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 2 years agoRelated Solutions
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