Hooke's Law is a physics principle that tells us how materials deform under stress. Discovered by 17th-century scientist Robert Hooke, he defines the property of elastic materials. An elastic material goes back to its original shape after it has been stretched or compressed.

According to Hooke's law, force is proportional directly to the distance through which a spring is extended or compressed. This factor is a constant characteristic of the stiffness of the spring. The property of elasticity states the following: it takes twice the much force to draw a spring twice as long. This linear dependence of displacement on stretching is called Hooke's law.

Formula 

Hooke's Law Formula is given by

F = - K x

where,

• F is the measure of force applied in N, i.e., in Newton

• x is the displacement in the spring in m, i.e., in meter

• k is the spring constant or force constant.

From the Hooke's law formula, force, displacement and force constant can be calculated for a stretched spring.

Solved Problems

Problem 1: A spring is stretched by 10 cm and its force constant is 2 cm /dyne. Find the Force applied.

Solution:

Given,

Force constant k is 2 cm/dyne,

Extension x = 10 cm.

The formula for force applied is given by

F = -k x

   = -2 × 10 cm

   = -20 N

Problem 2: Find the force constant if a force of 100 N is stretching a spring by 0.8 m.

Solution:

Given,

Force F = 100 N,

Extension, x = 0.2 m.

Force Constant Formula is given by

k = – F / x

= – 100 / 0.8

k = – 125 N/m.

 

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