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Physics Tutorial: Bungee Jumping with Elastic Force

 

Elastic substances return to their original shape after being deformed. Hooke’s Law tells us that the force

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an elastic object, such as a spring, uses to reinstate itself to an original length is relative to, but in the opposite direction, of the length the spring is stretched.

 

The force necessary to either stretch or compress a spring is represented as F=kx Where F=force, k=spring constant and x=length the spring is is stretched (or compressed). The spring constant is a number used to characterize the rigidity of the spring. This number varies with different springs.

 

Hooke’s law does have its limits though. If a force is too great, the elastic limit will be exceeded. After the elastic limit is an area called the plastic region. The object may be stretched further in this area, however it will not returned to its original shape and will be permanently distorted. Eventually, the object will reach its breaking point. If the force applied is within the elastic limit, the object will return to its original shape.


This principle may be used in regards to the sport of bungee jumping. A bungee cord works in the same manner as a spring. Familiarity with Hooke’s laws has great significance with bungee jumping. For example, cord producer must design cords to not only support specific weights, but to be a certain length at maximum (stretched out) distance.

 

 

EXAMPLE:

a) A cord is 20m long un-stretched. If its elasticity is 50% and the spring constant is 20 N/m, what is the maximum force that can be held?

 

Use the formula F=kx.

X is calculated by taking 50% of the un-stretched cord. Therefore x=10m.

Simply plug the values into the formula.

F=(20N/m)(10m)

F=200N

This is the maximum force that the cord can hold.

 

b) A cord is 45m long un-stretched. It has an elasticity of 75%. If the maximum force the cord can hold is 350N, what is the spring constant?

X is Calculated as in part a. x=33.75m

F=kx

350N=k(33.75m)

k= [(350N)/(33.75m)]

k=10.370 N/m

This is the spring constant of the particular cord.

 

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by Amanda Taphorn

LINKS:

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/hooke.cfm

http://www.darvill.clara.net/enforcemot/springs.htm