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218 CHAPTER 7 Work and Energy

QUESTION 2: A car is traveling at 80 km/h on a highway, and a truck is traveling at 40
km/h. Can these vehicles have the same kinetic energy? If so, what must be the ratio
of their masses?
QUESTION 3: Consider a golf ball launched into the air.The ball rises from the ground
to a highest point, and then falls back to the ground. At what point is the kinetic
energy largest? Smallest? Is the kinetic energy ever zero?
QUESTION 4: A horse is dragging a sled at steady speed along a rough surface, with fric-
tion. The horse does work on the sled, but the kinetic energy of the sled does not
increase. Does this contradict the work–energy theorem?
QUESTION 5: If you increase the speed of your car by a factor of 3, from 20 km/h to
60 km/h, by what factor do you change the kinetic energy?
(A) 1 (B) 1 (C) 1 (D) 3 (E) 9
9 3

PROBLEM-SOLVING TECHNIQUES CALCULATION OF WORK

In calculations of the work done by a force acting on a body, know the magnitude of the force and the angle, and use
keep in mind that the latter if you know the components.
• A force that has a component in the direction of the dis- • For a variable force, the calculation of the work involves
placement does positive work; a force that has a compo- integration along the path [Eq. (7.14)]; also, Eq. (7.15) can
nent in the direction opposite to the displacement does be used for the work during an infinitesimal displacement.
negative work.
• The work–energy theorem is valid only if the work is
• A force perpendicular to the displacement does no work calculated with the net force. When two of the three
[examples: the normal force acting on a body sliding on quantities (work done, initial kinetic energy, and final
a surface, the centripetal force acting on a body in circu- kinetic energy) are known, the theorem can be applied to
lar motion (uniform or not)]. determine the third: W K – K .
2 1
• For a constant force, the work can be calculated either
from Eq. (7.5) or from Eq. (7.9); use the former if you

Online 7.4 GRAVITATIONAL POTENTIAL ENERGY
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Concept
Tutorial As we saw in the preceding section, the kinetic energy represents the capacity of a par-
ticle to do work by virtue of its speed. We will now become acquainted with another
form of energy that represents the capacity of the particle to do work by virtue of its
position in space. This is the potential energy. In this section, we will examine the
special case of gravitational potential energy for a particle moving under the influence
of the constant gravitational force near the surface of the Earth, and we will formulate
a law of conservation of energy for such a particle. In the next chapter we will exam-
ine other cases of potential energy and formulate the General Law of Conservation
of Energy.
The gravitational potential energy represents the capacity of the particle to do work by
virtue of its height above the surface of the Earth. When we lift a particle to some height
above the surface, we have to do work against gravity, and we thereby store work in