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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

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Solution

The correct option is **D** 1.41m

Given KE= 3J.

Given KE= 3J.

let Ei is initial energy and Ef be final energy.

Ei=KEi+PEi

Ei=3J+0=3J

at maximum compression, block will stop for a moment so KEf=0

Ef=KEf+PEf

Ef=0+PEf

Total energy remains conserved

Ei=Ef

3J=PEf

Energy 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=2

x=√2=1.41m

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