Potential EnergyPotential Energy

HeightHeight

Work is a process.Work is a process. When a box is lifted, work is done on the box.When a box is lifted, work is done on the box. At the end, the box is resting – no kinetic energy.At the end, the box is resting – no kinetic energy. Where did the work go?Where did the work go?

y1

F = mg h

mghyymgW )( 12

y2

Energy ChangeEnergy Change

The state of the object changesThe state of the object changes• The box is higher after the work was doneThe box is higher after the work was done• Work can be stored in a new positionWork can be stored in a new position

y1h

mghyymgW )( 12

y2

Work from HeightWork from Height

The box can move down from its height and do work.The box can move down from its height and do work.

• The work done by gravity is converted to kinetic energyThe work done by gravity is converted to kinetic energy• The work done by gravity is opposed by some other force, The work done by gravity is opposed by some other force,

and less work is doneand less work is done

y1

F = mg h

2

12

)2/1(

)(

mvKW

mghyymgW

y2

Elastic EnergyElastic Energy

As a spring compresses work is As a spring compresses work is done.done.

• Work done by gravity on the ball, Work done by gravity on the ball, WW = = mghmgh

• Work done by the spring on the Work done by the spring on the ball, ball, WW = = (1/2)(1/2)kxkx22

• Work done by the spring to Work done by the spring to return the ball, return the ball, WW = (1/2) = (1/2)kxkx22

There is an elastic energy.There is an elastic energy.

-y

Fg = mg

Fs = k(y)

PotentialsPotentials

Energy due to position is called Energy due to position is called potential energy potential energy ((UU).).• An object has the potential to do workAn object has the potential to do work

Since the work isn’t done yet, Since the work isn’t done yet, UU = = WWintint..

• WWintint is the force acting internally to the object is the force acting internally to the object

The potential energy of gravity: The potential energy of gravity: UU = = mgymgy

The potential energy of a spring: The potential energy of a spring: UU = (1/2) = (1/2)kxkx22

No AbsoluteNo Absolute

The work done on an object from a force only reflects The work done on an object from a force only reflects a change in the state of the object.a change in the state of the object.• Work is a processWork is a process• Energy is a stateEnergy is a state

Potential energy reflects the work that may be done.Potential energy reflects the work that may be done.• The point The point UU = 0 is arbitrary = 0 is arbitrary• For instance, experiment at the top of a building of height For instance, experiment at the top of a building of height hh, ,

UU = = mgmg((yy++hh) = ) = mgymgy + + mghmgh = = mgymgy + + CC

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