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Elastic materials, such as rubber bands and springs, are flexible and return to their original shape once force is no longer applied. Any elastic material has a **limit of proportionality** - once this point has been passed, the material will lose all or part of its elasticity and will not return to its original size and shape. Elastic materials can also store energy. This **elastic potential energy** can then be used to drive other devices, such as wind-up toys and wind-up watches.

Elastic potential energy is the energy stored in an elastic object which will restore the object to its original shape - the force it creates is called the **restoring force**.

You can think of elastic potential energy as being similar to gravitational potential energy but it depends on the nature of the substance rather than on gravity. It's not just stretching that generates elastic potential energy, compression does too. When an elastic ball like a squash ball, football or basketball hits the ground, it is compressed and contains more elastic potential energy than before the impact. Work is done to generate the stored energy, so the ball becomes hotter. This is most noticeable with a squash ball - squash players always warm the ball thoroughly before starting the game to ensure that it becomes even more elastic and bounces better. They do this either by hitting it around the court a lot or sometimes, when the weather and the court is particularly cold, putting it in hot water for a few minutes!

When a force is applied to an elastic object, it stretches. When the force is doubled, the amount stretched is doubled and so on. We say that the stretch is **directly proportional** to the force applied. This was discovered by scientist Robert Hooke in the seventeenth century. We now know that this law is only an approximation and as the **elastic limit** is approached, Hooke's law ceases to work but it is good enough to be applied in many everyday situations. Mathematically, Hooke's law can be written as *F = k e* where *F* is the force (in newtons) required to extend a spring by a distance *e* which is small compared to the total possible stretch of the spring (in meters) and *k* is the spring constant (in newtons per meter) for that particular spring. This equation is also used to work out the restoring force.

You may have carried out some experiments using springs in which you have loaded a spring with masses and measured the extension. When you plot a graph from the readings, at first the graph is a straight line whose gradient is the spring constant. At the limit of proportionality, the gradient suddenly changes and becomes much steeper.

1.

A force acting on an object can do what to it?

Change its shape

Make it breakfast

Have no effect on it

Not allow the object to get married

A nice easy start. Remember that forces can do many more things to objects such as change its direction of movement and stop or start movement

2.

If a force acts on an elastic object stretching the object, what kind of energy is stored within the object?

Gravitational potential energy

Tidal energy

Chemical energy

Elastic potential energy

Any elastic device will always store energy as elastic potential energy when a force is applied to it

3.

Which of the following items can store elastic potential energy?

A paper clip

A pencil

A rubber band

A USB pen drive

It is the only one with elastic properties

4.

How is the extension of an elastic object related to the force applied?

Inversely proportional

Directly proportional

Dependent upon the material being extended

None of the above

This means that the more force that is applied to an object, the greater the amount of energy stored will be. Also, the energy will be a multiple of some constant

5.

Which formula correctly states the relationship between force and extension?

This only applies below the limit of proportionality

6.

What does k represent in the formula in question 5?

The force on the object

The extension of the object

The spring constant

The constant of extension

It is only relevant to elastic materials that obey Hooke's law

7.

If a material has a spring constant of 10 N/m and is extended by 1 m, what force must have been applied to the object?

5 N

10 N

20 N

50 N

The restoring force would also be 10 newtons

8.

What is the size of the extension of an object which has a spring constant of 30 N/m when a force of 15 N is applied?

0.5m

1m

2m

10m

This question requires you to rearrange the Hooke's law equation

9.

A slinky is stretched from being a length of 15 cm to a length of 2 m. One end of the slinky is affixed to a point whilst a child pulls on the other end with a force of 10 N. What is the spring constant of the slinky?

5.3 N/m

5.4 N/m

18.5 N/m

20 N/m

This needed the Hooke's law equation rearranging and also remember the extension must be in meters

10.

A spring is stretched to a point where, when released it does not return to its original length. What is this point called?

Fracture limit

Limit of proportionality

Torsion limit

Bohr's limit

If you continue to apply force after the limit of proportionality, the material will be permanently stretched