# 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?

## 2 Answers

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. – Samama Fahim Mar 25 '13 at 20:12
• @SamamaFahim ,But ideal situations are possible only if the object doesn't touch the ground. – newera Mar 25 '13 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. – Samama Fahim Mar 25 '13 at 20:25
• Ok, don't take. – newera Mar 25 '13 at 20:45