Reflect:
is always the force applied to one end of the spring, thus we did not need to double the 15.0 N force.
Consider a freebody diagram of a spring at rest; forces of equal magnitude and opposite direction are always applied
to both ends of every section of the spring examined.
7.28.
Set Up:
Use
and
for parts (a) and (b).
Solve: (a)
The corresponding work on the spring is:
(b)
Now
resulting in
To stretch the spring from
to
requires
of additional work.
Reflect:
Doubling
x
, doubles
Also, since the total work to stretch the spring from 0.0 m to 2.0 m is
the total work increases by a factor of four.
7.29.
Set Up:
The work done is the area under the graph of
versus
x
between the initial and final positions.
Solve: (a)
The area between
and
is a right triangle. The work is thus calculated as:
(b)
Since the area between
and
is a trapezoid, the work is calculated as:
Reflect:
The force is larger for
than for 5.0 cm and the work done in (b) is greater than that done in (a),
even though the displacement of the end of the spring is 5.0 cm in each case.
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 Spring '07
 Shoberg
 Energy, Force, Potential Energy, Work, Ugrav, Fon spring

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