Question

Two different masses M1 = 2kg and M2 = 3kg are attached to a rope which is placed over a pulley. Find the acceleration, tension and speed at which the body crosses the pulley.

Answer 1

Apply Newton's second law and assume that forces acting downward are positive, forces acting upward are negative:

$$M_1g-T=-M_1a,\\ M_2g-T=M_2a.$$

The solution of this system is

$$T=23.5\text{ N},\\ a=1.96\text{ m/s}^2.$$

The speed at which the body crosses the pulley can be found if we know the initial distance $d$ between the pulley and the 2-kg mass:

$$v=\sqrt{2ad}.$$