Hooke's Law
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
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
• Statics
Forces acting on bodies at rest under equilibrium conditions - loads, forces and torque, beams and columns.
Related Documents
Bolt Stretching and Tensile Stress
Tensile stress and Hooke's Law.
Harmonic Oscillator
A simple harmonic oscillator.
Metals and Alloys - Young's Modulus of Elasticity
Elastic properties and Young's modulus for metals and alloys like cast iron, carbon steel and more.
Speed of Sound - Equations
Calculate the speed of sound (the sonic velocity) in gases, fluids or solids.
Stress in Thick-Walled Cylinders or Tubes
Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure.
Stress, Strain and Young's Modulus
Stress is force per unit area - strain is the deformation of a solid due to stress.
Threaded Rods - Loads in Imperial Units
Weight rating of threaded hanger rods.