# 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 dl (1)*

*where *

*F = force (N)*

*k = spring constant (N/m)*

*dl = extension or compression 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

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

* = 4905 N*

* = 4.9 kN*

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

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

* = 49050 N/m*

* = 49 kN/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.

### 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) *

## Related Topics

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