Motion of two bodies - rough surface and smooth pulley:
THE HORIZONTAL SURFACE IS ROUGH AND THE STRING IS PASSING OVER SMOOTH PULLEY.
Figure shows two weights W1 and W2 connected by light inextensible string, passing over smooth pulley. The weight W2 is placed on rough horizontal surface, while the weight W1 is hanging free. Thus in this case force of friction is acting on weight W2 in opposite direction of motion of weight W2.
Let, μ = The coefficient of friction between weight W2 and horizontal surface. Force of friction = R2 = W2
Motion of W1 (Downward)
W1 - T = (W1/g).a ...(1)
Motion of W2
T - μg W2 = (W2/g).a ...(2)
Solve equations for Tension 'T' and Acceleration 'a'