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Question

A sphere of mass m and radius R rolls without sliding on a horizontal surface. It collides with a light spring of stiffness K with a kinetic energy E. If the surface (AB) under the spring is smooth and E 7J and K 10 N/m, mot find the maximum compression of the spring.
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Solution

springpotentialEsenergyisdefiendas,Es=12kx2herekisthespringconstantorstiffnessconstantandxisthecompressionorelongation.Ineqilibrium,Ek=Es=12kx2So,compression,x=v(2Ek/k)weget,x=v(2Ek/k)=v[2(7J)/10N/m]=1.18mRoundinguptoonesingnificantfigure,themaximumcompressionofthespringwillbe1m.

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