 cm. If a total of 11 J of work is done, the
angle between the force and the displacement is
a. 89
d. 24
b. 66
e. none of the above
c. 61
____ 16. A person picks a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The
work done on the macaroni by the person is
a. 0 J
d. 7.5 J
b. 0.77 J
e. –7.5 J
c. –0.77 J
____ 17. Which of the following is NOT a unit of energy?
a. J
d. Nm
b. W/s
e. kWh
c. kgm2/s2
____ 18. When an object doubles its speed, the kinetic energy increases by a factor of
a. 1
d. 6
b. 2
e. 8
c. 4
____ 19. The gravitational potential energy of a 3.4-g grasshopper 14 mm above the ground is
a. 4.7  102 J
d. 4.7  10–2 J
b. 4.7 J
e. 4.7  10–4 J
c. 0.47 J
____ 20. You raise a 1.00-kg object 1.00 m and then lower it 1.00 m. The total work done on the object by gravity is
a. 0 J
d. 19.6 J
b. 9.8 J
e. –19.6 J
c. –9.8 J
____ 21. A cyclist reaches the bottom of a hill with a speed of 18 m/s. Neglecting air resistance and other friction, to
what maximum height can they coast up the hill without pedalling?
a. 17 m
d. 20 m
b. 18 m
e. 21 m
c. 19 m
____ 22. A bullet with a momentum of 2.8 kgm/s [E] is travelling at a speed of 187 m/s. The mass of the bullet is
a. 0.015 g
d. 67 g
b. 0.067 g
e. not enough information
c. 15 g
____ 23. A 2200 kg car starts from rest and speeds up to 12 m/s in 5.2 s. The net force acting on the car is
a. 1.8  102 N
d. 5.1  103 N
b. 4.2  102 N
e. 1.4  105 N
4
c. 1.1  10 N
24. How much work is done to speed up a 2200-kg car from 12 m/s to 24 m/s?
25. A cannon ball is fired with a speed of 88 m/s from the top of a cliff. It strikes the plain below with a speed of
91 m/s. If we neglect air friction, how high is the cliff?
26. A 0.25-kg snowball moving at 15 m/s [E] collides and sticks with a 1.9-kg toy truck travelling at 2.8 m/s [W].
Neglecting friction, calculate the velocity of the snowball–truck system after the collision.
27. A 23-kg block slides 18 m on level ground before coming to rest. If 430 J of work are done by friction,
calculate the coefficient of friction between the block and the ground.
28. Compare yourself sprinting at 7.0 m/s with a 63-g bullet travelling at 150 m/s.
(a) Which has a larger momentum?
(b) Which has more energy?
(c) Which is more dangerous? Why?
29. During a free dance program in figure skating, Victor (m = 71 kg) glides at 2.1 m/s to a stationary Shae-Lynn
(52 kg) and hangs on. How far will the pair slide after the “collision” if coefficient of kinetic friction K
between their skates and the ice is 0.052?
30. During a game of billiards, the 0.30-kg cue ball, travelling at 2.1 m/s, glances off a stationary 0.28-kg billiard
ball so that the billiard ball moves off at 1.4 m/s at an angle of 38º from the cue ball’s original path. Find the
new speed of the cue ball.
31. A 38-g bullet is fired with a speed of 180 m/s into a 5.0-kg sandbag pendulum that is free to swing. To what
maximum vertical height will the pendulum rise?
SPH4U - Practice Test Unit 2: Work, Energy, and Collisions
Answer Section
TRUE/FALSE
1.
2.
3.
4.
5.
6.
T
T
F, scalar
F, the same amount of work is done
T
T
MULTIPLE CHOICE
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
E
D
D
D
B
D
E
D
E
B
C
E
A
A
C
D
SHORT ANSWER
24. ANS:
The work done to speed up the car is 4.8  105 J.
25. ANS:
The cliff is 27 m high.
26. ANS:
Choose east as the +x direction.
The final velocity is 0.73 m/s [W].
27. ANS:
The coefficient of friction is 0.11.
28. ANS:
Values of mass will vary with each student. Using an example value of 75 kg.
(a)
p of student is 7.0  75 = 5.2  102 kgm/s
p of bullet is 0.063  150 = 9.4 kgm/s
The student has a much larger momentum.
(b)
The student also has a larger kinetic energy.
(c)
The bullet is more dangerous because all of the energy is concentrated on a small part of a target (i.e., a tree, a
target, or a person). The work done to stop it is only supplied by a small area, and it passes through many
parts before enough work can be done to stop it. The person has the work supplied by a larger surface area
and is not as dangerous.
29. ANS:
Before the collision:
After the collision:
Now using the kinematics equations:
The pair coast a total of 1.4 m after the collision.
30. ANS:
The initial momentum of the cue ball, pc, is 0.30  2.1 = 0.63 kgm/s.
The final momentum of the billiard ball, pb, is 0.28  1.4 = 0.392 kgm/s.
The final momentum of the cue ball, p'c, is 0.30  v'c = 0.30v'c kgm/s.
Choose the +x direction to be the original direction of the cue ball.
 is the angle between the original direction of the cue ball and its new direction.
Now divide Equation 1 by Equation 2:
Substitute this value into Equation 1:
The new speed of the cue ball is 1.3 m/s.
31. ANS:
First use conservation of momentum for the collision:
Now use conservation of energy for the pendulum swing:
The sandbag will rise 9.4 cm vertically.