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# 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/s2)

= 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)

## Related Topics

• Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
• Statics - Loads - force and torque, beams and columns

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