Hooke's Law

Objectives

•  Know that the extension of a spring is proportional to the force applied, within the elastic region.

• Understand the terms elastic region, plastic region and limit of proportionality.

• Be able to calculate the spring constant from a graph of data collected.

Task 1

Forces acting on an object can change their shape as well as make them accelerate. Forces can stretch or squash objects.

A lot of the time forces that change the shape of an object are destructive. Think of car accidents or someone breaking a chair leg. These forces have all squashed or stretched material to breaking point.

However, forces changing the shape of an object can also be put to good use.  Look at this powerpoint presentation which explains a few examples.

Task 2

We are going to carry out an investigation to see how the extension of a spring is connected to the force applied.

Collect the following apparatus and set it up as shown in the diagram:

          • 1 x small spring

          • 1 x metre ruler

          • 1 x clamp + stand

          • 1 x G-clamp

          • 1kg of 100g masses with a mass hanger

Note: • Extended springs can store a lot of energy, so you must wear eye protection at all times. • Be aware that masses suspended above the ground could fall. • The retort stand must be firmly clamped to the desk.  Be aware that it could topple if too much weight is added. • Do not add more than 1kg of mass to your spring.

Carry out the experiment, following the instructions on this sheet and recording your results in the table provided.  Remember to measure the length of the unstretched spring before you start - you will need it to calculate the extensions!

Task 3

Task 4

1. Use your line of fit to find the extension for the following forces:

          a.) 2.5N                   b.) 5N                    c.) 10N

Copy and complete the sentences below in your exercise book:

• A force of 2.5N produces an extension of ______ cm

• A force of 5.0N produces an extension of ______ cm

• A force of 10.0N produces an extension of ______ cm

2. Does the extension double when the force doubles?  Use the numerical examples from question 1 to explain your answer.  What kind of relationship is this?  What features of your graph confirm this?

3. Calculate the gradient of the graph.  Label it "spring constant".  What does this quantity represent?  What will the units be?

Hint: think about the units of the quantities on each axis.

Task 4

You should have found that the extension of the spring is directly proportional to the force applied.  This is known as "Hooke's Law", named after the British scientist Robert Hooke.  Look at this powerpoint presentation which explains some uses of this relationship.

Task 5 - Demonstration

Hooke's law only applies up to a certain point (called the "limit of proportionality"), after which the spring starts to permanently deform.  Your teacher will demonstrate this by loading the spring with more mass.

Safety • Extended springs can store a lot of energy, so you must wear eye protection at all times. • Sit at least 1.5m back from the demonstration.

Sit a reasonable distance away and watch carefully to see what happens beyond the elastic region, in the region of plastic deformation (above the limit of proportionality).