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8-1 POTENTIAL ENERGY 183

Checkpoint 2

A particle is to move along an xaxis from x0 to x 1 while a conser-

vative force, directed along the xaxis, acts on the particle. The figure

shows three situations in which the xcomponent of that force varies

withx. The force has the same maximum magnitude F 1 in all three sit-

uations. Rank the situations according to the change in the associated

potential energy during the particle’s motion, most positive first.

F 1 F 1

• F 1

x 1

x 1 x 1

( 1 )( 2 )( 3 )

the ground, (3) at the limb, and (4) 1.0 m above the limb?

Take the gravitational potential energy to be zero at y0.

KEY IDEA

Once we have chosen the reference point for y0, we can

calculate the gravitational potential energy Uof the system

relative to that reference pointwith Eq. 8-9.

Calculations:For choice (1) the sloth is at y5.0 m, and

Umgy(2.0 kg)(9.8 m/s^2 )(5.0 m)

98 J. (Answer)

For the other choices, the values of Uare

(2) Umgymg(2.0 m)39 J,

(3) Umgymg(0)0J,

(4) Umgymg(1.0 m)

19.6 J20 J. (Answer)

(b) The sloth drops to the ground. For each choice of refer-

ence point, what is the change Uin the potential energy of

the sloth – Earth system due to the fall?

KEY IDEA

The changein potential energy does not depend on the

choice of the reference point for y0; instead, it depends

on the change in height y.

Calculation:For all four situations, we have the same y

5.0 m. Thus, for (1) to (4), Eq. 8-7 tells us that

Umgy(2.0 kg)(9.8 m/s^2 )(5.0 m)

98 J. (Answer)

Sample Problem 8.02 Choosing reference level for gravitational potential energy, sloth

Here is an example with this lesson plan: Generally you can
choose any level to be the reference level, but once chosen,
be consistent. A 2.0 kg sloth hangs 5.0 m above the ground
(Fig. 8-6).

(a) What is the gravitational potential energy U of the
sloth – Earth system if we take the reference point y0 to be
(1) at the ground, (2) at a balcony floor that is 3.0 m above

Additional examples, video, and practice available at WileyPLUS

0 –3 –5 –6

3 0 –2 –3

5 2 0

6 3 1 0

(1) (2) (3) (4)

Figure 8-6Four choices of reference point y0. Each yaxis is marked
in units of meters. The choice affects the value of the potential energy
Uof the sloth – Earth system. However, it does not affect the change
Uin potential energy of the system if the sloth moves by, say, falling.

becomes

which gives us

U(x)^12 kx^2 (elastic potential energy). (8-11)

U 0 ^12 kx^2 0,