Elastic Energy

Springy!

Elastic Potential

• Elastic PE is the energy stored in elastic materials as the result of their stretching or compressing.

Elastic Potential Energyo Rubber band—stretching it stores energyo Paddle ball—elastic band stores energy, then transfers

from paddle to ball.o Bouncing balls—rebound off of a hard surface—height of

bounce is determined by the elasticity of the ball

Notice the ball compressingand expanding

BUNGEE jumping utilizes a long elastic strap which stretches until it reaches a maximum length that is proportional to the weight of the jumper. The elasticity of the strap determines the amplitude of the resulting vibrations. If the elastic limit for the strap is exceeded, the rope will break.

Elasticity example—bungee!Elasticity example—bungee!

Photo © Vol. 10 PhotoDisk/Getty

Elastic Properties of Matter

An elastic body is one that returns to its original shape after a deformation.

An elastic body is one that returns to its original shape after a deformation.

Golf Ball Soccer BallRubber Band

Elastic Properties of Matter

An inelastic body is one that does not return to its original shape after a deformation.

An inelastic body is one that does not return to its original shape after a deformation.

Dough or BreadDough or Bread ClayClay Inelastic BallInelastic Ball

Elastic or Inelastic?

An elastic collision loses no energy. The deform-ation on collision is fully restored.

In an inelastic collision, energy is lost and the deformation may be permanent. (Click it.)

Example: A spring!

An Elastic SpringAA spring spring is an example of an elastic body that can is an example of an elastic body that can be deformed by stretching.be deformed by stretching.

A restoring force, F, acts in the direction opposite the displacement of the oscillating body.

F = -kx

A restoring force, F, acts in the direction opposite the displacement of the oscillating body.

F = -kx

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Hooke’s LawWhen a spring is stretched, there is a When a spring is stretched, there is a

restoringrestoring force that is proportional to the force that is proportional to the displacement.displacement.

F = -kxF = -kx

The spring constant k is a The spring constant k is a property of the spring given property of the spring given by:by:

F

x

m

Fk

x

Fk

x

The spring constant k is a measure of the elasticity of the spring.The spring constant k is a measure of the elasticity of the spring.

Example: Bow Energy Transfer

Procedure

1. Hold up bow and put arrow on string

2. Place fingers on string and pull string back

3. Anchor string and hand under the chin

4. Take aim

5. Release the string

6. Arrow hits target (hopefully!!!)

Can you identify the stages in these energy transfers?

Draw a Sankey diagram to show this.

Bow Energy Transfer (solution)

Procedure

1. Hold up bow and put arrow on string

2. Place fingers on string and pull string back

3. Anchor string and hand under the chin

4. Take aim

5. Release the string

6. Arrow hits target (hopefully!!!)

Main Energy transfer

Chemical in arm to kinetic in arm, string & limbs

Kinetic in arm & string to elastic potential in limbs

Elastic potential in limbs to kinetic in string, limbs and arrow

Kinetic in arrow and sound in limbs

Kinetic in arrow to heat and sound in target

Chemical in arm

Bow Energy Transfer (solution)

Kinetic in arm, string, & limbs

Sound in limbs; heat in arms; heat in limbs & string

Elastic potential in limbs

Kinetic in arrow

Heat and sound in target

Kinetic in string; sound in limbs and string; heat in limbs

Heat and sound of arrow in flight

Sankey Diagram Showing Losses

If Robin Hood had been Written by an Engineer.... And Robin didst slowly and with great determination put potential

energy equal to the work of his muscles into an elastic storage device.

And therewith Robin the Bold and Valiant didst convert this stored energy most quickly, efficiently, and accurately into the velocity of a sturdy and pointed dart (oft called arrow) such that almost all of its former potential energy didst become kinetic. Then this speedy dart didst split an arrow (oft called dart) already buried in most distant

target, having been previously hurled there at an equally great speed by a similar conversion of stored energy.

Summary: Elastic and Inelastic

An inelastic body is one that does not return to its original shape after a deformation.

An inelastic body is one that does not return to its original shape after a deformation.

In an inelastic collision, energy is lost and the deformation may be permanent.

An elastic collision loses no energy. The deform-ation on collision is fully restored.

An elastic body is one that returns to its original shape after a deformation.An elastic body is one that returns to its original shape after a deformation.