In the arrangement of figure the masses `m_0`, `m_1`, and `m_2` 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_0` comes down, and the tension of the thread binding together the bodies `m_1` and `m_2`, if the coefficient of friction between these bodies and the horizontal surface is equal to k. Consider possible cases.

Explanation

Let us write the fundamental equation of dynamics for all the three blocks in terms of projection, having taken the positive direction of x and y axes as shown in figure, and using the fact that kinematical relation between the acceleration is such that the blocks move with same value of acceleration (say w)
`m_0g-T_1=m_0w` (1)
`T_1-T_2-km_1g=m_1w` (2)
and `T_2-km_2g=m_2w` (3)
The simultaneous solution of Eqs. (1), (2) and (3) yields,
`w=g([m_0-k(m_1+m_2)])/(m_0+m_1+m_2)`
and `T_2=((1+k)m_0)/(m_0+m_1+m_2)m_2g`
As the blocks `m_0` moves down with acceleration w, so in vector from
`vecw=([m_0-k(m_1+m_2)]vecg)/(m_0+m_1+m_2)`