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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)=2xx3 (N). Then the maximum compression in the spring approximately

1364403_27ee5758a1c84ddaa8d097aa3e8d34b4.PNG

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 1.41m
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)=(2xx3)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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