InterviewSolution
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InterviewSolution
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A block of mass m strikes a light pan fitted with a vertical spring after falling through a distance h. If the stiffness of the spring is k, find the maximum compression of the spring. |
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Answer» Let the maximum compression in the spring be x. The reference level for potential energy is assumed at the position of maximum compression. Applying mechanical energy conservation, `DeltaK+DeltaU=0` As block is released from rest and finally comes to rest. Hence, net change in kinetic energy, `DeltaK=0`. Net change in potential energy, `DeltaU=DeltaU_(gr)+DeltaU_(sp)=[-mg(x+h)]+(1/2kx^2)` `0+[-mg(h+x)]+(1/2kx^2-0)=0` `x^2-2((mg)/(k))x-2((mg)/(k))h=0` After solving, we get `x=(mg)/(k)[1+sqrt(1+(2kh)/(mg))]` |
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