Solution for Homework 17 Motion in a Plane I, Work problems
Solution to Homework Problem 17.1()
Problem:
Can potential energy be associated between two elements if both are not within a system? Why or why not?
Solution
No. Potential energy always refers to the relative position of various parts of a system (between which there exists a
conservative
force), never to the position of various parts of a system relative to the environment.
Total Points for Problem: 2 Points
Solution to Homework Problem 17.2()
Problem:
An object moves in two dimensions. The object’s acceleration vector is perpendicular to its velocity vector
at all times. How is the object’s velocity affected, both in magnitude and direction? Explain.
Solution
The object’s speed is unchanged. Only the direction of the velocity vector changes. The component of acceleration that
is parallel to velocity changes speed, while the component perpendicular to the velocity vector changes its direction.
Since in this case acceleration is purely perpendicular to velocity, speed is unaffected. As we will learn later, this
situation produces uniform circular motion.
Total Points for Problem: 2 Points
Solution to Homework Problem 17.3()
Problem:
Starting from rest, a car pulls a trailer along a road that climbs from sea
level over a mountain and then back to sea level, where it continues to travel at a
constant speed. Car and trailer have identical inertias. In the process of climbing, the
car’s engine heats up substantially; you may neglect the heating of the surrounding
air. Using diagrams like the template in the figure, for each choice of system below
draw workenergy diagrams for the initial and final states described in the problem.
Make sure that the lengths of the bars in the diagrams for the different choices of
system are consistent with one another. Briefly explain your diagram, and, if work is
done on the system, indicate which forces do work and confirm the sign of the work.
(a)System: car, trailer, and earth.
(b)System: trailer only.
(c)System: car only.
Δ
E
source
Δ
K
Δ
U
Δ
E
diss
W
Solution to Part (a)
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Source energy (fuel) is converted to kinetic energy and dissipated en
ergy.
Δ
E
source
+ Δ
K
+ Δ
E
diss
= 0
Δ
E
source
Δ
K
Δ
U
Δ
E
diss
W
Grading Key: Part (a) 2 Points
Solution to Part (b)
The change in the kinetic energy of the trailer is half that of the car
and trailer in part (a), since they have the same mass. In the system
with only the trailer, this increase is due to work done by an external
agent, the car. Since force and displacement are parallel,
W >
0
.
Δ
E
source
Δ
K
Δ
U
Δ
E
diss
W
Grading Key: Part (b) 2 Points
Solution to Part (c)
Δ
E
source
and
Δ
E
diss
are the same as in part (a), but the kinetic
energy of the car is only half that of the car and trailer. In this system
the trailer does negative work on the car, since the force is opposite the
direction of displacement. The work has the same
magnitude
as that
in part b), since the force of the trailer on the car is exactly the same
size as the force of the car on the trailer, in other words
vector
F
c
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 Spring '08
 Stewart
 Physics, Energy, Force, Kinetic Energy, Mass, Potential Energy, Work

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