Please help with the following problem A. 5.X kg block is attached to a massless

Question

Please help with the following problem

A. 5.X kg block is attached to a massless spring with the spring constant of 220 N/m and is at rest on a horizontal surface with the coefficient of kinetic friction of mu_k = 0.1. The block is struck by a 1.1 kg stone traveling horizontally at 5.5 m/s as shown in the figure. The stone rebounds back at 2 m/s. Note that the friction must be taken into account. Find: (a) the speed of the block (in m/s) right after the collision with the stone (b) the maximum distance (in m) that the block compresses the spring after the collision (c) the work (in J) done by the friction force during this process

Explanation / Answer

PART-1: Applying conservation of linear momentum,

total momentum before collision = total momentum after collision

  MS*US + MB*UB = MS*VS + MB*VB   

US,UB and VS,VB are initial and final velocities of stone and block, before and after the collision.

1.1kg*5.5m/s + 5.5kg*0m/s = 1.1kg*2m/s + 5.5kg*VBm/s

VB = 0.8m/s

PART-2: Now balacing all the forces on the block,

Ma = kx + ukN

M(Vf - Vi) = kx + (uk*M*g)

5.5kg*(0-0.8m/s) = (220*x) + (0.1*5.5kg*10m/s2)

on solving we get the value of displacement of the spring,

x = 0.045m

PART-3: Work done by the friction force is given by,

W = F * x

W = uk*M*g*x

W = 0.1*5.5kg*10m/s2*0.045m

W = 0.247J

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