Elasticity

Elasticity

Elasticity is the ability of a sub-stance to recover its original shape and size after distortion.

Forces Between Atoms

The intermolecular forces consist of an attractive force and a repulsive force.

• At the equilibrium distance d, the attractive force equal to the repulsive force.
• If the 2 atoms are brought closer, the repulsive force will dominate, produces a net repulsive force between the atoms.
• If the 2 atoms are brought furhter, the attractive force will dominate, produces a net attractive force between the atoms.

Graph of Forces Between 2 atoms

x0 = Equilibrium Distance

When the particles are compressed, x < x0, the repulsive force between the particles increases.

When the particles are stressed, x > x0, the attractive force between the particles increases.

If the distance x exceeds the elastic limit, the attractive force will decreases.

Hooke's Law

Hooke's Law states that if a spring is not stretched beyond its elastic limit, the force that acts on it is directly proportional to the extension of the spring.

Elastic Limit

The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

Equation derived from Hooke's Law

From Hook's Law, we can derived that

Spring Constant

Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring.

It is a measure of the stiffness of a spring or elastic object.

Graph of Streching Force - Extension

Gradient = Spring constant

Area below the graph = Work done

F-x graph and spring constant

The higher the gradient, the greater the spring constant and the harder (stiffer) spring.

For example, the stiffness of spring A is greater than spring B.

System of Spring

Arrangement in series:
Extension = x × number of spring
Stiffness decreases
Spring constant = k/number of spring

Arrangement in parallel:
Extension = x ÷ number of spring
Stiffness increases
Spring constant = k × number of spring

Factors Affecting the Stiffness of Spring

	Stiffer	Less stiff
Material type of spring
Diameter of wire of spring
Diameter of the spring
Length of the string