Cal Poly State University, SLO
D. Niebuhr
Physics Department
Winter 2008
Phys 141
Homework Solutions
Chapter 11
Assigned Problems:
Ch. 11:
2, 6, 14, 16, 23, 28, 34, 45, 48, 54, 60, 53
11.2.
Visualize:
Please refer to Figure Ex11.2.
Solve:
(a)
cos
(3)(4)cos110
4.1.
A B
AB
α
⋅
=
=
° = 
r r
(b)
cos
(4)(5)cos180
20.
C D
CD
⋅
=
=
° = 
r
r
(c)
cos
(4)(3)cos30
10.4.
E F
EF
⋅
=
=
° =
r r
11.6.
Solve:
(a)
‚
y
¡º
ª
*
( 5.0
4.0 ) N (3.0 ) m
( 15.0
12.0
) J= 15.0 J.
W
F
r
i
j
i
i i
j i
=
⋅∆ = 
+
⋅
= 
⋅ +
⋅

r
r
r
(b)
‚
y
¡
≡♠
( 5.0
4.0 ) N ( 3.0 ) m
(15.0
12.0
) J= 12.0 J.
W
F
r
i
j
j
i j
j j
=
⋅∆ = 
+
⋅ 
=
⋅ 
⋅

r
r
r
11.14.
Model:
Use the workkinetic energy theorem.
Visualize:
Please refer to Figure Ex11.14.
Solve:
The workkinetc energy theorem is
f
i
f
x
2
2
f
i
i
f
x
2
2
2
f
f
0 m
1
1
area under the force curve from
to
2
2
1
1
1
(2 kg)(4.0 m/s)
16 J
area from 0 to
2
2
2
x
x
x
K
mv
mv
W
F dx
x
x
mv
mv
F dx
x
∆
=

=
=
=
⇒

=

=
=
∫
∫
2
f
f
2
f
f
1
1
At
2 m :
(2.0 kg)
16 J
( 10 N)(2 m)
10 J
2.45 m/s
2
2
1
At
4 m :
(2.0 kg)
16 J
0 J
4.0 m/s
2
x
v
v
x
v
v
=

=

= 
⇒
=
=

=
⇒
=
11.16.
Model:
Use the definition
/
.
s
F
dU ds
= 
Visualize:
Please refer to Figure Ex11.16.
Solve:
F
x
is the negative of the slope of the potential energy graph at position
x
. Between
x
=
0 cm and
x
=
10
cm the slope is
slope
=
f
i
f
i
(
)/(
)
(0 J 10 J)/(0.1 m
0.0 m)
100 N
U
U
x
x


=


= 
Thus,
F
x
=
100 N at
x
=
5 cm. The slope between
x
=
10 cm and
x
=
20 cm is zero, so
F
x
=
0 N at
x
=
15 cm.
Between 20 cm and 40 cm,
slope
=
(10 J
0 J)/(0.40 m
0.20 m)
50 N


=
At
x
=
25 cm and
x
=
35 cm, therefore,
F
x
=

50 N.
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View Full DocumentCal Poly State University, SLO
D. Niebuhr
Physics Department
Winter 2008
Phys 141
11.23.
Visualize:
Solve:
(a)
2
2
i
0
0
i
g0
0
2
2
ext
f
1
1
f
g1
1
1
0 J
(20 kg)(9.8 m/s )(3 m)
588 J
2
1
1
0 J
(20 kg)(2.0 m/s)
40 J
0 J
2
2
K
K
mv
U
U
mgy
W
K
K
mv
U
U
mgy
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
At the top of the slide, the child has gravitational potential energy of 588 J. This energy is transformed into
thermal energy of the child’s pants and the slide and the kinetic energy of the child. This energy transfer and
transformation is shown on the energy bar chart.
(b)
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 Winter '06
 staff
 Conservation Of Energy, Energy, Force, Potential Energy, Work, Physics Department PHYS, D. Niebuhr Winter

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