8/10/2019 Potential and Kinetic
1/42
Copyright 2012 Pearson Education Inc.
PowerPointLectures for
Universi ty Physics, Thir teenth Edi t ion
Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Chapter 7
Potential Energy andEnergy Conservation
8/10/2019 Potential and Kinetic
2/42
Copyright 2012 Pearson Education Inc.
Goals for Chapter 7
To use gravitational potential energy for vertical
motion
To use elastic potential energyfor a bodyattached to a spring
To solve problems involving conservativeand
non-conservativeforces
8/10/2019 Potential and Kinetic
3/42
Copyright 2012 Pearson Education Inc.
Potential Energy
Energy associated with a particular positionof a body
when subjected to or acted on by forces.
Field Forces act on bodies even if not touching, like
gravity, magnetism, electricity
Direct Contact forces, like springs
Energy associated with position ispotential energy.
Example: Gravitational potential energyis
Ugrav= mgyfor a position y.
But what is y? Where is y = 0??
Potential Energy is RELATIVE, not absolute
8/10/2019 Potential and Kinetic
4/42
Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity.
8/10/2019 Potential and Kinetic
5/42
Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity.
Work done by Gravity:
+mgDy
8/10/2019 Potential and Kinetic
6/42
Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity.
Work done by Gravity:
+mgDy
InitialPotential Energy:
mgy1
FinalPotential Energy:
mgy2
8/10/2019 Potential and Kinetic
7/42Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity.
Work done by Gravity:
+mgDy
Initial Potential Energy:
mgy1
Final PE:
mgy2
Difference: PEfinalPE initial
(mgy2mgy1)
8/10/2019 Potential and Kinetic
8/42Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity..
8/10/2019 Potential and Kinetic
9/42Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Changein gravitational potential energy is related to
work done by gravity..
Work done by Gravity:
-mgDy
Initial Potential Energy:
mgy1
Final PE:
mgy2
Difference: PEfinalPE initial
(mgy2mgy1)>0
8/10/2019 Potential and Kinetic
10/42Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Either moving DOWN or UP, changein gravitational
potential energy is equalin magnitude and oppositein sign
to work done by gravity.
Work done by Gravity down:mgDy
Difference: PEfinalPE initial
(mgy2mgy
1)< 0
8/10/2019 Potential and Kinetic
11/42Copyright 2012 Pearson Education Inc.
Gravitational potential energy
Either moving DOWN or UP, changein gravitational
potential energy is equalin magnitude and oppositein sign
to work done by gravity.
Work done by Gravity up:-mgDy
Difference: PEfinalPE initial
(mgy2mgy1)>0
8/10/2019 Potential and Kinetic
12/42Copyright 2012 Pearson Education Inc.
The conservation of mechanical energy
The total mechanical energyof a system is thesum of its kinetic energy and potential energy.
A quantity that always has the same value iscalled a conservedquantity.
8/10/2019 Potential and Kinetic
13/42Copyright 2012 Pearson Education Inc.
The conservation of mechanical energy
When onlyforce of gravity does work on a system,total mechanical energy of that system is conserved.
This is an example of the conservation of mechanicalenergy.
Gravity is known as a conservative force
8/10/2019 Potential and Kinetic
14/42
Copyright 2012 Pearson Education Inc.
An example using energy conservation
0.145 kg baseball thrown straight up @ 20m/s. How high?
8/10/2019 Potential and Kinetic
15/42
Copyright 2012 Pearson Education Inc.
An example using energy conservation
0.145 kg baseball thrown straight up @ 20m/s. How high?
Use Energy Bar Graphs to track total, KE, and PE:
8/10/2019 Potential and Kinetic
16/42
Copyright 2012 Pearson Education Inc.
When forces other than gravity do work
Now add the
launch force!(move hand
.50 m upward
while
acceleratingthe ball)
8/10/2019 Potential and Kinetic
17/42
Copyright 2012 Pearson Education Inc.
When forces other than gravity do work
Now add the
launch force!(move hand
.50 m upward
while
acceleratingthe ball)
8/10/2019 Potential and Kinetic
18/42
Copyright 2012 Pearson Education Inc.
Work and energy along a curved path
We can use the same
expression forgravitational
potential energy
whether the bodys
path is curved or
straight.
8/10/2019 Potential and Kinetic
19/42
Copyright 2012 Pearson Education Inc.
Energy in projectile motion example 7.3
Two identical balls leave from the same height with the
same speed but at different angles. Prove they have thesame speed at any height h (neglecting air resistance)
8/10/2019 Potential and Kinetic
20/42
Copyright 2012 Pearson Education Inc.
Motion in a vertical circle with no friction
Speed at bottom of ramp of radius R = 3.00 m?
8/10/2019 Potential and Kinetic
21/42
Copyright 2012 Pearson Education Inc.
Motion in a vertical circle with no friction
Speed at bottom of ramp of radius R = 3.00 m?
8/10/2019 Potential and Kinetic
22/42
Copyright 2012 Pearson Education Inc.
Motion in a vertical circle with no friction
Normal force DOES NO WORK!
8/10/2019 Potential and Kinetic
23/42
Copyright 2012 Pearson Education Inc.
Motion in a vertical circle with friction
Revisit the same ramp as in the previous example, but this time
with friction.
If his speed at bottom is 6.00 m/s, what was work by friction?
8/10/2019 Potential and Kinetic
24/42
Copyright 2012 Pearson Education Inc.
Moving a crate on an inclined plane with friction
Slide 12 kg crate up 2.5
m incline without
friction at 5.0 m/s.
With friction, it goes
only 1.6 m up the slope.
What isfk?
How fast is it moving at
the bottom?
