Potential and Kinetic

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


2/42


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


3/42


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


4/42


Gravitational potential energy

Changein gravitational potential energy is related to

work done by gravity.


5/42





Work done by Gravity:

+mgDy


6/42






+mgDy

InitialPotential Energy:

mgy1

FinalPotential Energy:

mgy2


7/42Copyright 2012 Pearson Education Inc.





+mgDy

Initial Potential Energy:

mgy1

Final PE:

mgy2

Difference: PEfinalPE initial

(mgy2mgy1)





work done by gravity..





work done by gravity..


-mgDy

Initial Potential Energy:

mgy1

Final PE:

mgy2


(mgy2mgy1)>0




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


(mgy2mgy

1)< 0




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


(mgy2mgy1)>0



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.



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


14/42


An example using energy conservation

0.145 kg baseball thrown straight up @ 20m/s. How high?


15/42


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:


16/42


When forces other than gravity do work

Now add the

launch force!(move hand

.50 m upward

while

acceleratingthe ball)


17/42


When forces other than gravity do work

Now add the

launch force!(move hand

.50 m upward

while

acceleratingthe ball)


18/42


Work and energy along a curved path

We can use the same

expression forgravitational

potential energy

whether the bodys

path is curved or

straight.


19/42


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)


20/42


Motion in a vertical circle with no friction

Speed at bottom of ramp of radius R = 3.00 m?


21/42



Speed at bottom of ramp of radius R = 3.00 m?


22/42



Normal force DOES NO WORK!


23/42


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?


24/42


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


25/42


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


26/42


Work done by a spring

Work on a block as spring is stretched and compressed.

El ti t ti l


27/42


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


28/42


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


29/42


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


30/42


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


31/42


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


32/42


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


33/42


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.



34/42



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


35/42


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?


36/42


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


37/42


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


38/42



In one dimension, a conservative force can be obtained from

its potential energy function using

Fx(x) = dU(x)/dx



39/42



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


40/42


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


41/42


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


42/42

Force and a graph of its potential energy function

Potential and Kinetic

Documents

Transcript of Potential and Kinetic