Chapter 8
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Chapter 8
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Chapter 8
Due: 11:59pm on Sunday, March 10, 2019
To understand how points are awarded, read the Grading Policy for this assignment.
A Bullet Is Fired into a Wooden Block
Description: Conceptual: A bullet embeds in a stationary, frictionless block: type of collision? what is conserved? v_final?
A bullet of mass mb is fired horizontally with speed vi at a wooden block of mass mw resting on a frictionless table. The bullet
hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with
the bullet in it, is traveling at speed vf .
Part A
Which of the following best describes this collision?
Hint 1. Types of collisions
An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic
energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely
inelastic and elastic collisions are.
ANSWER:
perfectly elastic
partially inelastic
perfectly inelastic
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Part B
Which of the following quantities, if any, are conserved during this collision?
Hint 1. When is kinetic energy conserved?
Kinetic energy is conserved only in perfectly elastic collisions.
ANSWER:
kinetic energy only
momentum only
kinetic energy and momentum
neither momentum nor kinetic energy
Part C
What is the speed of the block/bullet system after the collision?
Express your answer in terms of vi , mw , and mb .
Hint 1. Find the momentum after the collision
What is the total momentum ptotal of the block/bullet system after the collision?
Express your answer in terms of vf and other given quantities.
ANSWER:
ptotal
=
Hint 2. Use conservation of momentum
The momentum of the block/bullet system is conserved. Therefore, the momentum before the collision is the same
as the momentum after the collision. Find a second expression for ptotal, this time expressed as the total
momentum of the system before the collision.
Express your answer in terms of vi and other given quantities.
ANSWER:
p
total
=
ANSWER:
vf
=
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¡À Catching a Ball on Ice
Description: ¡À Includes Math Remediation. Find the final momentum of a person who catches a ball on a frictionless
surface. Find the final momentum of a person on a frictionless surface off of whom a ball bounces.
Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction
between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 10.5 m/s . Olaf's
mass is 68.6 kg .
Part A
If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward?
Express your answer numerically in meters per second.
Hint 1. How to approach the problem
Using conservation of momentum and the fact that Olaf's initial momentum is zero, set the initial momentum of the
ball equal to the final momentum of Olaf and the ball, then solve for the final velocity.
Hint 2. Find the ball's initial momentum
What is pi , the initial momentum of the ball?
Express your answer numerically in kilogram meters per second.
ANSWER:
p
i
=
= 4.20
kg?m
s
ANSWER:
vf
=
= 6.09¡Á10?2
m/s
Part B
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If the ball hits Olaf and bounces off his chest horizontally at 7.70 m/s in the opposite direction, what is his speed vf after
the collision?
Express your answer numerically in meters per second.
Hint 1. How to approach the problem
The initial momentum of the ball is the same as in Part A. Apply conservation of momentum, keeping in mind that
both Olaf and the ball have a nonzero final momentum.
Hint 2. Find the ball's final momentum
?
Taking the direction in which the ball was initially traveling to be positive, what is p ball,f
, the ball's final momentum?
Express your answer numerically in kilogram meters per second.
ANSWER:
?
p ball,f
=
= -3.08
kg?m
s
ANSWER:
vf
=
= 0.106
m/s
Collision at an Angle
Description: Straightforward application of momentum conservation in an inelastic collision.
Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at speed 2v, while
the second was traveling at speed v at an angle ? south of east (as indicated in the figure). After the collision, the two-car
system travels at speed vf inal at an angle ¦È east of north.
Part A
Find the speed vf inal of the joined cars after the collision.
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Express your answer in terms of v and ? .
Hint 1. Determine the conserved quantities
Which of the following statements is true for the collision described?
ANSWER:
Momentum is conserved but kinetic energy is not conserved.
Kinetic energy is conserved but momentum is not conserved.
Both kinetic energy and momentum are conserved.
Neither kinetic energy nor momentum is conserved.
Apply conservation of momentum:
.
f inal
?
Find both components (north and east) of the initial momentum p initial
using the information in the problem
?
introduction. The magnitude of p initial
is equal to the magnitude of the momentum vector for the two-car
system after the collision: pf inal = (2m)vf inal .
p?
initial
= p?
Hint 2. The component of the final velocity in the east-west direction
Find the component of vf? inal in the east-west direction.
Express your answer in terms of v and ? .
Hint 1. Find the east-west component of the initial momentum
What is pe , the magnitude of the total momentum p e? of the two cars in the east-west direction? (Take
eastward to be positive, westward negative.)
Express your answer in terms of m, v, and ? .
ANSWER:
p
e
=
Now use the conservation of momentum equation to find vf inal .
ANSWER:
vf inal
(east-west) =
Hint 3. Find the north-south component of the final momentum
Find the component of vf inal in the north-south direction.
Express your answer in terms of v and ? .
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