Answer to Question #158286 in Physics for rye

Question

A roller coaster of mass 800 kg starts from rest at the top of a hill with 1,500,000 J of potential energy. It ends up at ground level moving at 45 m/s. How much energy was lost to heat and friction? 

Answer 1

Find the kinetic energy at that speed:

$$E_K=\frac12mv^2=810000\text{ J}.$$

Assuming entire potential energy turned into kinetic energy, heat, and friction, the heat and friction are

$$E_L=1500000-810000=690000\text{ J}.$$