In: Physics
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.
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,