Question

A block is connected to an identical block through a weightless pulley by a weightless inextensible thread of length 2l (Fig. 37). The left block rests on a table at a distance l from its edge, while the right block is kept at the same level so that the thread is unstretched and does not sag, and then released. 

What will happen first: will the left block reach the edge of the table (and touch the pulley) or the right block hit the table?

Answer 1

The centre of mass of the system consisting of the blocks and the thread is acted upon in the horizontal direction only by the force exerted by the pulley. Obviously, the horizontal component of this force, equal to T (1 - cos φ), where T is the tension of the thread, is always directed to the right (Fig. 175).

Since at the initial moment the centre of mass is at rest above the pulley, during motion it will be displaced along the horizontal to the right. Hence it follows that the left block reaches the pulley before the right block strikes the table since otherwise the centre of mass would be to the left of the pulley at the moment of impact.