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

5 Platform

4 x m
Kinetic energy (J) 3 2

of spring constant k The spring is oriented vertically,
.
1 7. A small platform is attached to the top end of a spring
as shown in the figure. A block of mass m is placed
0 on the platform, and the spring is compressed a
.
0 1 2 3 distance x The spring is then released, and the block
Speed (m/s) travels upward a distance H above its starting point.
4. A single constant force is exerted on an object. The The spring is then replaced with one of spring con-

,
graph describes the object’s energy. How much stant 4 k and the procedure is repeated with the same
,
work was done to increase the speed of the object compression, x as before. To what distance above its
from 1.0 to 3.0 m/s? starting point will the block now travel?
(A) 1.5 J (B) 2.0 J (C) 4.0 J (D) 4.5 J (A) H /4 (B) H (C) 2 H (D) 4 H
8. A device is used to launch objects from the edge of

K f
h a platform 5.0 meters above the ground. To deter-
mine the speed with which the device launches the
objects, you set up a motion detector to measure
the final speed with which the objects strike the
30° m ground. The device can be set to launch the objects
5. A block of mass m is initially at rest at the bottom vertically upward, vertically downward, or hori-

of a plane inclined at 30° with the horizontal, as zontally from the same initial position, and with
shown in the figure. The block is pulled up the the same magnitude of initial velocity. How do
the components of the final velocities of the object
K The
plane. At a height h it has kinetic energy f .
v

,
coefficient of friction with the incline is µ Which compare when launched vertically upward, U hor-

.
v
v
,

of the following correctly represents the net work izontally, H and vertically downward, D ? We use
done on the block over this motion? the subscript x to represent the horizontal compo-
nent and y to represent the vertical component.
K
(A) f (B) K f + mgh (A) The final speeds and velocities are the same in

(C) K f − mgh (D) K f + µmgh all three cases.
(B) Hy = v Dy = v Uy ; v Dx = v Ux < v Hx
v
(C) Hy < v Dy = v Uy ; v Dx = v Ux < v Hx
v
k
v
Hx
(D) Hy < v Dy < v Uy ; v Dx = v Ux < v

s
grav
m U U U grav = 0, U = 0 9. Various boxes are being pushed along a horizon-
tal surface by a constant, external force exerted
on them horizontally, as shown in the figure. The
6. An object of mass m is attached to a spring hanging magnitude of the force and the mass of the block

from the ceiling as shown. It is initially supported are given in each case. The blocks and the surfaces
so the spring is unstretched. The object is released are the same materials in each case, and friction is
and falls. Which of the following correctly describes not negligible. Which of the following is the correct
the kinetic energy of the object when it has fallen a ranking of the cases in terms of the kinetic energy
distance h below the starting point? of the block after being pushed a distance d ?
1
2
(A) =K mgh − kh
2 Q F m R 2F m
1
2
(B) =K mgh + kh
2
F 2F
1 S 2m T 2m
2
(C) =−K mgh + kh
2
1 (A) >R (Q = T) > S (B) = T) > (Q = S)
(R
2
(D) =−K mgh − kh
2 (C) >S (Q = T) > R (D) > T > Q > S
R
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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