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

Prep for the AP ® Exam

Building Blocks (a) Construct a free-body diagram of the crate, in which

the magnitudes of the forces are consistent with the
1. A bumblebee has a mass of about 0.250 g. Calculate its crate having a constant velocity as it moves down the

kinetic energy when it is moving with a speed of 10.0 m/s. ramp.

EX 2. A man rides a scooter on a level road. The interaction (b) Use the free-body diagram representation, by identi-
7-3
between the scooter and the road causes the road to exert fying the forces that do work on the crate as it slides
a constant net force, F 1 on the scooter in the forward down the ramp, to predict the sign of the work done

,

.
direction over a distance, d The combined mass of the on the crate by those forces.
.
man and his scooter is m Suddenly, the wind picks up (c) Construct mathematical representations of each con-

and air resistance pushes against him in the direction tribution to the total work done on the crate using
opposite his motion over this same distance with a con- variables defined in your free-body diagram, and

stant force F 2 . needed given quantities and constants.

(a) If he is initially moving at a speed i v on a level road, (d) Calculate each contribution to the total work if the

how will you determine the man’s speed after the statue slides 3.00 m down the ramp with no acceler-
scooter has moved a distance d ? ation and the coefficient of kinetic friction between

(b) How will you determine whether the speed of the man the crate and the ramp is 0.540. The masses of the
will increase or decrease? statue and the crate are each 150 kg. The ramp is
(c) Use your methods to predict the speed of the inclined at 40.0.

°

man after moving a distance d given these values: (e) Explain why the sum of work done by the forces

= 800 N, = 90 kg , = 5m/s, and
v

m

F 1
= 1200 N, F 2 i exerted on the crate is zero.
= 20 m.
d
EX 3. A small truck has a mass of 2100 kg. What is the work Skills in Action
7-3 required to decrease the speed of the vehicle from 22.0 to
12.0 m/s on a level road? 7. A horizontal snow surface with a length ∆x at the base

of a slope allows a sled and rider to come to a stop after

Skill Builders descending the slope. Beyond the length ∆x is a sheer cliff.

As the Sun sets and the temperature falls the coefficient of
4. A 1000-kg car moves along a straight, level road. Initially kinetic friction is reduced.

the car’s velocity is 60 mph due east and later the car’s (a) Explain why a reduction in the coefficient of kinetic

velocity is 60 mph due west. friction is a cause for concern.

(a) Create a mathematical model of the change in kinetic (b) Express the minimum coefficient of kinetic friction in

energy as a function of time, ∆Kt(), of the car as time terms of the velocity of the sled and rider at the base

passes. Assume that the acceleration is constant so of the slope and the length ∆x .

that the change in velocity is a linear function of time. 8. A worker exerts a force, F on a box with mass m initially
,

(b) Construct a diagram of the function ∆Kt() you have at rest on a level floor. The force exerted by the worker
created for the time interval over which the velocity is directed downward at angle θ with the floor. The floor

changes from 60 mph due east to 60 mph due west. exerts a friction force on the box.

5. Explain how the kinematic equation, v 2 f = v 2 i + a x f − x ) i ; (a) The box does not move. Explain why changing the
2(

F = ma x ; and the definition of
Newton’s second law, ∑ ext,x angle that the external force makes with the floor
work lead to the work-energy theorem for an object. might get the box moving.

EX 6. A statue is crated and moved slowly down a ramp for (b) The strategy in part (a) works and the box starts
7-3 cleaning. In the figure, when the crate is on the ramp, the moving. Express the kinetic energy of the box in
curator pushes up, parallel to the ramp’s surface, so that terms of the force exerted by the worker, F ; the
the crate moves at a constant velocity down the ramp. mass, m ; the coefficient of kinetic friction, µ k ; and

the displacement of the box, ∆x .

0.540
m = 0.540 (c) If the worker continues to push on the box at the
k

same downward angle θ express how he should
,

reduce the force he exerts on the box, relative to the

initial force, F F/ initial , to displace the box with the
least amount of work.
m
3 3 3 3 3 m
m
m
40.0°
40.0°
40.0°
40.0°

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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