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426 CHAPTER 13 Dynamics of a Rigid Body

REVIEW PROBLEMS

86. A door is 0.80 m wide. What is the torque you exert about open position? Assume that the sailor pushes perpendic-
the axis passing through the hinges if you push against this ularly on the hatch at the edge that is farthest from the
door with a perpendicular force of 200 N at its middle? hinge.
What is it if you push at the edge? A wind is blowing against 92. With your bicycle upside down on the ground, and the
the other side of the door and trying to push it open. Where wheel free to rotate, you grasp the front wheel at the top
should you push to keep the door closed? and give it a horizontal push of 20 N. What is the instan-
87. An elevator of mass 900 kg is being lifted at constant speed taneous angular acceleration of the wheel? The wheel is a
by a cable wrapped around a wheel (see Fig. 13.39). The hoop of mass 4.0 kg and radius 0.33 m; ignore the mass of
radius of the wheel is 0.35 m. What torque does the cable the spokes.
exert on the wheel? 93. A toy top consists of a disk of radius 4.0 cm with a rein-
forced rim (a ring). The mass of the disk is 20 g, and the
0.35 m
mass of the rim is 15 g. The mass of the pivot of this top is
negligible.
(a) What is the moment of inertia of this top?
(b) When you give this top a twist and start it rotating at
100 rev/min on the floor, friction slows the top to a stop
in 1.5 min. Assuming that the angular deceleration is
uniform, what is the angular deceleration?
(c) What is the frictional torque on the top?
(d) What is the work done by the frictional torque?
FIGURE 13.39 94. The turntable of a record player is a uniform disk of radius
Elevator cable 0.15 m and mass 1.2 kg. When in operation, it spins at 33 1 3
attached to a wheel. rev/min. If you switch the record player off, you find that the
turntable coasts to a stop in 45 s.
88. Each of the two fuel turbopumps in the Space Shuttle deliv- (a) Calculate the frictional torque that acts on the turntable.
ers a power of 700 hp. The rotor of this pump rotates at Assume the torque is constant, that is, independent of
37000 rev/min. What is the torque that the rotor exerts the angular speed.
while pushing against the fuel?
(b) Calculate the power that the motor of the record player
89. A manual winch has a crank of length (radius) 0.25 m. If a must supply to keep the turntable in operation at
laborer pushes against its handle tangentially with a force of 33 1 3 rev/min.
200 N, how much work does the laborer do while turning the
*95. A barrel of mass 200 kg and radius 0.50 m rolls down a 40
crank through 10 revolutions?
ramp without slipping. What is the value of the friction force
90. A meterstick is initially standing vertically on the floor. If the acting at the point of contact between the barrel and the
meterstick falls over, with what angular velocity will it hit the ramp? Treat the barrel as a cylinder of uniform density.
floor? Assume that the end in contact with the floor experi-
*96. A disk of mass M is free to rotate about a fixed horizontal
ences no friction and slips freely.
axis. A string is wrapped around the rim of the disk, and a
*91. A heavy hatch on a ship is made of a uniform plate of steel mass m is attached to this string (see Fig. 13.40). What is the
that measures 1.2 m 1.2 m and has a mass of 400 kg. downward acceleration of the mass?
The hatch is hinged along one side; it is horizontal when
closed, and it opens upward. A torsional spring assists in
the opening of the hatch. The spring exerts a torque of
3
2.00 10 N m when the hatch is horizontal and a torque
3
of 0.30 10 N m when the hatch is vertical; in the range
of angles between horizontal and vertical, the torque
M
3
decreases linearly (e.g., the torque is 1.15 10 N m when
the hatch is at 45 ).
m
(a) At what angle will the hatch be in equilibrium so the
spring exactly compensates the torque due to the weight?
FIGURE 13.40 A mass m hanging from a disk.
(b) What minimum push must a sailor exert on the hatch to
open it from the closed position? To close it from the