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Chapter 8: Potential Energy and Conservation of Energy
Solutions to Problems
6.
Picture the Problem
: The cliff diver plunges straight downward due to the force of gravity.
Strategy:
Solve equation 83 for the weight of the diver.
Let
y
= 0 correspond to the surface of the water.
Solution:
Solve equation 83 for
mg
:
25,000 J
540 N
0.54 kN
46 m
U
U
mgy
mg
y
=
⇒
=
=
=
=
Insight:
If you set
U
= 0 at the top of the cliff, then
U
= ±25 kJ and
46 m
y
= 
when the diver enters the water.
17.
Picture the Problem
: As the ball flies through the air and gains altitude
some of its initial kinetic energy is converted into gravitational potential
energy.
Strategy:
Set the mechanical energy at the start of the throw equal to the
mechanical energy at its highest point.
Let the height be
i
0
y
=
at the start
of the throw, and find
f
y
at the highest point.
Solution:
1. (a)
Set
i
f
E
E
=
and solve for
f
y
:
( )
( ) ( )
( )
i
f
i
i
f
f
2
2
1
1
i
f
f
2
2
2
2
2
2
f
i
f
2
0
8.30 m/s
7.10 m/s
1
0.942 m
2
2 9.81 m/s
E
E
K
U
K
U
mv
mv
mgy
y
v
v
g
=
+
=
+
+
=
+

=

=
=
2.
(b)
Insight:
A more massive ball would have more kinetic energy at the start, but would require more energy to change its
height by 0.942 m, so the mass cancels out.
18.
Picture the Problem
: As the ball flies through the air and gains altitude some of its initial kinetic energy is converted
into gravitational potential energy.
Strategy:
Set the mechanical energy just after the bounce equal to the mechanical energy when it is caught.
Let the
height be
i
0
y
=
at the bounce, and find
f
y
at the catch.
Solution:
1. (a)
Set
i
f
E
E
=
and solve for
f
y
:
( )
( ) ( )
( )
i
f
i
i
f
f
2
2
1
1
i
f
f
2
2
2
2
2
2
f
i
f
2
0
16 m/s
12 m/s
1
5.7 m
2
2 9.81 m/s
E
E
K
U
K
U
mv
mv
mgy
y
v
v
g
=
+
=
+
+
=
+

=

=
=
2.
(b)
The height change is independent of the mass, so it is not necessary to know the mass of the tennis ball.
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