Page 220 - Fisika Terapan for Engineers and Scientists

420 CHAPTER 13 Dynamics of a Rigid Body

force generate about the center of mass of the automobile?
T
Will this torque tend to lift the front end of the automobile or
R 1 R 2 tend to depress it? Assume that the center of mass of the auto-
mobile is 60 cm above the surface of the road.
*19. A tractor of mass 4500 kg has rear wheels of radius 0.80 m.
T '
What torque and what power must the engine supply to the
FIGURE 13.29 Motor and pump rear axle to move the tractor up a road of slope 1:3 at a con-
wheels connected by a drive belt. stant speed of 4.0 m/s?
*20. A bicycle and its rider have a mass of 90 kg. While accelerat-
(c) By taking the product of torque and angular velocity, cal-
ing from rest to 12 km/h, the rider turns the pedals through
culate the power delivered by the motor to the drive belt,
three full revolutions. What torque must the rider exert on the
and the power removed by the pump from the drive belt.
pedals? Assume that the torque is constant during the acceler-
Are these powers equal?
ation and ignore friction within the bicycle mechanism.
9. The Wright Cyclone engine on a DC-3 airplane delivers a
*21. A meterstick is held to a wall by a nail passing through the
power of 850 hp with the propeller revolving steadily at 2100
60-cm mark (Fig. 13.30). The meterstick is free to swing
rev/min. What is the torque exerted by air resistance on the
about this nail, without friction. If the meterstick is released
propeller?
from an initial horizontal position, what angular velocity will
10. A woman on an exercise bicycle has to exert an (average) tan- it attain when it swings through the vertical position?
gential push of 35 N on each pedal to keep the wheel turning
at constant speed. Each pedal has a radial length of 0.18 m. If
she pedals at the rate of 60 rev/min, what is the power she
expends against the exercise bicycle? Express your answer in FIGURE 13.30 A meterstick.
watts and in kilocalories per minute.
11. With what translational speed does the upper end of the *22. A uniform solid sphere of mass M and radius R hangs from a
meterstick in Example 2 hit the floor? If, instead of a 1.0-m string of length R 2. Suppose the sphere is released from an
stick, we use a 2.0-m stick, with what translational speed does initial position making an angle of 45 with the vertical
it hit? (Fig. 13.31).
12. A ceiling fan uses 0.050 hp to maintain a rotational frequency (a) Calculate the angular velocity of the sphere when it
of 150 rev/min. What torque does the motor exert? swings through the vertical position.
13. The motor of a grinding wheel exerts a torque of 0.65 N m to (b) Calculate the tension in the string at this instant.
maintain an operating speed of 3450 rev/min. What power
does the motor deliver?
14. From the human-body data of Fig. 10.17, calculate (a) the
torque about the shoulder for an arm held horizontally and (b)
the torque about the hip for a leg held horizontally.
15. A large grinding table is used to thin large batches of silicon
wafers in the final stage of semiconductor manufacturing, a
process called backlap. If the driving motor exerts a torque of FIGURE 13.31 A hanging sphere.
250 N m while rotating the table 1200 times for one batch of
wafers, how much work does the motor do? *23. The maximum (positive) acceleration an automobile can
16. Recently, a microfabricated torque sensor measured a torque as achieve on a level road depends on the maximum torque the
small as 7.5 10 24 N m. If the torque is produced by a force engine can deliver to the wheels.
applied perpendicular to the sensor at a distance of 25 m (a) The engine of a Maserati sports car delivers a maximum
from the axis of rotation, what is the smallest force that the torque of 441 N m to the gearbox. The gearbox
sensor can detect? steps down the rate of revolution by a factor of 2.58;
*17. The angular position of a ceiling fan during the first two that is, whenever the engine makes 2.58 revolutions,
2
seconds after start-up is given by Ct , where C the wheels make 1 revolution. What is the torque deliv-
2
7.5 radians/s and t is in seconds. If the fan motor exerts a ered to the wheels? Ignore frictional losses in the gear-
torque of 2.5 N m, how much work has the motor done box.
after t 1.0 s? After t 2.0 s? (b) The mass of the car (including fuel, driver, etc.) is 1770
*18. While braking, a 1500-kg automobile decelerates at the rate kg, and the radius of its wheels is 0.30 m. What is the
2
of 8.0 m/s . What is the magnitude of the braking force that maximum acceleration? Ignore the moment of inertia of
the road exerts on the automobile? What torque does this the wheels and frictional losses.