Question

In the arrangement of Fig. 1.9 the masses m_o, m₁, and m₂ of bodies are equal, the masses of the pulley and the threads are negligible, and there is no friction in the pulley. Find the acceleration w with which the body m_o comes down, and the tension of the thread binding together the bodies m₁ and m₂, if the coefficient of friction between these bodies and the horizontal surface is equal to k. Consider possible cases.

Answer 1

Let us write the fundamental equation of dynamics for all the three block in terms of projection, having taken the positive direction of x and y-axes as shown in Fig; and using the fact that kinematical relation between the acceleration is such that the blocks move with same value of acceleration (say w)

As the block m_o moves down with acceleration w, so in vector from