86. We apply the work-energy theorem to the object in question. It starts from a point at
the surface of the Earth with zero initial speed and arrives at the center of the Earth with
final speed
v
f
. The corresponding increase in its kinetic energy, ½
mv
f
2
, is equal to the
work done on it by Earth’s gravity:
(
)
Fdr
Kr dr
=−
³³
(using the notation of that Sample
Problem referred to in the problem statement). Thus,
00
22
11
()
f
RR
mv
F dr
Kr dr
KR

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