Page 222 - Fisika Terapan for Engineers and Scientists

422 CHAPTER 13 Dynamics of a Rigid Body

36. An electric blender uniformly accelerates from rest beginning (and produce clouds of smoke and burn marks on the runway,
at t 0; at t 0.50 s, the blender has reached 250 radians/s which you may have noticed; see Fig. 13.34), until the sliding
and continues accelerating. If the rotating components have a friction force has accelerated the wheels to the rotational speed
2
moment of inertia of 2.0 10 4 kg m , at what instantaneous required for rolling without slipping. From the following data,
rate is the motor delivering energy at t 0.50 s? calculate how far the wheel of an airliner slips before it begins
37. A basketball is released from rest on a 15 incline. How many to roll without slipping: the wheel has a radius of 0.60 m and a
revolutions will the basketball undergo in 4.0 s? Assume the mass of 160 kg, the normal force acting on the wheel is 2.0
5
basketball is a thin spherical shell with a diameter of 23 cm, 10 N, the speed of the airliner is 200 km/h, and the coeffi-
and that it rolls without slipping. cient of sliding friction for the wheel on the runway is 0.80.
Treat the wheel as a uniform disk.
38. A 25-cm length of thin string is wound on the axle of a toy
gyroscope that rotates in fixed bearings; the radius of the
winding is 2.0 mm. If the string is pulled with a steady force
of 5.0 N until completely unwound, how long does it take to
complete the pull? What is the final angular velocity? The
moment of inertia of the gyroscope (including axle) is
2
5.0 10 5 kg m .
39. A phonograph turntable driven by an electric motor acceler-
ates at a constant rate from 0 to 33.3 revolutions per minute
in a time of 2.0 s. The turntable is a uniform disk of metal,
of mass 1.2 kg and radius 15 cm. What torque is required to
produce this acceleration? If the driving wheel makes con-
tact with the turntable at its outer rim, what force must it
exert? FIGURE 13.34 A landing airliner.
*40. A bowling ball sits on the smooth floor of a subway car. If the
car has a horizontal acceleration a, what is the acceleration of
the ball? Assume that the ball rolls without slipping.
*41. A hoop rolls down an inclined ramp. The coefficient of static 13.3 Angular Momentum and its
friction between the hoop and the ramp is . If the ramp is Conser vation
s
very steep, the hoop will slip while rolling. Show that the criti-
cal angle of inclination at which the hoop begins to slip is 46. You spin a hard-boiled egg on a table, at 5.0 rev/s. What is the
given by tan 2 . s angular momentum of the egg? Treat the egg as a sphere of
mass 70 g and mean diameter 5.0 cm.
*42. A solid cylinder rolls down an inclined plane. The angle of
inclination of the plane is large so that the cylinder slips 47. The Moon moves around the Earth in an (approximately)
8
while rolling. The coefficient of kinetic friction between the circular orbit of radius 3.8 10 m in a time of 27.3 days.
cylinder and the plane is . Find the rotational and transla- Calculate the magnitude of the orbital angular momentum of
k
tional accelerations of the cylinder. Show that the translational the Moon. Assume that the origin of coordinates is centered
acceleration is the same as that of a block sliding down the on the Earth.
plane. 48. At the Fermilab accelerator, protons of momentum 5.2 10 16
**43. Suppose that a tow truck applies a horizontal force of 4000 N kg m/s travel around a circular path of diameter 2.0 km. What
to the front end of an automobile similar to that described in is the orbital angular momentum of one of these protons?
Problem 63 of Chapter 12. Taking into account the rotational Assume that the origin is at the center of the circle.
inertia of the wheels and ignoring frictional losses, what is the 49. Prior to launching a stone from a sling, a Bolivian native
acceleration of the automobile? What is the percentage differ- whirls the stone at 3.0 rev/s around a circle of radius 0.75 m.
ence between this value of the acceleration and the value cal- The mass of the stone is 0.15 kg. What is the angular momen-
culated by neglecting the rotational inertia of the wheels? tum of the stone relative to the center of the circle?
**44. A cart consists of a body and four wheels on frictionless axles. 50. A communications satellite of mass 100 kg is in a circular
7
The body has a mass m. The wheels are uniform disks of mass orbit of radius 4.22 10 m around the Earth. The orbit is in
M and radius R. Taking into account the moment of inertia of the equatorial plane of the Earth, and the satellite moves along
the wheels, find the acceleration of this cart if it rolls without it from west to east with a speed of 4.90 10 m/s. What is
2
slipping down an inclined plane making an angle with the the magnitude of the angular momentum of this satellite?
horizontal.
51. According to Bohr’s (oversimplified) theory, the electron in
**45. When the wheels of a landing airliner touch the runway, they the hydrogen atom moves in one or another of several possible
are not rotating initially. The wheels first slide on the runway circular orbits around the nucleus. The radii and the orbital