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11. (a) If
K
i
is the kinetic energy of the flake at the edge of the bowl,
K
f
is its kinetic
energy at the bottom,
U
i
is the gravitational potential energy of the flake-Earth system
with the flake at the top, and
U
f
is the gravitational potential energy with it at the bottom,
then
K
f
+
U
f
=
K
i
+
U
i
.
Taking the potential energy to be zero at the bottom of the bowl, then the potential energy
at the top is
U
i
=
mgr
where
r
= 0.220 m is the radius of the bowl and
m
is the mass of the
flake.
K
i
= 0 since the flake starts from rest. Since the problem asks for the speed at the

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