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, what happens to the spring?WHY???

Answer Gravitational force (Fg) or the weight of the

mass pulls the spring down (stretches spring). This creates potential ELASTIC energy (energy due to the shape of the spring).

The more mass on the end of the spring, the farther it goes down and the more potential energy it has.

The force from the spring is equal to the force of gravity.

Springs – What happens when you add more weight?

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

xkgmkxmg

22

What kind of energy is this? Potential Energy

Elastic Potential Energy to be exact!

Compression Springs can also compress. If you

compress a spring it can gain potential energy as well. When you let go, the spring transforms the potential elastic energy into another type of energy (kinetic in the case of the push toys).

What else besides springs has elastic potential energy? Diving boards Bows (bow and arrows) Bungee cord

Elastic Energy – Summary Slide Ee = The potential energy that is stored in

elastic/stretchy things like: elastics, springs, diving boards, bungee cords, bows (bow and arrows), etc.

Elastic potential energy is due to the shape of the elastic or spring- either compressed or stretched.

Elastic or Spring Force Summary The force that is used to create the

compression or stretch in the spring/elastic.

This equation will be explained soon

kxFspring

Restoring Force Summary The restoring force is the force that is

needed to put the spring back to equilibrium. It is in the opposite direction of the force that compressed or stretched the spring to store the energy originally.

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

Hooke’s Law The restoring force

is opposite to the applied force. (negative sign)

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

kxFspring

Hooke’s Law (summary slide)

Fspring: Applied force to stretch/compress springx : displacement of the spring from the

equilibrium position (units: m)k: the spring constant (units: N/m)

The spring constant is unique to the spring (similar to coefficient of friction). A large spring or coil has a large k value.

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 (Hooke’s Law) 133 = k(0.71) (sub in values) k = 133/0.71 (rearrange) k = 187.32 N/m 190 N/m

Practice Problems Textbook

Page 258 35-37

http://www.youtube.com/watch?v=yXnbvZx9iWs

Elastic Potential Energy of a Spring (summary) Formula: Ee = ½ kx2

k is the spring constant x is the displacement from

equilibrium position 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 Remember: Energy cannot be created or

destroyed. Using the same equation as before, Ei = Ef,

now we can add another type of energy in:

Eg+Ek+Ee (initial)= Eg+Ek+Ee (final)

In presence of friction: Eg+Ek+Ee (initial)= Eg+Ek+Ee (final)+ Q

Quick Lab – Spring Constant

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 steps 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?

Practice Problems Textbook

Page 261 38-40

Section review (p 261) 1-10