Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: where is a constant factor characteristic of the spring, its stiffness. One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law. Hooke's Law is that which says that how much stress we apply on any body that much strain will be observed on it. which means** Stress $\propto$ Strain.**

**Hooke's Law Formula** is given by

Where,

$F$ is the amount of force applied in $N$,

$x$ is the displacement in the spring in $m$

$k$ is the spring constant or force constant.

Hooke's law formula is used to determine the force constant, displacement and force in a stretched spring.

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Below are some problems on Hooke's law which may be helpful for you.

### Solved Examples

**Question 1: **A spring is stretched by 5 cm and has force constant of 2 cm /dyne. Calculate the Force applied?

** Solution: **

Given: Force constant k = 2 cm/dyne,

Extension x = 5 cm.

The force applied is given by F = - kx

= - 2cm/dyne $\times$ 5 cm

= - 10 cm/dyne.

**Question 2: **A force of 100 N is stretching a spring by 0.2 m. Calculate the force constant?

** Solution: **

Given: Force F = 100 N,

Extension x = 0.2 m.

The force constant is given by k = - $\frac{F}{x}$

= - $\frac{100N}{0.2 m}$

= - 500 N/m.

Given: Force constant k = 2 cm/dyne,

Extension x = 5 cm.

The force applied is given by F = - kx

= - 2cm/dyne $\times$ 5 cm

= - 10 cm/dyne.

Given: Force F = 100 N,

Extension x = 0.2 m.

The force constant is given by k = - $\frac{F}{x}$

= - $\frac{100N}{0.2 m}$

= - 500 N/m.

More topics in Hooke's Law Formula | |

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