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## Physics Tutorials

### Hooke’s Law and Rubber Bands

Hooke’s Law states that the amount of deformation of an elastic object is proportional to the force applied to deform it.

The concept of Hooke’s Law is that the amount of force applied to a spring or elastic object is proportional to the amount of deformation (length of stretch or compression). The greater the force applied to an elastic object, the more deformation (stretch or compression) there is. With less force applied, there will be less deformation in the spring. The formula for Hooke’s Law is F=kx where “F” is the force applied, “k” is the force constant of the spring, and “x” is the amount of deformation in meters. To determine whether there is a stretch or compression in the spring, we use a method of signs. If the spring is compressed, both “x” and “F” are negative(-) and when stretched both are positive(+).

A rubber band behaves according to Hooke’s Law. When the rubber band is pulled on (force applied), the rubber band stretches and the force is proportional to the stretch of the rubber band. The more force there is, the more stretch. With less force, the rubber band does not stretch as much. After a person has applied a force to the rubber band by pulling it and starts to let it go, easing on the force applied, the stretch of the rubber band becomes less. Therefore, the force applied is proportional to the amount of deformation on the rubber band.

#### EXAMPLE

What is the force required to stretch a spring whose constant value is 100 N/m by an amount of 0.50 m?

SOLUTION: Using the formula F=kx solve the question
F=force(N)
k=force constant(N/m)
x=stretch or compression(m)

F=(100)(0.50)
F=50 N

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