Types of Forces III (Elastic Force and Tension)

In these revision notes for Types of Forces III (Elastic Force and Tension), we cover the following key points:

• What are elastic objects?
• How to determine whether an object is elastic or not?
• What happens when an object is not elastic?
• What are the factors affecting the elasticity of objects?
• Where does the elastic force depend on?
• How to represent graphically a situation involving the elastic behaviour of matter?
• What is limit of elasticity and breaking point?
• What is tension?
• Where does the tension differ from elastic force?

Types of Forces III (Elastic Force and Tension) Revision Notes

Elastic objects, are made from materials which after being deformed due to the action of a distorting force, return to their original shape when this distorting force stops acting.

Examples of elastic materials include: steel, rubber, sponge, bamboo tree, etc.

On the other hand, objects that remain deformed after a distorting force has acted on them are known as non-elastic (plastic) objects.

Examples of non-elastic materials include: clay, iron, glass, etc.

There are three kind of materials considering their elastic behaviour. They are:

1. Perfectly (absolutely) elastic. These materials regain their previous shape after the restoring force stops acting on them, even if they have been used multiple times.
2. Absolutely non-elastic (plastic). These materials keep exactly the actual shape after the restoring force stops acting on them.
3. An intermediate category in which objects try to regain their original shape after the restoring force stops acting. However, they remain deformed at a certain extent. Certain alloys, in which an elastic and a non-elastic material are mixed, manifest such a behaviour.

The equation used to determine the magnitude of the elastic force (restoring force) is known as the Hooke's Law. Mathematically, it is written as

where k is a constant known as "coefficient of elasticity" or "spring constant" which depends on the properties of material, thickness of spring etc., and x⃗ = L - L₀ is the extension or compression of the spring, i.e. the difference between the actual length L and the initial length L₀ of the spring.

The graphical representation of Hooke's Law shows a linear function whose graph is a slope that starts from the origin. When the F_e vs x graph is not linear, the force used in the spring has exceeded the limit of elasticity. As a result, the spring cannot turn anymore to its original length when the force that has caused the extension stops acting.

When the force is very large, the spring breaks in two pieces and therefore, no F_e vs x graph exist anymore.

Tension is another resistive force that appears when a string is pulling a load. In other words, tension is the resistive force of a string against deformation caused when it is pulling an object. It is obvious that tension is in the opposite direction of the pulling force.

Tension has an intermolecular nature, i.e. it appears when the molecules of the string (which is a solid and as such, its molecules have a strong connection between them) display resistance towards extension.

Tension is different from elastic force, as it appears when the string is non-elastic. Therefore, no visible extension appears in the string, but even in cases when this extension is considerable, the string does not turn back to its original length, and as a result, it is considered as a non-elastic material. Therefore, the Hooke's Law cannot be used to calculate the value of tension.