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 W_{1} and W_{2} connected by light inextensible string, passing over smooth pulley. The weight W_{2} is placed on rough horizontal surface, while the weight W_{1} is hanging free. Thus in this case force of friction is acting on weight W_{2} in opposite direction of motion of weight W_{2}.
Let, μ = The coefficient of friction between weight W2 and horizontal surface. Force of friction = R_{2} = W_{2}
Motion of W_{1} (Downward)
W_{1} - T = (W_{1}/g).a ...(1)
Motion of W_{2}
T - μg W_{2 }= (W_{2}/g).a ...(2)
Solve equations for Tension 'T' and Acceleration 'a'