Hooke’s Law

Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched.

Recall: How does a spring stretch when a force is applied to it?

Try stretching a piece of thin copper wire and an elastic.

How do they differ from the springs?

What does it feel like as you pull harder and harder?

Can you sketch a graph to show how the force affects the extension.

How different materials behave

Elastic and wire

Different materials react differently when a force is applied to them.

How does a spring behave?

Aim: We shall conduct an experiment to determine how the extension of a spring varies with the stretching force.

A spring is hung vertically from a fixed point and a force is applied in stages by hanging weights from the spring.

Extension = present length – original length

Diagram The apparatus is set

up as shown. For the purposes of this experiment we shall be using loads of 100g, and the extension of the spring shall be measured in metres.

Method: What is the independent

variable? (range?)

What is the dependent variable? ( How will this be measured accurately?)

What are the control variables?

Table:

single spring Equilibrium

length __________m

Total Hangi

ng Mass

(g)

Total Hangi

ng Mass

(kg)

Total force (mg) g= 10 N/kg

Stretched length (m)

Extension (m)

100      

200      

300      

400      

500      

600      

700      

800      

900      

1000

1600      

 

Graph: Plot a graph of force against extension.

Conclusion: Comment on the shape of the

best fit line, try to describe the pattern which appears. Have you found any simple rule for springs?

What happened to the stretch when you doubled the load? And three times?

Can you work out the gradient? What does this gradient mean?

What happens when large loads are added to the spring?

How would the plot look if you replaced the spring with a stiffer spring? weaker spring?

For

ce (

N)

Extension (m)

Hooke’s Law

"Hooke's Law" is about stretching springs and wires.

Hooke's Law states:- the extension is proportional to the force

the spring will go back to its original length when the force is removed

so long as we don't exceed the elastic limit.

Elastic Limit

Below the elastic limit, we say that the spring is showing "elastic behaviour": the extension is proportional to the force, and it'll go back to it's original length when we remove the force.

Beyond the elastic limit, we say that it shows "plastic behaviour". This means that when a force is applied to deform the shape, it stays deformed when the force is removed.

Elastic limit

Elas

tic b

ehav

iour

Plastic behaviour

Repeat the experiment using an elastic

What do you notice?

Does an elastic obey Hooke’s Law?

Class Experiment – Stretching a wire – Vernier Scale Two wires of the same

material are suspended side by side from the same support. The main scale is kept taut by the weight L. The extension of the wire for different loads is obtained from the vernier.

Elastic and wire Different materials react

differently when a force is applied to them.

If a material obeys Hooke's Law, its extension is proportional to the applied force. If the force is removed, the material returns to its original length.

Springs and metal wire obey Hooke's law up to the elastic limit. Beyond this point, they are permanently deformed. They will not return to its original length when the force is removed.

copper

rubberF

F

e

e

HysteresisrubberF What do you notice about

the plot when you load and unload an elastic?

What does the area under a graph represent?

ENERGY!!! See for yourself!! – Take

an elastic and repeatedly stretch the elastic while it is in contact with your top lip.

What do you notice? How could this energy be

measured from the graph?