Hooke’s Law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid. Hooke's Law of elasticity is an approximation that states that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress). If the elastic limit is not exceeded, the material returns to its original shape and size after the force is removed, other it remains deformed or stretched.
Force:
F
_{x} = -k(x-x
_{0})
Spring Force Constant:
k = F_{x} / x-x_{0}
Distance from Equilibrium:
x = x_{0} – (F_{x}/ k)
Spring Equilibrium Position:
x_{0} = (F_{x}/ k)+x
Where,
F
_{x} = Force,
k = Spring Force Constant,
x = Distance from Equilibrium,
x
_{0} = Spring Equilibrium Position.
Hooke’s Law is related to the elasticity within the elastic limit of a solid material, the deformation (strain) produced by a force (stress) of any kind is proportional to the force. Law of elasticity discovered by the English scientist Robert Hooke in 1660, which states that, for relatively smalldeformations of an object, the displacement or size of thedeformation is directly proportional to the deforming force or load.
Example:
Calculate the Force (F_{x}) as per Hooke’s law for the given details.
Spring Force Constant (k) = 10 N/m
Distance from Equilibrium(x) = 30 m
Spring Equilibrium Position(x_{0}) = 40 m
Solution:
Apply Formula:
F_{x} = -k(x-x_{0})
F_{x} = -10 (30-40)
F_{x} = -10 * -10
F_{x} = 100 N
Force (F_{x}) = 100 N