Elastic Potential Energy - Energy

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If the force you apply to a spring is directly proportional to stretch, how many times would you have to increase your force to get 4 times the stretch?

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Fill in the Blank Notes

Elastic P.E.

work stored in a deformed spring

a) General Equation

PE_s = F x

F = Average Force needed to deform the spring

x = distance deformed (stretch or compress)

Noble and Greenough School HS

Ideal Spring

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b) Hooke's Law

Force needed to deform an ideal spring a given amount is directly proportional to its displacement (deformation).

Hooke's Law illustration
Graphic from Learning-Connections Clipart

Hooke's Law Through History

Explore five ways springs have helped people measure time, weight, motion, and position. Select an image to enlarge it and read the explanation.

Mechanical Watches illustrated explanation — A hairspring keeps a balance wheel oscillating to measure equal intervals of time.

Navigation at Sea illustrated explanation — Accurate spring-controlled clocks helped sailors find their longitude.

Spring Scales illustrated explanation — A spring stretches until its upward force balances the object's weight.

Earthquake Recorders illustrated explanation — A suspended mass and spring help record vibrations of the ground.

Spacecraft Accelerometers illustrated explanation — The displacement of a small test mass helps measure acceleration.

Robert Hooke

'Newton's bitter rival'

Robert Hooke Website

Ex) Ideal Spring

F (Force to Deform) (N)	x (distance deformed) (m)
2.0	0.30
4.0	0.60
6.0	0.90
8.0	1.2

Hooke's Law — University of Colorado PhET

slope = F / x

x = stretch

c) Spring Constant (k) — Ideal Spring

quantifies the stiffness of a spring

k = F / x

(N/m)

Question

What is the spring constant of the spring that produced the data above?

F (N)	x (m)
2.0	0.30
4.0	0.60
6.0	0.90
8.0	1.2

↓

k = 2.0 N / 0.30 m

k = 6.7 N/m

Which is the stiffer spring?

Spring A is the stiffer spring

More force is required for the same stretch

Ex) Plots and k

Pick any point on the line

k = F / x

↓

k = 20. N / 0.40 m

k = 50. N/m

d) Elastic P.E.

= area of the triangle under the F vs x graph

PE_s = (½) base × height

PE_s = 6 Joules

Try This at Home!

What crushed this can?

S.M.U. Physics

The can implodes because the atmospheric pressure is greater than the pressure inside the can.

When the can was submerged in the water it caused the water vapor inside the can to rapidly cool. When a gas is cooled, its pressure goes down. This drop in pressure causes the pressure inside the can to be lower than the atmospheric pressure.

Note: Use less than 1 cm of water in this experiment (about ½ inch).

PE and k →