# Hooke's Law

## Hooke's law - force, elongation and spring constant

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Hooke's Law express the force needed to extend or compress a spring - and can be expressed as

*F = - k x (1)*

*where *

*F = force (N)*

*k = spring constant (N/m)*

*x = extended or compressed distance (m)*

### Example - Car Suspension

The maximum compression of the suspension of a car with mass *2000 kg (500 kg on each wheel)* shall not exceed *0.1 m*.

The force acting on each spring can be calculated using Newton's Second Law as

* F = (500 kg) (9.81 m/s ^{2}) *

* = 4905 N*

The required spring constant for the suspension can be calculated by rearranging *(1)* as

*k = - ( 4905 N) / (- 0.1 m)*

* = 49050 (N/m)*

Note that this is the value only for the static load of the car. You may probably at least double this value for the car to handle dynamic forces, potholes and similar.

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