Question

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

Please help with the following problem

Answer 1

PART-1: Applying conservation of linear momentum,

total momentum before collision = total momentum after collision

  M_S*U_S + M_B*U_B = M_S*V_S + M_B*V_B   

U_S,U_B and V_S,V_B 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*V_Bm/s

V_B = 0.8m/s

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

Ma = kx + u_kN

M(Vf - V_i) = kx + (u_k*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 = u_k*M*g*x

W = 0.1*5.5kg*10m/s²*0.045m

W = 0.247J