Question

A light frictionless pulley carries a light cord to which is attached at one end a 50 N weight and at the other an 80 N weight. The weights are suddenly released. Find the acceleration and tension of the cord

Answer 1

Apply Newton's second law for both bodies (assume positive Y is downward):

$$80: (80/9.8)a=80-T ,\\ 50: -(50/9.8)a=50-T.$$

Divide one by another:

$$-\frac{8}{5}=\frac{80-T}{50-T},\\ T=61.5\text{ N}.$$

The acceleration (expressing from one of the first equations) will be 2.26 m/s².