7 Momentum and Impulse
Answers to Questions
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
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Q20
Yes. Impulse is the product of the average force times the time the force acts.
The first force is the larger force because impulse is equal to the product of force and time. If the second
time is twice that of the first, then the first force must be twice that of the second force.
Momentum is mass times velocity, so a fast baseball could possess the same momentum as a slow
bowling ball.
No. Impulse and force are not the same thing. Impulse depends on force, but it also depends on the length
of the time interval the (average) force was applied.
No. Impulse and momentum are not the same thing. Impulse is equal to the change in momentum, either
its magnitude or its direction or both.
a. Yes. Momentum is a vector pointing in the direction of the velocity, so a change in direction implies a
change in momentum.
b. Yes. The force exerted by the wall on the ball first slows the ball down and continues to act on the ball
as it starts to speed up in the opposite direction until it clears the wall. The impulse is the average
force on the ball times the time it acts.
The change in momentum of the baseball depends on the impulse. By following through, the bat can
remain in contact with the ball longer, yielding a larger impulse.
A padded dashboard gives a longer impact time; the change of momentum (impulse) takes longer thus
decreasing the average force of the dash against the rider’s face/body. Average force is decreased
because the force is given a longer time to vary. Force is the change of velocity over time and a longer time
gives a smaller force for the same change of velocity.
The airbag lengthens the amount of time and distance to stop the occupant. This reduces the amount of
force necessary to stop the occupant.
A hard, rapidly expanding airbag is somewhat equivalent to a hard dashboard and does not significantly
lengthen the amount of impact time.
Yes. This will result in a longer impact time and the change of momentum will increase, thus decreasing the
average force of the ball against the hand.
The truck will require the larger impulse to stop it. Impulse is the change of momentum and though both the
bicycle and the truck are going from the same velocity to zero, the truck’s larger mass gives it the greater
momentum change.
Momentum is conserved for any system when the net force acting on the system is equal to zero.
No. Momentum is not conserved since there is a net force on the ball, which is the component of weight
along the incline.
No, but the total momentum of the two-body system remains constant. An object exerts an impulse on a
second object changing the momentum of the second object. The reaction of the second object provides an
impulse on the first object changing its momentum. Overall, since the action and reaction forces are equal
and opposite and the time each force acts is the same for both, the change in momentum of the second will
be equal and opposite to the change in momentum of the first leaving the total momentum of the system
unchanged.
Conservation of momentum for a single body follows from Newton's first law. For a system of interacting
bodies, Newton's third law justifies the fact that there is no net force on the system as a whole, which is the
condition for the total momentum to be conserved.
a. The magnitude of the average force on each vehicle will be the same.
b. Since the force on each vehicle and the time the force acts are the same, each has the same impulse
in magnitude.
c. Both vehicles experience the same magnitude of change of momentum, since each experiences the
same impulse.
d. The compact car will suffer the greater acceleration. The acceleration is force divided by mass. Both
vehicles will be acted upon by the same magnitude of force, but the mass of the compact car is much
less than that of the truck.
It is possible if the lighter defensive’s momentum is greater than the heavier fullback’s.
Zero. Because of the third law, the force on each skater is equal and opposite in direction. The momentum
gained by one skater will be equal and opposite that gained by the other.
If free to move, both shotguns will possess the same momentum upon recoiling. The lighter one will recoil
faster. The impulse delivered to the shooter's shoulder will be the same for both.
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Q21
Q22
Q23
Q24
Q25
Q26
Q27
Q28
Q29
Q30
Q31
Q32
Q33
Q34
Q35
Yes. The total momentum of the boat + gun before firing is zero. After firing the shell, the forward
momentum of the shell plus the backward momentum of the boat (with gun) must still be zero; hence, the
recoil of the boat. Since the boat can be very massive compared to the shell, the recoil speed of the boat
may be quite small.
The rocket moves forward because the exhaust material ejected backwards relative to the motion of the
rocket exerts a reaction force on the rocket.
Throw the bag of oranges away thus propelling me in the opposite direction. This would be equivalent to
“pushing off’’ against the bag of oranges. One might also toss away the oranges singly for a more
controlled mode of travel.
