Arrangement in series:	Arrangement in parallel:
Extension = x × number of spring Stiffness decreases Spring constant = k/number of spring	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 (A steel spring is stiffer than a copper spring)
Diameter of wire of spring (The greater the diameter of the wire, the stiffer the spring)
Diameter of the spring (The smaller the diameter of spring, the stiffer the spring)
Length of the string (Shorter spring is stiffer)

External Link


Interactive Animation

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.

External Link


Interactive Animation

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 attractive force between the particles increases.

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

External Link


Interactive Animation

Energy

Energy is defined as the capacity to do work. Work is done when energy is converted from one form to another.
Nm or Joule(J)

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object as the result of its vertical position (i.e., height).

Formula:


Example 1
A ball of 1kg mass is droppped from a height of 4m. What is the maximum kinetic energy possessed by the ball before it reached the ground?

Answer
According to the principle of conservation of energy, the amount of potential energy losses is equal to the amount of kinetic energy gain.

Maximum kinetic energy
= Maximum potentila energy losses
= mgh = (1)(10)(4) = 40J


Elastic Potential Energy
Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.

Formula:

Example 2

Diagram above shows a spring with a load of mass 0.5kg. The extention of the spring is 6cm, find the energy stored in the spring.

Answer:

The energy stored in the spring is the elestic potential energy.

\[ E_P = \frac{1}{2}Fx \hfill \\ \]
\[ E_P = \frac{1}{2}(5)(0.06) = 0.15J \hfill \\ \]

External Link


Interactive Animation