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Potential energy of a conservative force (Section 8.1)
1. Mass–spring system
• Context in the textbook: Before Example 1 in Section 8.1.
2. Conservative force: Path integrals
• Context in the textbook: Section 2.1 considers conservative force in one
dimension. This example verifies the pathindependent property of a
conservative force in two dimensions. It may be used at the end of Section
8.1.
Potential energy due to gravity plus spring force (Section 8.2)
The following exercises may be used before Example 4 in Section 8.2:
3. Spring toy: Maximum height
4. Spring toy: Special points of
U
5. Releasing a compressed spring
6. Spring–pulley system with friction
Power (Section 8.5)
Two exercises before Example 9 of Section 8.5:
7. Climbing up a hill
8. Maximum speed on a flat road
Contents
PhysiQuiz
67
chapter
8
Conservation of Energy
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View Full Document Consider a mass–spring system. The spring force asserted on the block is
given by Hooke’s Law:
F
spring
52
k
D
x
. Denote the potential energy of the
spring by
U
(
x
). At
x
5
0 the spring is relaxed:
U
(0)
5
0.
U
(
x
) is the work
done by the stretching force in going from
x
5
O to
x
5
x
9
, which is given
by which of the following?
AB
C
D
2
kx
2
kx
2
E
x
9
0
kxdx
2
E
x
0
kxdx
Extra:
Release the mass from rest at
x
5
x
9
. Determine the kinetic energy at
x
5
0 in terms of
x
9
,
k
,
m
.
Hint:
Not all the quantities here need to be used.
Explanation:
When the spring is pulled to the right, both the pulling force
and the displacement are in the same direction. The pulling force is opposite
to the spring force. The latter obeys Hooke’s Law:
F
pull
F
spring
5
k
D
x
. So
work done in stretching the spring from
x
5
O to
x
5
x
9
is given by
Answer C.
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This note was uploaded on 09/10/2009 for the course PHY 76875 taught by Professor Turner during the Summer '09 term at University of Texas at Austin.
 Summer '09
 Turner
 Conservation Of Energy, Energy, Force, Mass, Potential Energy

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