Question

A block of mass M is resting on a rough horizontal surface with coefficient of friciton μ. The block is attached to an ideal spring of spring constant ‘k’ and the other end of the spring is fixed to a rigid wall 1 as shown. The block is imparted a sudden impulse resulting in a compression ‘b’ in the spring before coming to rest for the first time. The impulse imparts an initial velocity ‘u’ to the block. The co-efficient of friction μ between the block and the horizontal surface is

(1) \(\frac{μ^2}{2g}\)

(2) \(\frac{Mμ^2+kb^2}{2Mgb}\)

(3) \(\frac{Mμ^2-kb^2}{Mgb}\)

(4) \(\frac{Mμ^2-kb^2}{2Mgb}\)

Answer 1

  (4) \(\frac{Mμ^2-kb^2}{2Mgb}\)

The initial K.E. of the block in used to store elastic potential energy in the block and to perform work against friction.