Answer to Question #137268 in Physics for Rancis B. Wood

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

For the two masses, we will use Newton's second law. Keep in mind that we were given weights, not masses. In order to find the mass, we will need to divide the weight by the acceleration due to gravity g. Take g=10 m/s² for simplicity, which will give masses of 8 kg for 80-N load and 5 kg for a 50-N weight. Assume that the positive Y direction is downward. Of course, when we release the system, the 80-N weight will move down and 5-kg up.

$$80\text{ N}: 8a=80-T ,\\ 50\text{ N}: -5a=50-T.$$

Divide one by another:

$$-\frac{8}{5}=\frac{80-T}{50-T},\\ T=61.5\text{ N}.\\ a=\frac{80-T}{8}=2.3\text{ m/s}^2.$$