She should remove a wrench from her tool belt and throw it in the opposite direction to the location of the
space shuttle. By conservation of momentum, she will then gain an equal amount of recoil momentum in
the direction of the shuttle.
a. At fan: to the right. At sail: to the left.
b. On fan: to the left. On sail: to the right.
c. If he doesn't furl the sail, he won't go anywhere. The fan blowing air against the sail is an example of
internal force. Internal forces do not impart acceleration to a body. With the sail furled he can move
opposite the way the fan is blowing. The fan will then be blowing against an external body (the
atmosphere).
The skateboard will slow down. By adding the mass of the skateboarder to that of the skateboard, the total
mass of the system will increase. By conservation of momentum, if the mass increases, the velocity must
decrease in order for the momentum mv to remain constant.
Momentum is conserved, therefore momentum after the collision must equal momentum before the
collision (due to the lack of external forces in this problem). Because the mass of the moving system is
increased by the addition of the second car, the velocity will decrease.
The coupling of the two cars after collision satisfies the conditions for a perfectly inelastic collision.
No. Momentum is conserved in all collisions, elastic or inelastic, as long as there is no net external force.
No. There is a loss of kinetic energy in the collision, so it is inelastic.
a. No. The direction of the ball’s momentum vector was changed by an external force (the wall).
b. Define the system as the ball, the wall anchored to Earth; then yes, momentum of the system is
conserved.
Yes. The collision is elastic. There has been no change in the kinetic energy of the system.
The resultant momentum will point in the direction of the larger momentum, p1, and will have a magnitude
(p1 - p2).
No. In this problem the final momentum will be in a direction making a 45o degree angle with respect to
each of the initial momentum vectors.
If the velocities had been equal, the direction of motion after the perfectly inelastic collision would have
been at a 45o angle with respect to the direction of A. Since the angle is smaller, A must have had a larger
momentum and thus was traveling faster.
Q36
The momentum of the truck is twice that of the car, so the final direction of the coupled vehicles is closer to
the original direction of the truck than that of the car.
Q37
before
after
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Answers to Exercises
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
E13
E14
E15
E16
a. 12.0 Ns
b. 12.0 kg m/s
P = 32.4x103 Ns
The bowling ball has the larger momentum.
a. 9 Ns
b. 9 kg m/s
4.8 Ns
a. 24 Ns
b. 160 N
a. 1080 Ns
b. 2700 N
a. 5.0 Ns
b. 5.0 Ns
a. -7.5 kg m/s
b. -7.5 Ns
a. Pfb = 350 kg m/s; Pdb = -480 kg m/s
b. 130 kg m/s (east)
c. In the initial direction of the defensive back, east.
a. Zero
b. -7.5 m/s
a. 3.1 kg m/s
b. 2.58 m/s
2.0 x 104 kg m/s in the forward direction.
a. 1.44 x 105 kg m/s
b. 4.8 m/s
a. 2.25 x 106 J
b. .45 x 106 J
c. Kinetic energy is not conserved; some is lost to
frictional energy during coupling.
a. Pt = 4.0 x 104 kg m/s north; Pc = 2.4 x 104 kg m/s south.
b. 1.6 x 104 kg m/s, north
E17
a.
Ptruck
Pcar
Scale: 0.5 cm = 104 kg m/s
b.
Pnet
Scale: 0.5 cm = 104 kg m/s
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E18
a.
Scale: 1 cm = 104 kg m/s
b. 5.0 x 104 kg m/s
Answers to Synthesis Problems
SP1
SP2
a.
b.
c.
d.
a.
b.
c.
SP3
a.
b.
c.
SP4
a.
b.
c.
SP5
a.
b.
c.
d.
e.
12 kg m/s
Yes. Momentum changed direction.
12 Ns
300 N
2.07 m/s
2.49 kg m/s
Essentially, yes. The mass of the block is large compared to the mass of the bullet so the block carries
most of the final momentum.
Case B
Case B
For the ball alone, momentum is not conserved because direction changes. For the system of ball plus
wall attached to the earth, momentum is conserved in both cases.
-1620 kg m/s
Impulse = 1620 kg m/s
Wearing a seatbelt distributes the stopping force along the portions on the body restrained by the belt,
usually muscular areas of the body. Hitting the dashboard places all the force at the small contact
point where the head hits the windshield. The time of action will be slightly longer in the seatbelt
scenario because of the action of the seatbelt stop action and the possible stretching of the belt.
30,000 kg m/s, South
5 m/s South
9.75 x 105 J
75 x 103 J
No. The collision is inelastic; the vehicles stuck together and kinetic energy was not conserved.
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