Can someone explain me the logic behind this exercise?

Question

Two objects (35.5 and 18.4 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find the acceleration of the objects and the tension in the string.

-acceleration

-tension

Answer 1

Imagine a system of a pulley in which a string with masses at the two ends passes through (you do not need to consider the mass of the string). So, there are two forces acting on each mass; one weight acting downwards and the other a tension in the string acting upwards. So, the net force acting on mass 33.5 kg at one end can be expressed as 35.5 * g (acceleration due to gravity = 9.8) - T (Tension acting on the string upward) = 35.5 * a (acceleration). Similarly, for another block, it can be 18.4 * g - T = 18.4 * a. Now you can solve these two equations to obtain the value of 'a' and tension on the string. It would be more clear to show with figures, which I cannot draw here. Please, let me know if you need further explanation. Thanks.