Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

378 Chapter 13 Energy and Power

Conservation of Mechanical Energy

In the absence of heat transfer, and assuming negligible losses and no work, the conservation of

mechanical energystates that the total mechanical energy of a system is constant. Stated another way,

the change in the kinetic energy of the object, plus the change in the elastic energy, plus the change

in the potential energy of the object is zero. This statement is represented mathematically as follows.

(13.7)

Equation (13.7) states that energy content of a system can change form, but the total energy

content of the system is constant.

Example 13.4 In a manufacturing process, carts are rolling down an inclined surface, as shown in Figure 13.7.

Estimate the height from which the cart must be released so that, as it reaches pointA, the cart

has a velocity of 2.5 m/s. Neglect rolling friction.

¢KE¢PE¢EE 0

H

1

2

A

■Figure 13.7 A schematic diagram for Example 13.4.

We can solve this problem using Equation (13.7)

And solving forHwe have

Note, the minus sign associated with change in potential energy indicates (shows) that poten-

tial energy of the cart is decreasing.

H0.318 m

1

2

m 1 2.5 m/s 2

2

ma9.81

m

s

2 bH^0

¢PEmg ¢hma9.81

m

s

2 bH

¢EE 0

¢KE

1

2

mV

2

2 

1

2

mV

2

1 

1

2

m 1 2.5 m/s 2

2

 0

¢KE¢PE¢EE 0

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