9781118230725.pdf

Conservation of Energy

We now have discussed several situations in which energy is transferred to or
from objects and systems, much like money is transferred between accounts.
In each situation we assume that the energy that was involved could always be
accounted for; that is, energy could not magically appear or disappear. In more
formal language, we assumed (correctly) that energy obeys a law called the law of
conservation of energy,which is concerned with the total energyEof a system.
That total is the sum of the system’s mechanical energy, thermal energy, and any
type of internal energyin addition to thermal energy. (We have not yet discussed
other types of internal energy.) The law states that

8-5 CONSERVATION OF ENERGY 195

The total energy Eof a system can change only by amounts of energy that are

transferred to or from the system.

8-5CONSERVATION OF ENERGY

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

8.15For an isolated system (no net external force), apply the
conservation of energy to relate the initial total energy
(energies of all kinds) to the total energy at a later instant.
8.16For a nonisolated system, relate the work done on the
system by a net external force to the changes in the vari-
ous types of energies within the system.

8.17 Apply the relationship between average power, the

associated energy transfer, and the time interval in which

that transfer is made.

8.18Given an energy transfer as a function of time (either as

an equation or a graph), determine the instantaneous

power (the transfer at any given instant).

Learning Objectives

●The total energy Eof a system (the sum of its mechanical

energy and its internal energies, including thermal energy)

can change only by amounts of energy that are transferred to

or from the system. This experimental fact is known as the law

of conservation of energy.

●If work Wis done on the system, then

WEEmecEthEint.

If the system is isolated (W 0 ), this gives

EmecEthEint 0

and Emec,2Emec,1EthEint,

where the subscripts 1 and 2 refer to two different instants.

●The power due to a force is the rateat which that force

transfers energy. If an amount of energy Eis transferred by

a force in an amount of time t, the average power of the

force is

●The instantaneous power due to a force is

On a graph of energy Eversus time t, the power is the slope

of the plot at any given time.

P

dE

dt

.

Pavg

E

t

.

Key Ideas

The only type of energy transfer that we have considered is work Wdone on a
system by an external force. Thus, for us at this point, this law states that

WEEmecEthEint, (8-35)

whereEmecis any change in the mechanical energy of the system,Ethis any
change in the thermal energy of the system, and Eintis any change in any
other type of internal energy of the system. Included in Emecare changes Kin
kinetic energy and changes Uin potential energy (elastic, gravitational, or any
other type we might find).
This law of conservation of energy is notsomething we have derived from
basic physics principles. Rather, it is a law based on countless experiments.