Energy

Elastic PE and the Spring Constant

Hooke's Law, the Spring Constant k, and Elastic Potential Energy

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Do Now warm-up prompt

Spring Constant (k) - a measure of a spring's stiffness; how much force is needed to stretch or compress it a given distance

What is the shape of a plot that shows a direct square relationship?

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Fill in the Blank Notes

Review - Spring Constant

Spring constant review diagram

PE and k

e) PEs in terms of k — Ideal Spring

1. PEs = Fx

Average Force: F = F/2

2. PE = (F/2)x

substitute F = kx (on reference)

3. PEs = (1/2)(kx)x

(on reference)

PEs = 1/2(kx2)

Ex 1

Given

A force of 12. N stretches a spring and makes it .15 m longer.
Find: a) the spring constant (k) of this spring.

Spring stretching under an applied force
↓

k = F/x = 12. N / .15 m

k = 80. N/m

Spring diagram Spring diagram Spring diagram

Ex 1 (cont.)

Given

b) What is the PE of this spring?

↓

PEs = (1/2)kx2

= 1/2(80. N/m)(.15 m2)

Be sure to use parenthesis when calculating!!

PEs = .90 Joules

Bungee jumper attached to a stretched spring

Ex 2

Given

If 15. joules of energy are stored in the stretched spring below, what is the value of the spring constant?

Spring stretched by 0.50 m storing 15 joules of elastic PE

(on reference)

PEs = 1/2(kx2)

↓

15. J = (1/2)k(.50 m)2

(1/2 in decimal form is .50)

15. J = .50k(.25)

15 = .125k

Divide both sides by .125

k = 120 N/m

What's Wrong With This Picture?

PEs = (1/2)kx2   (x = elongation)

Incorrect PE versus x graph drawn as a straight line

PEs = 1/2(kx2) — PE, x direct square

Plot should be curved

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