# How does an object falling at terminal velocity lose the gravitational potential energy it gained when being raised to the point where it is dropped?

Every object reaches terminal velocity at a certain stage. Before falling the object would have a certain amount of gravitational potential energy that it gained from being raised. My question is, if an object always gains gravitational potential energy as it is being raised but can only reach a certain speed as it falls (it's terminal velocity) then where does the excess gravitational potential energy go that is not needed to reach terminal velocity? (This is assuming that the object has been dropped from a point higher than the point needed for it to reach terminal velocity on the way down)

Thanks

• Until the body reaches the terminal velocity, potential energy is converted to kinetic energy, after which energy is lost to the surroundings, predominantly as heat. – user191954 Jun 7 '18 at 8:24
• Thanks, but the if the object is falling at it's terminal velocity for an indefinite amount of time will it reach a maximum temperature or keep increasing? – James Cuadra Jun 7 '18 at 8:28
• This is interesting, I never thought about that... I would say that it keeps increasing and even starts changing phase, since hail stones are known to melt into normal rain on the way down, but let's see what the answers say. – user191954 Jun 7 '18 at 8:32
• Because the object will also radiate energy away, the temperature will converge toward some maximum temperature, given by the terminal speed. If this max temperature is larger than e.g. the melting point, it will melt. – pela Jun 7 '18 at 11:36
• Thanks for the answer. Is there a way to calculate that temperature? What specifics would one need to know to calculate it – James Cuadra Jun 7 '18 at 13:10

## 1 Answer

The gravitational potential energy released during your fall through the atmosphere shows up as an increase in your velocity and hence your kinetic energy as you accelerate downwards. As your speed through the air increases, so does the viscuous drag being applied to your body by the air through which you are moving.

Terminal velocity is reached when the rate of release of gravitational energy during your fall is exactly balanced by the rate of energy loss because of air friction. Ignoring for now the increase in air density with decreasing altitude, at that point your velocity and hence your kinetic energy remains constant for the remainder of your descent and all the "extra" gravitational potential energy being released beyond that point is being continuously dissipated by air friction.

That dissipated energy shows up as sound waves (noise) and heat in the air.