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88. (a) We take the gravitational potential energy of the skierEarth system to be zero
when the skier is at the bottom of the peaks. The initial potential energy is
U
i
=
mgH
,
where
m
is the mass of the skier, and
H
is the height of the higher peak. The final
potential energy is
U
f
=
mgh
, where
h
is the height of the lower peak. The skier initially
has a kinetic energy of
K
i
= 0, and the final kinetic energy is
Km
v
f
=
1
2
2
, where
v
is the
speed of the skier at the top of the lower peak. The normal force of the slope on the skier
does no work and friction is negligible, so mechanical energy is conserved:
2
1
2
ii
f
f
UKU
K
m
g
Hm
g
h
m
v
+=
+
¡
=+
Thus,
2
2 (
)
2(9.8m/s )(850 m 750 m)
44 m/s
vg
H
h
=−
=
−=
.
(b) We recall from analyzing objects sliding down inclined planes that the normal force
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 Spring '08
 Any
 Physics, Energy, Mass, Potential Energy

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