Energy 4 – Elastic EnergyEnergy 4 – Elastic Energy

Mr. JeanMr. Jean

Physics 11Physics 11

The plan:The plan:

Video clip of the dayVideo clip of the day Potential EnergyPotential Energy Kinetic EnergyKinetic Energy Restoring forcesRestoring forces Hooke’s LawHooke’s Law Elastic Potential EnergyElastic Potential Energy

Elastic Potential Energy in SpringsElastic Potential Energy in Springs

If you pull on a spring and If you pull on a spring and stretch it out, you do work stretch it out, you do work on the spring.on the spring.

W = FdW = Fd Since work is a transfer of Since work is a transfer of

energy, then energy must energy, then energy must be transferred into the be transferred into the spring.spring.

Work becomes stored in the Work becomes stored in the spring as potential energy.spring as potential energy.

When you stretch a spring, it When you stretch a spring, it has the potential to “spring” has the potential to “spring” back. This is stored energy.back. This is stored energy.

When you compress a spring, When you compress a spring, it has the potential to “spring” it has the potential to “spring” forwards. This is stored forwards. This is stored energy.energy.

Work & Elastic Potential Energy:Work & Elastic Potential Energy:

EEee = ½ k x = ½ k x22

EEee = elastic potential energy in J (joules) = elastic potential energy in J (joules)

k = spring constant N/m (Newtons per meters)k = spring constant N/m (Newtons per meters) x = length of extension m (meters)x = length of extension m (meters)

Energy Stored in a SpringEnergy Stored in a Spring If a spring’s stretch/compression is directly If a spring’s stretch/compression is directly

proportional to the the amount of force applied proportional to the the amount of force applied to it then the elastic potential energy stored in a to it then the elastic potential energy stored in a spring is given by:spring is given by:

Where x is the Where x is the DISTANCEDISTANCE the spring is the spring is stretched or compressedstretched or compressed

K is called a “spring constant”. K is called a “spring constant”.

If a spring is not stretched or compressed, then If a spring is not stretched or compressed, then there is no energy stored in it.there is no energy stored in it.

It is in its equilibrium position. (it’s natural It is in its equilibrium position. (it’s natural position)position)

Hooke’s Law:Hooke’s Law:

ProblemProblem It requires 100 J of work to stretch a spring It requires 100 J of work to stretch a spring

out 0.10 m. Find the spring constant of out 0.10 m. Find the spring constant of the spring.the spring.

Hookes Law:Hookes Law: The force exerted by a The force exerted by a spring is proportional to the distance spring is proportional to the distance the spring is stretched or compressed the spring is stretched or compressed from its relaxed position.from its relaxed position.

FFXX = -k x = -k x Where Where xx is the displacement from is the displacement from the the

relaxed position and relaxed position and kk is the is the constant of constant of proportionality.proportionality.

(often called “spring constant”)(often called “spring constant”)

x > 0

kmJ

km

J

mkJ

mkJ

kxEe

2

2

2

2

2

/20000

010.0

200

)010.0(200

)10.0(2

1100

2

1

At Rest:At Rest:

m

xx=0

Extended (Potential Energy)Extended (Potential Energy)

m

xx=0

Compressed (Potential Energy)Compressed (Potential Energy)

m

xx=0

Conservation of Energy:Conservation of Energy:

m

xx=0

Etotal = 1/2 mv2 + 1/2 kx2 = constant

KE PE

Conservation of Energy:Conservation of Energy:

EEk1k1 + E + Ep1p1 + E + Ee1e1 = E = Ek2k2 + E + Ep2p2 + E + Ee2e2

EEk1k1 = kinetic energy before event (J) = kinetic energy before event (J)

EEp1p1 = gravitational potential energy before event (J) = gravitational potential energy before event (J)

EEe1 e1 = elastic potential energy before event. (J)= elastic potential energy before event. (J)

EEk2k2 = kinetic energy after event (J) = kinetic energy after event (J)

EEp2p2 = gravitational potential energy after event (J) = gravitational potential energy after event (J)

EEe2 e2 = elastic potential energy after event. (J)= elastic potential energy after event. (J)

Questions to do:Questions to do:

Hooke’s Law Investigation:Hooke’s Law Investigation:

Tomorrow we are doing a mini-lab on Tomorrow we are doing a mini-lab on Hooke’s law and spring constants. Hooke’s law and spring constants.