Answer to Question #121924 in Physics for Avneet

Question

A horizontal spring is compressed, and a 274 g metal sphere is touching it, but not attached. When the spring is released, it does work on the metal sphere. 8.78 J of elastic potential energy is stored in the spring, and the system is 77.9 percent efficient in converting the elastic potential energy of the spring into kinetic energy of the sphere. Based on the system being 77.9% efficient, the velocity of the metal sphere as the spring is released is

Answer 1

0.779 of the elastic potential energy was converted to the kinetic energy:

$$0.779EP=KE,\\ 0.779EP=\frac{mv^2}{2},\\\space\\ v=\sqrt{\frac{2\cdot0.779EP}{m}}=\sqrt{\frac{2\cdot0.779\cdot8.78}{0.274}}=7.1\text{ m/s}.$$