Answer to Question #143789 in Physics for Norma castrellon

Question

A string attaches a 4.55 kg and a 7.65 kg mass over a frictionless pulley as shown. The 7.65 kg mass is 3.8 m above the floor and the masses are released from rest. How fast will the 7.65 kg mass be traveling when it reaches the floor?

Answer 1

Consider the problem from the viewpoint of conservation of energy: the heavier mass has potential energy which converts to kinetic energy. Also, this potential energy must pull up the smaller mass and provide kinetic energy to this smaller mass. Since the string connecting the masses is inextensible, their speeds will be equal:

$$Mgh-mgh=\frac12Mv^2+\frac12mv^2,\\\space\\ gh(M-m)=\frac{v^2}{2}(M+m),\\\space\\ v=\sqrt{\frac{2gh(M-m)}{M+m}}=4.35\text{ m/s}.$$