Ch06 pt 2

6.3 Gravitational Potential Energy
( )sFW θcos=
( )fo hhmgW −=gravity

Example 7 A Gymnast on a Trampoline
The gymnast leaves the trampoline at an initial height of 1.20 m
and reaches a maximum height of 4.80 m before falling back
down. What was the initial speed of the gymnast?

2
2
12
f2
1
W omvmv −=
( ) 2
2
1
ofo mvhhmg −=−
( )foo hhgv −−= 2
( )( ) sm40.8m80.4m20.1sm80.92 2
=−−=ov

fo mghmghW −=gravity
DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY
The gravitational potential energy PE is the energy that an
object of mass m has by virtue of its position relative to the
surface of the earth. That position is measured by the height
h of the object relative to an arbitrary zero level:
mgh=PE
( )Jjoule1mN1 =⋅

6.4 Conservative Versus Nonconservative Forces
DEFINITION OF A CONSERVATIVE FORCE
Version 1 A force is conservative when the work it does
on a moving object is independent of the path between the
object’s initial and final positions.
Version 2 A force is conservative when it does no work
on an object moving around a closed path, starting and
finishing at the same point.

Version 1 A force is conservative when the work it does
on a moving object is independent of the path between the
object’s initial and final positions.

Version 2 A force is conservative when it does no work
on an object moving around a closed path, starting and
finishing at the same point.
fo hh =( )fo hhmgW −=gravity

An example of a nonconservative force is the kinetic
frictional force.
( ) sfsfsFW kk −=== 
180coscosθ
Work done by the kinetic frictional force is always negative.
So, it’s impossible for the work it does on an object that
moves around a closed path to be zero.
The concept of potential energy is not defined for a
Non-conservative force.

In normal situations both conservative and nonconservative
forces act simultaneously on an object, so the work done by
the net external force can be written as
ncc WWW +=
KEKEKE of ∆=−=W
PEPEPE fogravity ∆−=−=−== foc mghmghWW

ncc WWW +=
ncW+∆−=∆ PEKE
THE WORK-ENERGY THEOREM
PEKE ∆+∆=ncW

6.5 The Conservation of Mechanical Energy
( ) ( )ofof PEPEKEKEPEKE −+−=∆+∆=ncW
( ) ( )f f o oKE PE KE PEncW = + − +
of EE −=ncW
If the net work on an object by nonconservative forces
is zero, then its energy does not change:
of EE =

THE PRINCIPLE OF CONSERVATION OF
MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an object
remains constant as the object moves, provided that the net
work done by external nononservative forces is zero.

Example 8 A Daredevil Motorcyclist
A motorcyclist is trying to leap across the canyon by driving
horizontally off a cliff at 38.0 m/s. Ignoring air resistance, find
the speed with which the cycle strikes the ground on the other
side.

of EE =
2
2
12
2
1
ooff mvmghmvmgh +=+
2
2
12
2
1
ooff vghvgh +=+

2
2
12
2
1
ooff vghvgh +=+
( ) 2
2 ofof vhhgv +−=
( )( ) ( ) sm2.46sm0.38m0.35sm8.92
22
=+=fv

Ch06 pt 2

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Ch06 pt 2