M i i li d l i h f i i
8/10/2019 Potential and Kinetic
25/42
Copyright 2012 Pearson Education Inc.
Moving a crate on an inclined plane with friction
Slide 12 kg crate up 2.5
m incline without
friction at 5.0 m/s.
With friction, it goes
only 1.6 m up the slope.
What isfk?
How fast is it moving at
the bottom?
W k d b i
8/10/2019 Potential and Kinetic
26/42
Copyright 2012 Pearson Education Inc.
Work done by a spring
Work on a block as spring is stretched and compressed.
El ti t ti l
8/10/2019 Potential and Kinetic
27/42
Copyright 2012 Pearson Education Inc.
Elastic potential energy
A body is elasticif it returns
to its original shape after
being deformed.
Elastic potential energyis
the energy stored in an
elastic body, such as a
spring.
The elastic potential energy
stored in an ideal spring is
Uel= 1/2 kx2.
Figure 7.14 at the rightshows a graph of the elastic
potential energy for an idealspring.
Sit ti ith b th it ti l d l ti f
8/10/2019 Potential and Kinetic
28/42
Copyright 2012 Pearson Education Inc.
Situations with both gravitational and elastic forces
When a situation involves both gravitational and elastic forces,
the total potential energy is thesumof the gravitational potential
energy and the elastic potential energy: U = Ugrav+ Uel.
Figure 7.15 below illustrates such a situation.
Follow Problem-Solving Strategy 7.2.
M ti ith l ti t ti l
8/10/2019 Potential and Kinetic
29/42
Copyright 2012 Pearson Education Inc.
Motion with elastic potential energy
Glider of mass 200 g on frictionless air track, connected to spring
with k = 5.00 N/m. Stretch it 10 cm, and release from rest.
What is velocity when x = 0.08 m?
M ti ith l ti t ti l
8/10/2019 Potential and Kinetic
30/42
Copyright 2012 Pearson Education Inc.
Motion with elastic potential energy
Glider of mass 200 g on frictionless air track, connected to spring
with k = 5.00 N/m. Stretch it 10 cm, and release from rest.
What is velocity when x = 0.08 m?
A t h i t t ti l i d f i ti
8/10/2019 Potential and Kinetic
31/42
Copyright 2012 Pearson Education Inc.
A system having two potential energies and friction
Gravity, a spring,
andfriction all act on
the elevator.
2000 kg elevator
with broken cables
moving at 4.00 m/s
Contacts spring at
bottom, compressing
it 2.00 m.
Safety clamp applies
constant 17,000 N
friction force as it
falls.
A t h i t t ti l i d f i ti
8/10/2019 Potential and Kinetic
32/42
Copyright 2012 Pearson Education Inc.
A system having two potential energies and friction
What is the spri ng
constant kfor the
spring so it stops in
2.00 meters?
C ti d ti f
8/10/2019 Potential and Kinetic
33/42
Copyright 2012 Pearson Education Inc.
Conservative and nonconservative forces
A conservative forceallows conversion between kinetic and
potential energy. Gravity and the spring force are
conservative.
The workdone between two points by any conservative forcea) can be expressed in terms of a potential energy function.
b) is reversible.
c) is independentof the pathbetween the two points.
d) is zero if the starting and ending points are the same.
Conservative and nonconservative forces
8/10/2019 Potential and Kinetic
34/42
Copyright 2012 Pearson Education Inc.
Conservative and nonconservative forces
A conservative forceallows conversion between kinetic and
potential energy. Gravity and the spring force are
conservative.
A force (such as friction) that is not conservative is called a
non-conservative force, or a dissipativeforce.
Frictional work depends on the path
8/10/2019 Potential and Kinetic
35/42
Copyright 2012 Pearson Education Inc.
Frictional work depends on the path
Move 40.0 kg futon 2.50 m across room; slide it
along paths shown. How much work required ifmk= .200
Conservative or nonconservative force?
8/10/2019 Potential and Kinetic
36/42
Copyright 2012 Pearson Education Inc.
Conservative or nonconservative force?
Suppose force F = Cx in the y direction. What is work
required in a round trip around square of length L?
Conservation of energy
8/10/2019 Potential and Kinetic
37/42
Copyright 2012 Pearson Education Inc.
Conservation of energy
Nonconservative forces do not store potential
energy, but they do change the internal energyof asystem.
The law of the conservation of energymeans that
energy is never created or destroyed; it only changesform.
This law can be expressed as DK+ DU + DUint= 0.
Force and potential energy in one dimension
8/10/2019 Potential and Kinetic
38/42
Copyright 2012 Pearson Education Inc.
Force and potential energy in one dimension
In one dimension, a conservative force can be obtained from
its potential energy function using
Fx(x) = dU(x)/dx
Force and potential energy in one dimension
8/10/2019 Potential and Kinetic
39/42
Copyright 2012 Pearson Education Inc.
Force and potential energy in one dimension
In one dimension, a conservative force can be obtained from
its potential energy function using
Fx(x) = dU(x)/dx
Force and potential energy in two dimensions
8/10/2019 Potential and Kinetic
40/42
Copyright 2012 Pearson Education Inc.
Force and potential energy in two dimensions
In two dimension, the components of a conservative
force can be obtained from its potential energyfunction using
Fx=U/dx and Fy=U/dy
Energy diagrams
8/10/2019 Potential and Kinetic
41/42
Copyright 2012 Pearson Education Inc.
Energy diagrams
An energy diagramis a
graph that shows both the
potential-energy function
U(x) and the total
mechanical energyE.
Force and a graph of its potential-energy function
8/10/2019 Potential and Kinetic
42/42
Force and a graph of its potential energy function
Top Related