13.1 Work, Mechanical Energy, Thermal Energy 375

the gravitational pull of the earth on the object (see Figure 13.2). The change in the potential

energy of the object when its elevation is changed is given by

(13.4)

where

mmass of the object (kg)

gacceleration due to gravity (9.81 m/s

2

)

¢hchange in the elevation ( m)

The SI unit for potential energy is also joule, a derived unit, and is obtained by substitut-

ing kg for the units of mass, and m/s

2

for the units of acceleration due to gravity, and m for the

elevation change:

In the British Gravitational U.S. Customary systems, the unit of potential energy is expressed

in lbf ft. As in the case with kinetic energy, keep in mind that it is the change in the poten-

tial energy that is of significance in engineering calculations. For example, the energy required

to lift an elevator from the first floor to the second floor is the same as lifting the elevator from

the third floor to the fourth floor, provided that the distance between each floor is the same.

Example 13.2 Calculate the energy required to lift an elevator and its occupant with a mass of 2000 kg for the

following situations: (a) between the first and the second floor,

(b) between the third and the fourth floor, (c) between the first

and the fourth floor. (See Figure 13.3.) The vertical distance

between each floor is 4.5 m.

We can use Equation (13.4) to analyze this problem; the

energy required to lift the elevator is equal to the change in its

potential energy, starting with

(a) change in potential energy mg¢h

(b) change in potential energy mg¢h

(c) change in potential energy mg¢h

 1 2000 kg2a9.81

m

s

2 b113.5 m^2 264,870 J

 1 2000 kg2a9.81

m

s

2 b14.5 m^2 88,290 J

 1 2000 kg2a9.81

m

s

2 b14.5 m^2 88,290 J

potential energymgh 1 kg2a

m

s

2 b1m^2 N

#mJ

d

N

change in potential energy¢PEmg ¢h

h

m

m

■Figure 13.2

Change in potential energy of

an object.

m

h = 4.5 m

m

h = 4.5 m

m

h = 4.5 m

m

1

2

3

4

■Figure 13.3

A schematic diagram for

Example 13.2.

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