27. We convert to SI units and choose upward as the +
y
direction. Also, the relaxed
position of the top end of the spring is the origin, so the initial compression of the spring
(defining an equilibrium situation between the spring force and the force of gravity) is
y
0
= –0.100 m and the additional compression brings it to the position
y
1
= –0.400 m.
(a) When the stone is in the equilibrium (
a
= 0) position, Newton's second law becomes
net
spring
G
Fm
a
g
k
=
−=
−−
−
=
0
0100
8 00 9 8
0
(. )(
.)
(
.
)
where Hooke's law (Eq. 721) has been used. This leads to a spring constant equal to
k
=
784 N/m.
(b) With the additional compression (and release) the acceleration is no longer zero, and
the stone will start moving upwards, turning some of its elastic potential energy (stored in
the spring) into kinetic energy. The amount of elastic potential energy at the moment of
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Force

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