Hooke’s law states that “extension of a string is directly proportional to the applied force provided the elastic limit is not exceeded”. This law is mathematically, as;

F=KE            Where; K = Spring constant

K= FE                       F = force

F1e1= F2e2                      e = extension

 Example: A string of length 0.1m obeys Hooke’s law. When a force of 200N is hung vertically on its free end, the length of the spring becomes 0.115m. Calculate the new length when the force is 600N.

Solution

F1e2= F2e1   But F₁ = 200N; F₂ = 600N

e₁ = (0.1 – 0.115) m = 0.015m

e2=  F2e1F1=600N*0.015m200N=0.04J 

e₂ = 0.04J

The S.I. unit of the spring constant is N/m

Elastic limit is defined as the minimum force required stretching a material permanently. Beyond the elastic limit there is atomic slip and the material is likely to break. The S.I. unit of elastic limit is the newton (N).

A material is said to be elastic if it returns to its original length or size, if the stretching force is removed.

Example: A machine uses 140J of energy to produce 98J of energy. Calculate the efficiency of the machine.

Solution

EfficiencyΩ= EoutEin*100 

E_out = 98J   and E_in = 140J

Ω= 98140* 100 = 70J

Ω=70J 

Exercise: A ball of mass 2kg is falling from a height of 10m. Given that acceleration due to gravity is equal to 10m/s². Calculate the velocity of the ball when it is just about to touch the ground.