A 20 kg body is released from rest so as to slide in between vertical rails and compresses a vertical spring `(k=1920(N)/(m)`) placed at a distance `h=1.0`m from the strating position of the body. The rails offer a frictional force of 40 N opposing the motion of body. Find (a) the velocity v of the body just before striking with the spring, (b) the maximum compression of the spring and (c ) the distance `h^(')` through which the body is rebounded up.

Explanation

According to the question, we draw the following diagram.

(i) Between diagram (1) and (2)
Loss in PE=gain in KE+work done against friction.
`mgh=(1)/(2)mv^(2)+fh " " ( :. h=s)`
`20xx10xx1=(1)/(2)xx20v^(2)+40xx1implies v=4 m//s`
(ii) Between diagram (2) and (3)
Loss in PE+loss in KE=gain in spring energy +work done against friction
`mgx+(1)/(2)xxmv^(2)=(1)/(2)kx^(2)+fx`
`20xx10xxx+(1)/(2)xx20xx4^(2)=(1)/(2)xx1920x^(2)+40x`
`960x^(2)-160x-160=0implies6x^(2)-x-1=0`
`implies x=(1+-sqrt(1+4xx6xx1))/(12)=(1+-5)/(12)=(1)/(2)m`
(C ) Between diagram (3) and (4)
`(1)/(2)kx^(2)=mgh'+fh'`
`(1)/(2)xx1920((1)/(2))^(2)=(20xx10+40)h'implies h'=1 m`