Unlock the Mystery of Hooke's Law: Stress Proportional to Strain

In summary, Hooke's Law states that stress is proportional to strain within the elastic limit. This means that the amount of load applied is directly related to the amount of deformation that occurs. The reason for this proportionality can be explained in two ways: the math reason, which uses a Taylor series expansion to show that small displacements are proportional to small forces, and the physical reason, which states that pulling on something stretches atomic bonds or straightens polymer chains, inducing a restoring force to bring the atoms back to their equilibrium spacing.
  • #1
koolraj09
167
5
Hi guys.
Hooke's Law is stated as: Stress is proportional to strain within elastic limit (or load proportional to deformation).
But I can't really figure out why this happens. I mean what is the cause of this proportionality?
 
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  • #2
I'm not sure whether you're interested in the math reason or the physical reason. Math reason: every generalized "displacement" (e.g., distance or strain) is proportional to generalized "force" (e.g., load or stress) for small displacements, as can be shown by a Taylor series expansion,

[tex]f(x_0+\Delta x)\approx f(x_0)+f^\prime(x_0)\Delta x[/tex]

where the first term is zero because [itex]x_0[/itex] is the equilibrium position.

Physical reason: pulling on something stretches atomic bonds* and induces a restoring force so that the atoms can go back to their equilibrium spacing.

*Or straightens polymer chains, in elastomers, where the restoring force is entropic. (This is a more advanced topic.)
 
  • #3
Mapes said:
Physical reason: pulling on something stretches atomic bonds* and induces a restoring force so that the atoms can go back to their equilibrium spacing.

*Or straightens polymer chains, in elastomers, where the restoring force is entropic. (This is a more advanced topic.)

I think he were looking for this answer! Great explanation.
 

1. What is Hooke's Law?

Hooke's Law is a principle in physics that states the force required to extend or compress a spring is directly proportional to the distance the spring is stretched or compressed. This relationship is known as stress proportional to strain.

2. Who discovered Hooke's Law?

Hooke's Law was discovered by English scientist Robert Hooke in the 17th century. He observed that the force needed to stretch a spring was directly proportional to the distance it was stretched.

3. What is the formula for Hooke's Law?

The formula for Hooke's Law is F = -kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its original position.

4. What are some practical applications of Hooke's Law?

Hooke's Law is used in various fields, such as engineering, material science, and biomechanics. It is used to design and test springs, measure the elasticity of materials, and understand the behavior of muscles and tendons in the human body.

5. Is Hooke's Law applicable to all materials?

No, Hooke's Law is only applicable to certain materials known as "Hookean" materials, which have a linear relationship between stress and strain. These materials include most metals, rubber, and some biological tissues.

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