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Chapter 7 – Student Solutions Manual
3. (a) From Table 21, we have
vv
. Thus,
a
2
0
2
2
=+Δ
x
()
(
)
2
27
1
5
2
0
2
2.4 10 m/s
2 3.6 10
m/s
0.035 m
2.9 10 m/s.
a
x
=+
Δ
=
×
+
×
=
×
7
(b) The initial kinetic energy is
(
)
2
22
7
7
0
11
1.67 10
kg
2.4 10 m/s
4.8 10
J.
i
Km
v
−−
==
×
×
=
×
1
3
The final kinetic energy is
(
)
2
7
7
1.67 10
kg
2.9 10 m/s
6.9 10
J.
f
v
×
×
=
×
1
3
The change in kinetic energy is
Δ
K
= 6.9
×
10
–13
J – 4.8
×
10
–13
J = 2.1
×
10
–13
J.
17. (a) We use
to denote the upward force exerted by the cable on the astronaut. The
force of the cable is upward and the force of gravity is
mg
downward. Furthermore, the
acceleration of the astronaut is
g
/10 upward. According to Newton’s second law,
F
–
mg
=
mg
/10, so
F
= 11
mg
/10. Since the force
G
F
G
F
and the displacement
G
d
are in the same
direction, the work done by
G
is
F
2
4
11
11 (72 kg)(9.8 m/s )(15 m)
1.164 10 J
10
10
F
mgd
WF
d
=
=
×
which (with respect to significant figures) should be quoted as 1.2
×
10
4
J.
(b) The force of gravity has magnitude
mg
and is opposite in direction to the
displacement. Thus, using Eq. 77, the work done by gravity is
24
(72 kg)(9.8 m/s )(15 m)
1.058 10 J
g
Wm
g
d
=−
×
which should be quoted as – 1.1
×
10
4
J.
(c) The total work done is
W
. Since the
astronaut started from rest, the workkinetic energy theorem tells us that this (which we
round to 1
) is her final kinetic energy.
=×−×=
×
1164
.
10 J
1.058 10 J
1.06 10 J
44
3
1
.
×
10 J
3
(d) Since
v
=
1
2
2
, her final speed is
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K
m
==
×
=
22
1
0
6
1
0
54
3
(.
.
J)
72 kg
m/s.
19. (a) We use
F
to denote the magnitude of the force of the cord on the block. This force
is upward, opposite to the force of gravity (which has magnitude
Mg
). The acceleration is
downward. Taking the downward direction to be positive, then Newton’s
second law yields
G
ag
=
/4
G
G
Fm
aM
g
F
M
g
net
=⇒
−
=
F
H
G
I
K
J
4
so
F
= 3
Mg
/4. The displacement is downward, so the work done by the cord’s force is,
using Eq. 77,
W
F
= –
Fd
= –3
Mgd
/4.
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 Winter '08
 Naik
 Physics, Energy, Kinetic Energy

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