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226 CHAPTER 7 Work and Energy

QUESTIONS FOR DISCUSSION

1. Does the work of a force on a body depend on the frame of ground) is instantaneously at rest if the wheel is not slipping.
reference in which it is calculated? Give some examples. What force gives the body of the automobile energy? Where
2. Does your body do work (external or internal) when standing does this energy come from? (Hint: Consider the force that
at rest? When walking steadily along a level road? the rear axle exerts against its bearings.)
3. Consider a pendulum swinging back and forth. During what 9. Why do elevators have counterweights? (See Fig. 5.40.)
part of the motion does the weight do positive work? Negative 10. A parachutist jumps out of an airplane, opens a parachute, and
work? lands safely on the ground. Is the mechanical energy for this
2
2
1
2
2
2
4. Since v v v v , Eq.(7.23) implies K mv motion conserved?
x y z 2 x
1 mv mv . Does this mean that the kinetic 11. If you release a tennis ball at some height above a hard floor, it
2
2
1
2 y 2 z
energy has x, y, and z components? will bounce up and down several times, with a gradually
5. Consider a woman steadily climbing a flight of stairs. The decreasing amplitude. Where does the ball suffer a loss of
external forces on the woman are her weight and the normal mechanical energy?
force of the stairs against her feet. During the climb, the 12. Two ramps, one steeper than the other, lead from the floor to a
weight does negative work, while the normal force does no loading platform (Fig. 7.25). It takes more force to push a
work. Under these conditions how can the kinetic energy of (frictionless) box up the steeper ramp. Does this mean it takes
the woman remain constant? (Hint: The entire woman cannot more work to raise the box from the floor to the platform?
be regarded as a particle, since her legs are not rigid; but the
upper part of her body can be regarded as a particle, since it is
rigid. What is the force of her legs against the upper part of
her body? Does this force do work?)
6. An automobile increases its speed from 80 to 88 km/h. What
is the percentage of increase in kinetic energy? What is the
percentage of reduction of travel time for a given distance?
7. Two blocks in contact slide past one another and exert friction FIGURE 7.25 Two ramps of different steepness.
forces on one another. Can the friction force increase the
kinetic energy of one block? Of both? Does there exist a refer- 13. Consider the two ramps described in the preceding question.
ence frame in which the friction force decreases the kinetic Taking friction into account, which ramp requires less work
energy of both blocks? for raising a box from the floor to the platform?
8. When an automobile with rear-wheel drive is accelerating on, 14. A stone is tied to a string. Can you whirl this stone in a verti-
say, a level road, the horizontal force of the road on the rear cal circle with constant speed? Can you whirl this stone with
wheels does not give the automobile any energy because the constant energy? For each of these two cases, describe how
point of application of this force (point of contact of wheel on you must move your hand.

PROBLEMS

7.1 Work † 4. It requires 2200 J of work to lift a 15-kg bucket of water from
the bottom of a well to the top. How deep is the well?
1. If it takes a horizontal force of 300 N to push a stalled auto- 5. A child drags a 20-kg box across a lawn for 10 m and along a
mobile along a level road at constant speed, how much work sidewalk for 30 m; the coefficient of friction is 0.25 for the first
must you do to push this automobile a distance of 5.0 m? part of the trip and 0.55 for the second. If the child always pulls
2. In an overhead lift, a champion weight lifter raises 254 kg from horizontally, how much work does the child do on the box?
the floor to a height of 1.98 m. How much work does he do? 6. A man moves a vacuum cleaner 1.0 m forward and 1.0 m back
3. Suppose that the force required to push a saw back and forth 300 times while cleaning a floor, applying a force of 40 N
through a piece of wood is 35 N. If you push this saw back during each motion. The pushes and pulls make an angle of
and forth 30 times, moving it forward 12 cm and back 12 cm 60 with the horizontal. How much work does the man do on
each time, how much work do you do? the vacuum cleaner?
†
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