9781118230725.pdf

Conservation of Mechanical Energy

The mechanical energyEmecof a system is the sum of its potential energy Uand

the kinetic energy Kof the objects within it:

EmecKU (mechanical energy). (8-12)

In this module, we examine what happens to this mechanical energy when only

conservative forces cause energy transfers within the system — that is, when

frictional and drag forces do not act on the objects in the system. Also, we shall

assume that the system is isolatedfrom its environment; that is, no external force

from an object outside the system causes energy changes inside the system.

When a conservative force does work Won an object within the system, that

force transfers energy between kinetic energy Kof the object and potential

energyUof the system. From Eq. 7-10, the change Kin kinetic energy is

KW (8-13)

and from Eq. 8-1, the change Uin potential energy is

UW. (8-14)

Combining Eqs. 8-13 and 8-14, we find that

KU. (8-15)

In words, one of these energies increases exactly as much as the other decreases.

We can rewrite Eq. 8-15 as

K 2 K 1 (U 2 U 1 ), (8-16)

where the subscripts refer to two different instants and thus to two different

arrangements of the objects in the system. Rearranging Eq. 8-16 yields

K 2 U 2 K 1 U 1 (conservation of mechanical energy). (8-17)

In words, this equation says:



the sum of K and U for

any state of a system 

the sum of K and U for

any other state of the system,

184 CHAPTER 8 POTENTIAL ENERGY AND CONSERVATION OF ENERGY

8-2CONSERVATION OF MECHANICAL ENERGY

After reading this module, you should be able to...

8.05After first clearly defining which objects form a system,
identify that the mechanical energy of the system is the
sum of the kinetic energies and potential energies of those
objects.

8.06For an isolated system in which only conservative forces

act, apply the conservation of mechanical energy to relate

the initial potential and kinetic energies to the potential and

kinetic energies at a later instant.

Learning Objectives

Key Ideas

●The mechanical energy Emecof a system is the sum of its
kinetic energy Kand potential energy U:

EmecKU.

●An isolated system is one in which no external force causes
energy changes. If only conservative forces do work within
an isolated system, then the mechanical energy Emecof the

system cannot change. This principle of conservation of

mechanical energy is written as

K 2 U 2 K 1 U 1 ,

in which the subscripts refer to different instants during an

energy transfer process. This conservation principle can also

be written as

EmecKU0.

©AP/Wide World Photos

In olden days, a person would be tossed
via a blanket to be able to see farther
over the flat terrain. Nowadays, it is
done just for fun. During the ascent of
the person in the photograph, energy is
transferred from kinetic energy to gravita-
tional potential energy. The maximum
height is reached when that transfer is
complete. Then the transfer is reversed
during the fall.