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3. (a) The force of gravity is constant, so the work it does is given by
W Fd
=⋅
G
G
, where
G
F
is the force and
G
d
is the displacement. The force is vertically downward and has
magnitude
mg
, where
m
is the mass of the flake, so this reduces to
W
=
mgh
, where
h
is
the height from which the flake falls. This is equal to the radius
r
of the bowl. Thus
Wm
g
r
==
×
×
=×
−−
−
(.
)
( .
200 10
220 10
32
kg)(9.8 m s
m)
4.31 10 J.
23
(b) The force of gravity is conservative, so the change in gravitational potential energy of

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