Name: _____________________ Date: ___________________ SPH4U Momentum Unit Test
KU:
/12
TI:
𝑝𝑖→ = 𝑝𝑓→
∑𝐹 → ∆𝑡 = ∆𝑝→
Section 1: Multiple Choice
/18
C:
𝑝𝑥 𝑖 = 𝑝𝑥 𝑓
1
𝐸𝑘 = 𝑚𝑣 2
2
/12
Total:
/42
𝑝𝑦𝑖 = 𝑝𝑦𝑓
𝐸𝑔 = 𝑚𝑔ℎ
/ 6 KU (1 mark each)
1. In an inelastic collision,
a) kinetic energy and momentum are both conserved
b) initial kinetic energy does not equal the final kinetic energy after the collision
c) momentum is not conserved
d) none of these
2. The law of the conservation of momentum states that
(a) the momentum of a closed system remains constant
(b) the momentum of objects before a collision is equal to the momentum after a collision
(c) if there is no net force in a system of interacting objects, then the linear momentum of
the system before the interaction equals the linear momentum of the system after the
interaction
(d) if there is no net force in a system of interacting objects, then the linear momentum of
the objects prior to the collision remains constant throughout the entire experiment
3. A rubber bullet R and a metal bullet M of equal mass strike a test Target T with the
same speed. The metal bullet penetrates the target and comes to rest inside it, while the
rubber bullet bounces off the target. Which statement is true?
(a) M and R exert the same impulse on T
(b) M exerts a greater impulse on T than R does
(c) R exerts a greater impulse on T than M does
(d) The magnitudes of the change in momentum of M and R are equal
(e) none of these
4. An elastic super ball of mass 3-kg is thrown towards a wall with a velocity of 10 m/s [E].
During the collision when the wall feels the greatest force from the ball, the momentum of
the ball is
a) 30 N∙s [E]
b) 30 N∙s [W]
c) 0 N∙s (direction unspecified until after collision)
d) 60 N∙s [W]
5. The magnitude of the impulse imparted
during the interaction represented in the
figure to the right is (choose the best
answer)
a) 4.0 N∙s
b) 15 N∙s
c) 8.5 N∙s
d) 18 N∙s
6. The average force acting on the objecting
during the collision represented in the
force-time graph to the right is (choose the
best answer)
a) 4.0 N
b) 15 N
c) 8.5 N
d) 18 N
Section 2: Short problems
7. A man of mass 75-kg is standing on a stationary raft of mass 55-kg. The man then walks
toward one end of the raft at a velocity of 2.3 m/s [E] relative to the water. Fluid friction is
negligible. Determine the resulting velocity of the raft relative to the water.
/ 2 KU
8. An automobile of mass 1500-kg collides with a wall. The initial and final velocities of
the automobile are 15.0 m/s [W] and 2.6 m/s [E], respectively. The collision lasts for
0.150 s.
a) Determine the impulse due to the collision.
/ 2 KU
b) Determine average force exerted on the automobile.
/ 2 KU
Section 3: Communication
9. Describe the three types of collisions that can occur between objects and the
conservation laws that apply to each collision.
/6C
10. From bird’s eye view, four objects of equal mass and of equal speed are travelling 90
degrees apart from one another. All four objects collide completely inelastically at the
same time and become one unit. Define your own notation and communicate how you
arrived to each answer. You do not need to know the mass or the speed. Write the general
equations.
a) Provide a drawing of the scenario before collision.
/1C
b) In considering the momentum of each object, what is the magnitude of the total
momentum before the collision?
/1C
c) What is the magnitude of the total momentum after the collision?
/1C
d) If the magnitude of the momentum before the collision differs from the magnitude of
the momentum after collision, according to your work in b) and c), explain if this is a
violation of the conservation of momentum.
/3C
Section 4: Thinking and Inquiry
11. A 2.0-kg ball is attached to a 10-m piece of string. The ball
is first raised so that the string is taut and horizontal, then the
ball is released so that, at the bottom of its swing, it undergoes
an elastic head-on collision with a 1.0-kg stationary ball on a
frictionless horizontal surface. Use g = 9.8 m/s 2.
a) Determine the speed of the ball when it reaches the bottom just before impacting the
stationary ball.
/ 1 TI
b) Determine the momentum of each ball after the collision. Rule out the answers that are
physically and intuitively illogical. If needed, the quadratic equation is =
−𝑏±√𝑏 2 −4𝑎𝑐
2𝑎
.
/ 5 TI
12. A 38-kg child is standing on a 43-kg raft that is drifting with a velocity of 1.1 m/s [N]
relative to the water. Fluid friction between the raft and water is negligible.
a) Determine the initial momentum of the system.
/ 1 TI
b) The child then walks on the raft with a net velocity of 0.71 m/s [E] relative to the water.
Determine the momentum of the child.
/1 TI
c) Write the conservation of momentum equation.
/ 1 TI
d) Determine the magnitude of the raft’s momentum.
/ 1 TI
e) Determine the velocity of the raft relative to the water.
/ 2 TI
13. An explosive is used to break apart a spherical body. A snapshot of the experiment
shows the fragmentation of the spherical body into three pieces immediately after the
explosion. The top piece gains a momentum of 200 N∙s [N] and a velocity of 50 m/s [N].
The bottom left mass (8-kg) is ejected 20o [S of W] and the bottom right mass (6-kg) is
ejected at 45o [S of E]. Neglect the mass and size of the explosive.
Before explosion
After explosion
y
y
x
a) Determine the total mass of the system.
x
/ 1 TI
b) Determine the momentum of the bottom left and bottom right pieces after the
explosion. In writing the x and y components of the conservation of momentum equation,
write the momentum of each object just like we wrote forces as either positive or
negative. For example, the momentum of an object heading 60o [N of W] would have a
positive vertical component of 𝑚𝑣𝑠𝑖𝑛60 and a horizontal component of −𝑚𝑣𝑐𝑜𝑠60.
/ 5 TI