p08_017.pdf

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Chapter 8 - 8.17
17. We take the reference point for gravitational potential energy at the position of the marble when the
spring is compressed.
(a) The gravitational potential energy when the marble is at the top of its motion is U g = mgh ,where
h = 20m is the height of the highest point. Thus,
U g = 5 . 0
×
10 − 3 kg 9 . 8m / s 2 (20m) = 0 . 98 J .
0 . 98 J.
(c) We take the spring potential energy to be zero when the spring is relaxed. Then, our result in the
previous part implies that its initial potential energy is U s =0 . 98 J. This must be 2 kx 2 ,where k
is the spring constant and x is the initial compression. Consequently,
∆ U g =
−
k = 2 U s
x 2
=
2(0 . 98 J)
(0 . 080 m) 2 =3 . 1
×
10 2 N / m=3 . 1N / cm .
(b) Since the kinetic energy is zero at the release point and at the highest point, then conservation of
mechanical energy implies ∆ U g +∆ U s =0,where∆ U s is the change in the spring’s elastic potential
energy. Therefore, ∆ U s =
−
 

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