Chapter 6 continued
62. Hammer Throw An athlete whirls a
7.00-kg hammer 1.8 m from the axis of
rotation in a horizontal circle, as shown in
Figure 6-14. If the hammer makes one revolution in 1.0 s, what is the centripetal
acceleration of the hammer? What is the
tension in the chain?
vtang
(4p 2)(0.050 m)
(1.80 s)
5 }}
5 0.61 m/s2
2
r 5 10.0 cm:
(4p 2)(0.100 m)
(1.80 s)
4p 2r
T
a c 5 }}
2 5 }}
2
5 1.22 m/s2
r 5 15.0 cm:
4p 2r
T
(4p 2)(0.150 m)
(1.80 s)
a c 5 }}
2 5 }}
2
5 1.83 m/s2
c. What force accelerates the coin?
frictional force between coin and
record
■
d. At which of the three radii in part b
would the coin be most likely to fly off
the turntable? Why?
Figure 6-14
15.0 cm, the largest radius; the
friction force needed to hold it is
the greatest.
2
4p r
ac 5 }
2
T
(4p 2)(1.8 m)
(1 . 0 s)
5 }}
2
5 71 m/s2
Fc 5 mac
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5 (7.00 kg)(71 m/s2)
5 5.03102 N
Level 2
63. A coin is placed on a vinyl stereo record
1
that is making 33}} revolutions per minute
3
on a turntable.
a. In what direction is the acceleration of
the coin?
The acceleration is toward the
center of the record.
b. Find the magnitude of the acceleration
when the coin is placed 5.0, 10.0, and
15.0 cm from the center of the record.
T5
1
}
f
5
1
}
1}
33}} rev/min
3
5 (0.0300 min)1 } 2 5 1.80 s
60 s
1 min
r 5 5.0 cm:
4p 2r
T
ac 5 }}
2
Physics: Principles and Problems
64. A rotating rod that is 15.3 cm long is spun
with its axis through one end of the rod so
that the other end of the rod has a speed of
2010 m/s (4500 mph).
a. What is the centripetal acceleration of
the end of the rod?
v2
r
(2010 m/s)2
0.153 m
ac 5 } 5 }}
5 2.643107 m/s2
b. If you were to attach a 1.0-g object to
the end of the rod, what force would be
needed to hold it on the rod?
Fc 5 mac
5 (0.0010 kg)(2.643107 m/s2)
5 2.63104 N
65. Friction provides the force needed for a car
to travel around a flat, circular race track.
What is the maximum speed at which a car
can safely travel if the radius of the track is
80.0 m and the coefficient of friction is 0.40?
Fc 5 Ff 5 mFN 5 mmg
mv 2
mv 2
But Fc 5 } , thus } 5 mmg.
r
r
Solutions Manual
131