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and
(b)
Reflect:
Its translational kinetic energy at the base of the hill is
Its total kinetic energy is
20.9 J. This equals its final potential energy:
9.50. Set Up:
The marble is a solid sphere and has
Since the marble rolls without slipping,
The block of ice has only translational kinetic energy. At the bottom of the hill, the marble has speed
and
the block has speed
Use coordinates where
is upward and
at the bottom of the hill. Then
and
for each object.
Solve: (a)
Conservation of energy gives
so
marble:
so
and
block of ice:
and
(b)
The ice is moving faster at the bottom.
(c)
For each object,
They have the same kinetic energy at the bottom.
9.51. Set Up:
The solid cylinder has
and the solid sphere has
for each. Use
coordinates where
is upward and
at the bottom of the hill. Then
and
for each object. Let the
maximum heights
h
be
and
Solve: (a)
Conservation of energy gives
so
cylinder:
and
sphere:
and
(b)
The cylinder has a larger
and hence more initial kinetic energy.
(c)
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 Spring '07
 Shoberg
 Energy, Kinetic Energy

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