Springs and Hooke’s Law

Physics 11

Springs

A mass-spring system is given below. As mass is added to the end of the spring, how would you expect the spring to stretch?

Springs

mgFg

gmFg 1

gmFg 2

gmFg 3

x x

x

x

springg FF

springF

Springs

2 times the mass results in a 2 times of the displacement from the equilibrium point…

3 time the mass… 3 times the displacement…

springg FF kxFspring

xkgm

kxmg

22

What kind of energy is this?

Potential Energy Elastic Potential Energy to be exact!

What else besides springs has elastic potential energy?

Diving boards Bows (bow and arrows) Bungee cord

Hooke’s Law

Fspring: Applied force

X : displacement of the spring from the equilibrium position (units: m)

K: the spring constant (units: N/m)

kxFspring

Hooke’s Law

the restoring force is opposite the applied force. (negative sign)

Gravity applied in the negative direction, the restoring force is in the positive direction

kxFspring

Example

An archery bow requires a force of 133N to hold an arrow at “full draw” (pulled back 71cm). Assuming that the bow obeys Hooke’s Law, what is its spring constant?

F = kx 133 = k(0.71) k = 133/0.71 k = 187.32 N/m 190 N/m

Restoring Force

The restoring force is the force that is needed to put the spring back to equilibrium.

Example: If you stretch a spring by 0.5m and you had to use 150N of force, the restoring force is -150N.

Practice Problems

Textbook Page 258

35-37

Elastic Potential Energy of a Spring

Formula: Ee = ½ kx2

Units: Joules (J)

Example:

A spring with spring constant 75 N/m is resting on a table.

A) If the spring is compressed a distance of 28cm, what is the increase in its potential energy?

B) What force must be applied to hold the spring in this position?

Answer:

A) Ee = ½ kx2

Ee = ½ (75)(0.28)2

Ee = 2.9 J B) F = kx F= 75(0.28) F = 21 N

Practice Problems

Page 261, questions 38, 39, 40 Page 261 (Section Review)

1, 2, 3, 4, 7

Conservation of Energy with a Spring

Ex. 1: A 4.0 kg block slides across a frictionless table with a velocity of 5.0m/s into a spring with a stiffness of 2500 N/m. How far does the spring compress?

Answer

X = 0.20m

Example 2:

A 70. kg person bungee jumps off a 50.m bridge with his ankles attached to a 15m long bungee cord. Assume the person stops at the edge of the water and he is 2.0m tall, what is the force constant of the bungee cord?

Answer: 64 N/m

Conservation of Energy Worksheet

Practice Problems

Textbook Page 261

38-40 Section review (p 261)

1-10