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296 Chapter 7 Conservation of Energy and an Introduction to Energy and Work

THE TAKEAWAY for Section 7-2

✔ If a force is exerted on an object that undergoes a dis- ✔ Whether the work done is positive, negative, or zero
placement, the object or system exerting that force can do depends on the angle between the direction in which the
work on that object. force is exerted on an object and the direction of the object’s

✔ For a constant force and linear displacement, the amount displacement.
of work done on an object equals the displacement of the ✔ For objects in contact, if one object does negative work

object multiplied by the component of the force exerted on on a second object, the second object must do an equal amount
the object parallel to that displacement. of positive work on the first object.
Prep for the AP ® Exam
Building Blocks forces exerted on the
box, one of which
EX 1. You lift a 100-g apple upward from the ground at a con- is shown. Friction d
7-1 Case (a)
stant speed for a distance of 1 m. Answer the following between the box and
questions, taking the system to be the apple alone. the floor is negligible.
(a) Describe how it is that you know the size of the force The magnitudes of

that you exert on the apple. the forces shown in d
(b) Describe how you can determine the quantity of work each situation are Case (b)

done by you on the apple. identical. Rank the

(c) Describe how you can determine the sign of the work four situations in
done by you on the apple. order of increasing d
(d) You release the apple from rest and it falls 1 m. Describe work done on the Case (c)

how you know that work is done on the apple as it falls. box by the force
(e) Identify the force that does the work on the apple as it shown as the box

falls and describe how you would determine the quan- goes through the dis- d
tity of work done by that force on the apple. Neglect placement, d . Case (d)
air resistance.
(f) Compare the quantities of work done on the apple for Skill Builders

the processes in parts (a) and (d) and any assumptions
that are useful in making this comparison. 5. In the men’s weight-lifting competition at the 2008 Beijing

(g) Compare accelerations and net forces for the processes Olympics, Matthias Steiner made his record lift of 446 kg
in parts (b) and (d). Describe how your answer to from the floor to over his head (2.0 m). How much work
part (b) would change if work done by the net force did Steiner do on the weights during the lift?
exerted on the apple was considered, instead of only 6. The work done on an object is W = Fd cos θ where the

,

considering the force exerted by you. magnitude of the displacement of the object is d the mag-
,

(h) When the apple fell, energy was transferred. Describe nitude of the force exerted on the object is F and the angle
,
how the energy of the apple changed during the pro- between the direction of displacement and the direction of
cess from when the apple started falling to when it the force is θ. Evaluate this relationship to identify all the

came to rest on the ground. Also describe the sizes and possible conditions where the work done by this force is
directions of the forces exerted by the apple on the equal to zero.
ground and the ground on the apple, and justify your 7. You (i) lift a 10-N box to a height of 1 m from the floor
description in terms of the change in the apple’s energy. at a constant vertical speed, (ii) carry it horizontally 3 m
2
2. A crane lifts a 2 00. × 10 -kg crate a vertical distance of across the room at constant speed, and (iii) set it back

15.0 m at a slow, constant speed. How much work in down on the floor, also at constant speed. (In this ques-
joules does the crane do on the crate? tion, neglect the brief changes in speed as you first pick

EX 3. A constant force, F , F it up and then bring it to rest vertically at the end of the
7-2 is exerted on a box, lift and start moving it horizontally, and similarly as you
dragging the box a θ change its direction to put it back down.)
distance d across a (a) Construct a free-body diagram on the box for each

floor. F makes an straight segment of the path (i–iii), clearly labeling

angle θ with the horizontal as shown in the figure. This is each force exerted on the box.
repeated several times; each time the angle θ is increased (b) Construct representations of the displacement for

by a few degrees, but the magnitude of the force F each straight segment of the overall path of the box.
remains unchanged. Describe how the work done by the (c) Predict the work done by you on the box along each

force F in dragging the box changes. straight segment of the overall path of the box and

4. The figure shows four situations in which a box slides the total work done by you on the box during the
to the right a distance d across a floor as a result of overall path.
Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.
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