9781118230725.pdf

defined as the rate at which work is done by a force. In a more general sense,

powerPis the rate at which energy is transferred by a force from one type to

another. If an amount of energy Eis transferred in an amount of time t, the

average powerdue to the force is

(8-40)

Similarly, the instantaneous powerdue to the force is

P (8-41)

dE

dt

.

Pavg

E

t

.

198 CHAPTER 8 POTENTIAL ENERGY AND CONSERVATION OF ENERGY

on the glider to get it moving, a spring force does work on

it, transferring energy from the elastic potential energy of

the compressed spring to kinetic energy of the glider. The

spring force also pushes against a rigid wall. Because there

is friction between the glider and the ground-level track,

the sliding of the glider along that track section increases

their thermal energies.

System:Let’s take the system to contain all the interact-

ing bodies: glider, track, spring, Earth, and wall. Then, be-

cause all the force interactions are withinthe system, the

system is isolatedand thus its total energy cannot change.

So, the equation we should use is not that of some external

force doing work on the system. Rather, it is a conservation

of energy. We write this in the form of Eq. 8-37:

Emec,2Emec,1Eth. (8-42)

This is like a money equation: The final money is equal to

the initial money minusthe amount stolen away by a thief.

Here, the final mechanical energy is equal to the initial me-

chanical energy minusthe amount stolen away by friction.

None has magically appeared or disappeared.

Calculations:Now that we have an equation, let’s find

distanceL. Let subscript 1 correspond to the initial state

of the glider (when it is still on the compressed spring)

and subscript 2 correspond to the final state of the glider

(when it has come to rest on the ground-level track). For

both states, the mechanical energy of the system is the

sum of any potential energy and any kinetic energy.

We have two types of potential energy: the elastic po-

tential energy (Ue^12 kx^2 ) associated with the compressed

Sample Problem 8.06 Lots of energies at an amusement park water slide

Figure 8-17 shows a water-slide ride in which a glider is shot
by a spring along a water-drenched (frictionless) track that
takes the glider from a horizontal section down to ground
level. As the glider then moves along ground-level track, it is
gradually brought to rest by friction. The total mass of the
glider and its rider is m200 kg, the initial compression of
the spring is d5.00 m, the spring constant is k3.20
103 N/m, the initial height is h35.0 m, and the coefficient
of kinetic friction along the ground-level track is mk0.800.
Through what distance Ldoes the glider slide along the
ground-level track until it stops?

KEY IDEAS

Before we touch a calculator and start plugging numbers
into equations, we need to examine all the forces and then
determine what our system should be. Only then can we
decide what equation to write. Do we have an isolated sys-
tem (our equation would be for the conservation of en-
ergy) or a system on which an external force does work
(our equation would relate that work to the system’s
change in energy)?
Forces:The normal force on the glider from the track
does no work on the glider because the direction of this
force is always perpendicular to the direction of the
glider’s displacement. The gravitational force does work
on the glider, and because the force is conservative we can
associate a potential energy with it. As the spring pushes

spring and the gravitational potential energy (Ugmgy) as-

mL

k

m 0

k

h

Figure 8-17A spring-loaded amusement park water slide.

sociated with the glider’s elevation. For the latter, let’s take

ground level as the reference level. That means that the

glider is initially at height yhand finally at height y0.

In the initial state, with the glider stationary and ele-

vated and the spring compressed,the energy is

Emec,1 K 1 Ue 1 Ug 1

 0 ^12 kd^2 mgh. (8-43)