# Kinetic energy with no velocity

When a body is displaced against the gravitational field of force it gains potential energy. When we drop the body it begins to move downward with a certain amount of acceleration, and the potential energy turns into kinetic energy. Kinetic energy is given by the equation: $$E_k = \frac{1}{2}mv^2$$ When the body falls off the ground, and it stops moving then its velocity is zero, and therefore the kinetic energy is also zero in this case. In which form of energy does this kinetic energy usually convert into?

It is zero, because kinetic energy is the one associated only with an object in motion. It is maximum just before it touches the ground. And once it reaches the ground, most of the energy is perceived as sound, lost as heat and some as stress, which causes deformation of the body. If the body can't sustain the stress on its impact with the ground, it breaks.

Though principle of conservation of energy seems to fail here, it doesn't. When you throw a body upward there is not kinetic and potential energy being converted with each other but instead it is loosing its energy continuously due to the friction with air molecules. However it is not so significant. But at the height zero, it is not a good idea to take the help of mechanical energy only, instead you need to take the whole system. The mechanical energy will get converted into heat , sound , electrical and other sources of energy. There are some numerical questions in which you need to calculate the heat energy produced due to conversion of mechanical energy based on same idea.

• We're discussing about ideal situations. Commented Mar 25, 2013 at 20:12
• @SamamaFahim ,But ideal situations are possible only if the object doesn't touch the ground. Commented Mar 25, 2013 at 20:17
• I mean to say that if we do not take into account the loss of energy due to friction with air molecules. Commented Mar 25, 2013 at 20:25
• Ok, don't take. Commented Mar 25, 2013 at 20:45

Practical physical answers are not so clear-cut. I will defend that most energy will still be kinetic. That is, after the first collision.

Saying "When the body falls off the ground, and it stops moving" is very much an assumption. What is this body?

Is it a rubber ball? It will BOOOIIINK back - mostly kinetic energy.

Is it something that breaks, like a teapot? Fragments launch in every direction like a grenade - mostly kinetic energy.

Usually things can break or boink. Another case is a liquid, where "breaking" gets replaced with "scattered around". Liquid also encompasses the darker options of the experiment. This is still - mostly kinetic energy.

Is the ground soft? Much energy will be converted into potential by compressing it - think Wile E. Coyote holes.

Body deformation and sound seem to take the smaller portion. But again, I might be focusing too much on experiments with high initial kinetic energy.