Cal Poly State University, SLO
D. Niebuhr
Physics Department
Winter 2008
Phys 141
Homework Solutions
Chapter 10
Assigned Problems:
Ch. 10:
2, 5, 9, 12, 16, 18, 23, 30, 31, 42, 47, 54
10.2.
Model:
Model the hiker as a particle.
Visualize:
The origin of the coordinate system chosen for this problem is at sea level so that the hiker’s position in Death
Valley is
0
8.5 m.
y
= 
Solve:
The hiker’s change in potential energy from the bottom of Death Valley to the top of Mt. Whitney is
gf
gi
f
i
f
i
2
6
(
)
(65 kg)(9.8 m/s )[4420 m ( 85 m)]
2.87 10 J
U
U
U
mgy
mgy
mg y
y
∆
=

=

=

=
 
=
×
Assess:
Note that
∆
U
is independent of the origin of the coordinate system.
10.5.
Model:
Model the car (C) as a particle. This is an example of free fall, and therefore the sum of kinetic
and potential energy does not change as the car falls.
Visualize:
Solve:
(a)
The kinetic energy of the car is
2
2
5
C
C C
1
1
(1500 kg)(30 m/s)
6.75 10 J
2
2
K
m v
=
=
=
×
(b)
Let us relabel
K
C
as
K
f
and place our coordinate system at
f
0
y
=
m so that the car’s potential energy
U
gf
is
zero, its velocity is
v
f
, and its kinetic energy is
K
f
. At position
y
i
,
i
i
0 m/s or
0 J,
v
K
=
=
and the only energy the
car has is
gi
i
.
U
mgy
=
Since the sum
K
+
U
g
is unchanged by motion,
f
gf
i
gi
K
U
K
U
+
=
+
. This means
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View Full DocumentCal Poly State University, SLO
D. Niebuhr
Physics Department
Winter 2008
Phys 141
f
f
i
i
f
i
i
5
f
i
i
2
0
(
)
(6.75 10 J
0 J)
45.9 m
(1500 kg)(9.8 m/s )
K
mgy
K
mgy
K
K
mgy
K
K
y
mg
+
=
+
⇒
+
=
+

×

⇒
=
=
=
(c)
From part (b),
(
29
2
2
2
2
f
i
f
i
f
i
i
1
1
(
)
2
2
2
mv
mv
v
v
K
K
y
mg
mg
g



=
=
=
Free fall does
not
depend upon the mass.
10.9.
Model:
Model the skateboarder as a particle. Assuming that the track offers no rolling friction, the sum
of the skateboarder’s kinetic and gravitational potential energy does not change during his rolling motion.
Visualize:
The vertical displacement of the skateboarder is equal to the radius of the track.
Solve:
The quantity
K
+
U
g
is the same at the upper edge of the quarterpipe track as it was at the bottom. The
energy conservation equation
f
gf
i
gi
K
U
K
U
+
=
+
is
2
2
2
2
f
f
i
i
i
f
f
i
2
2
2
i
i
1
1
2 (
)
2
2
(0 m/s)
2(9.8 m/s )(3.0 m
0 m)
58.8 m/s
7.67 m/s
mv
mgy
mv
mgy
v
v
g y
y
v
v
+
=
+
⇒
=
+

=
+

=
⇒
=
Assess:
Note that we did not need to know the skateboarder’s mass, as is the case with
freefall motion.
10.12.
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 Winter '06
 staff
 Energy, Kinetic Energy, Potential Energy, Work, Physics Department PHYS, SLO Physics Department, D. Niebuhr Winter

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