Page 219 - Fisika Terapan for Engineers and Scientists

Problems 419

14. Stand a pencil vertically on its point on a table and let go. The what is the direction of the angular momentum of the auto-
pencil will topple over. mobile? Is the angular momentum constant as the automobile
(a) If the table is very smooth, the point of the pencil will slip travels along this road?
in the direction opposite to that of the toppling. Why? 16. Is the angular momentum of the orbital motion of a planet
(b) If the table is somewhat rough, or covered with a piece of constant if we choose an origin of coordinates on the Sun?
paper, the point of the pencil will jump in the direction of 17. A pendulum is swinging back and forth. Is the angular
the toppling. Why? (Hint: During the early stages of the momentum of the pendulum bob constant?
toppling, friction holds the point of the pencil fixed; thus 18. What is the direction of the angular-momentum vector of the
the pencil acquires horizontal momentum.) rotation of the Earth?
15. An automobile travels at constant speed along a road consist- 19. A bicycle is traveling east along a level road. What are the
ing of two straight segments connected by a curve in the form directions of the angular-momentum vectors of its wheels?
of an arc of a circle. Taking the center of the circle as origin,

PROBLEMS

13.1 Work, Energy, and Power in 3. The repair handbook for an automobile specifies that the
Rotational Motion; Torque cylinder-head bolts are to be tightened to a torque of 62 N m.
If a mechanic uses a wrench of length 20 cm on such a bolt,
1. The operating instructions for a small crane specify that when the what perpendicular force must he exert on the end of this
boom is at an angle of 20 above the horizontal (Fig. 13.27), the wrench to achieve the correct torque?
maximum safe load for the crane is 500 kg. Assuming that this 4. A 2.0-kg trout hangs from one end of a 2.0-m-long stiff fish-
maximum load is determined by the maximum torque that the ing pole that the fisherman holds with one hand by the other
pivot can withstand, what is the maximum torque for 20 in end. If the pole is horizontal, what is the torque that the
terms of length R of the boom? What is the maximum safe load weight of the trout exerts about the end the fisherman holds?
for 40 ? For 60 ? If the pole is tilted upward at an angle of 60 ?
5. You hold a 10-kg book in your hand with your arm extended
horizontally in front of you. What is the torque that the
weight of this book exerts about your shoulder joint, at a dis-
20° tance of 0.60 m from the book?
6. If you bend over, so your trunk is horizontal, the weight of
your trunk exerts a rather strong torque about the sacrum,
where your backbone is pivoted on your pelvis. Assume that
the mass of your trunk (including arms and head) is 48 kg, and
that the weight effectively acts at a distance of 0.40 m from
the sacrum. What is the torque that this weight exerts?
FIGURE 13.27 Small crane.
7. The engine of an automobile delivers a maximum torque of
2. A simple manual winch consists of a drum of radius 4.0 cm to 203 N m when running at 4600 rev/min, and it delivers a
which is attached a handle of radius 25 cm (Fig. 13.28). When maximum power of 142 hp when running at 5750 rev/min.
you turn the handle, the rope winds up on the drum and pulls What power does the engine deliver when running at maxi-
the load. Suppose that the load carried by the rope is 2500 N. mum torque? What torque does it deliver when running at
What force must you exert on the handle to hold this load? maximum power?
8. The flywheel of a motor is connected to the flywheel of a
25 cm
pump by a drive belt (Fig. 13.29). The first flywheel has a
radius R , and the second a radius R . While the motor wheel
2
1
is rotating at a constant angular velocity , the tensions in the
1
upper and the lower portions of the drive belt are T and
T
, respectively. Assume that the drive belt is massless.
2500 N (a) What is the angular velocity of the pump wheel?
FIGURE 13.28 (b) What is the torque of the drive belt on each wheel?
Manual winch.
4.0 cm