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Question

# A block of a mass mkg moving with kinetic energy 3J on a smooth horizontal surface hits the free end of a spring, whose other end is attached to a rigid wall as shown in the figure. If restoring force applied by the spring is given by f(x)=âˆ’2xâˆ’x3 (N). Then the maximum compression in the spring approximately

A
2.20m
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B
1.51m
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C
1.41m
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D
1.67m
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Solution

## The correct option is D 1.41mGiven KE= 3J.let Ei is initial energy and Ef be final energy.Ei=KEi+PEi Ei=3J+0=3Jat maximum compression, block will stop for a moment so KEf=0Ef=KEf+PEf Ef=0+PEfTotal energy remains conservedEi=Ef3J=PEfEnergy by Force fx is given by −∫f(x)dx PE(x)=−∫f(x)dx PE(x)=−(−2x−x3)dx PE(x)=x2+x44 from above result PEf= PE(xmax)=x2+x44 3=x2+x44 x2=2x=√2=1.41m

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