Figure shows a force compression curve of a spring. A body of mass `5kg` moving with the velocity of `8m//s` hits the spring. Calculate the force constant of the spring and also the compression produced in the spring when the body hits it.

Explanation

From figure, force constant of spring
`k=(F)/(x)=` slope of `F-x` curve`=(AB)/(OB)`
`=(32)/(0.4)=80N//m`
If `x` is the compression produced on hitting the spring, then as
Work done `=`K.E.`:.(1)/(2)kx^(2)=(1)/(2)m upsilon^(2)`
`x=sqrt(m(upsilon^(2))/(k))=upsilonsqrt((m)/(k))=8sqrt((5)/(80))=2m`