A block of mass 50 kg is projected horizontal on a rough horizontal floor. The coefficient of friction between the block and the floor is 0.1. The block strikes a light spring of stiffness `k = 100 N//m` with a velocity `2 m//s`, the maximum compression of the spring is

Options

A. 1 m
B. 2 m
C. 3 m
D. 4 m

Answer

A

Explanation

`W_S+W_f=DeltaK`
`-DeltaU+W_f=-K_i`
`-U_f+mumgx=-K_i`
`1/2K pi^2=mumgx=1/2 mu^2`
`100x^2+2(0.1)(50)(10)x=50xx4`
`x^2+x-2=0`
x=1 m