# Hooke's Law

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

The force required to extend or compress a spring can be expressed with Hooke's Law as

*F = - k s (1)*

*where *

*F = force (N)*

*k = spring constant (N/m)*

*s = extension or compression distance (m)*

#### Example - Car Suspension

The maximum compression of a car suspension 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

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

* = 4905 N*

* = 4.9 kN*

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

*k = - F / s*

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

* = 49050 N/m*

* = 49 kN/m*

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

### Hook's Law of Elasticity

In the generalized variation of Hooke's law it states that the strain/deformation of an elastic object or material is proportional to the stress applied to it. It may be expressed mathematically as

*σ = E ε (2)*

*where *

*σ = stress (Pa) *

*E = Young's Modulus of Elasticity (Pa)*

*ε = strain (m/m) *