Question

In: Physics

Energy can be stored in an elastic band by stretching it. Let x be the distance...

Energy can be stored in an elastic band by stretching it.
Let x be the distance over which the band is stretched.
If the force which the band exerts to restore itself to its original
shape is given by F = ax + bx2
, where a and b are constants,
find work done in stretching the band from x=0 to x=L.

(a) aL+ bL2
(b) (aL2+ bL3)/2
(c) aL2/2+ bL3/3
(d) (aL2/2+ bL3/3)/2.

Solutions

Expert Solution

Infinitesimal Work   done to stretch the rubber band by infinitesimal length   under the application of force will be given as,

Integrating above equation over variable from to , we will get, the net work done in stretching the rubber band by length as,

work done to stretch the rubber band by length of ,,

Using given expression for force that is in above integral we will get,

Solving the integrals we get,

So, we get the work done in stretching rubber band from as,

genius_generous answered 3 years ago
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