p08_028.pdf

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Chapter 8 - 8.28
28. We place the reference position for evaluating gravitational potential energy at the relaxed position of
the spring. We use x for the spring’s compression, measured positively downwards (so x> 0 means it is
compressed).
7 . 22 J for the work done by the spring force.
Using Newton’s third law, we conclude the work done on the spring is 7 . 22 J.
(b) As noted above, W s =
−
2 kx 2 =
−
7 . 22 J.
(c) Energy conservation leads to
K i + U i = K f + U f
mgh 0 =
−
mgx + 1
2 kx 2
which (with m =0 . 700 kg) yields h 0 =0 . 862 m.
(d) With a new value for the height h 0 =2 h 0 =1 . 72 m, we solve for a new value of x using the
quadratic formula (taking its positive root so that x> 0).
mgh 0 =
−
mgx + 1
2 kx 2
=
⇒
x = mg + ( mg ) 2 +2 mgkh 0
k
which yields x =0 . 261m.
1
(a) With x =0 . 190 m, Eq. 7-26 gives W s =
−
 

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