Motion of two bodies - rough surface and rough pulley:
THE HORIZONTAL SURFACE IS ROUGH AND THE STRING IS PASSING OVER ROUGH PULLEY.
Figure shows two weights W1 and W2 connected by string, passing over rough pulley. The weight W2 is placed on rough horizontal surface, while the weight W1 is hanging free. Thus in this case force of friction will be acting on weight W2 in opposite direction of motion. As string is passing over rough pulley. The tension on both sides of string will not be same.
Let, μ1 = Coefficient of Friction between Weight W2 and Horizontal plane μ2 = Coefficient of Friction between String and pulley T1 = Tension in string to which weight W1 is attached
T2 = Tension in the string to which weight W2 is attached
Force of friction = μ1R2 = μ1W2
Consider block W1
W1 - T1 = (W1/g).a ...(1)
Consider block W2
T2 - μ2.W2 = (W2/g).a ...(2)
Another equation is, T1/T2 = e μ.θ ...(3)
Solve all the three equation for value of 'a', 'T1' and 'T2'