# Potential energy being converted into kinetic energy

It is said that the potential energy gets converted into kinetic energy for a freely falling body. But when a freely falling body comes to rest, that is, the velocity becomes 0, does the object still have kinetic energy in that case or not?

Because when a moving object comes to a stop, its kinetic energy is converted to potential energy, so shouldn't that also be the case for a freely falling body?

• "When a freely falling body comes to rest" do you mean when the body hits ground? Commented Dec 14, 2023 at 14:06
• "... the velocity becomes 0, does the object still have kinetic energy in that case or not?" No. The kinetic energy is $T=\frac{1}{2}mv^2$ so if $v=0$ then $T=0$.
– hft
Commented Dec 14, 2023 at 18:04
• Related/duplicate? Shouldn't falling water heat up eventually? Commented Dec 14, 2023 at 23:14

True, as a freely falling body falls it converts its potential energy to kinetic energy. However, when a falling object comes to rest by say hitting the ground, the conservation of energy no longer applies because the system has now been subjected to external forces. So, the ground absorbs the kinetic energy from the object and does work on it to diminish its momentum so that it comes to a stop over some time interval specific to the collision. The impact causes a dissipation of the kinetic energy to heat, sound, etc.; it does not store it away as potential energy. Once the object comes to rest it possesses only the gravitational potential energy intrinsic to its resting spot. Kinetic energy is always associated with motion.

• the conservation of energy no longer applies. I think that you meant to write the conservation of mechanical energy no longer applies Commented Dec 14, 2023 at 23:12
• @Farcher. Yes, I am indeed referring to the mechanical aspect of the problem. Globally, energy is neither created or destroyed. Commented Dec 15, 2023 at 15:06

If the ball is held at rest some distance from the ground, we say that the ball has gravitational potential energy (grav PE). [It would be more accurate to say that the system of the Earth and the ball has grav PE.]

As the ball falls, the system loses grav PE and the ball gains KE. So too – if viewed from a frame of reference in which the pre-ball-drop Earth was at rest – does the Earth, but its share is utterly negligible.

When the ball hits the ground it comes to rest (possibly after a few bounces). It no longer has kinetic energy. But energy is still conserved; the atoms in the ball and in the patch of Earth that it hits are made to increase their mean random energies of vibration. This vibration energy is half elastic potential energy due to alternate stretching and shrinking of the atoms' bonds with their neighbours, and half kinetic energy of the atoms. [This doesn't contradict my statement that the ball has lost its KE: the ball's centre of mass remains almost stationary because the atomic vibrations are in random directions.]

The increased vibration energy of atoms in the ball and the ground that it hits would show up on sensitive thermometers as a rise in temperature. As a result energy (we call it heat) gradually flows out of the ball and the patch into the surrounding ground and surrounding air. Energy is still conserved, but we have to consider a larger system than just the ball and the patch of Earth that it hits.

When the velocity becomes zero by the equation of kinetic energy you can know that it's kinetic energy is zero. Object attains maximum kinetic energy just before hitting the ground because at that instant it has the maximum velocity. But the instant it hits the ground the energy of the ball is not conserved anymore because the energy the ball had is now lost to the surrounding, for example some energy would have been transferred to the ground and some would have got converted into sound energy.

for a free falling object, the potential energy of the object is converted into kinetic energy.

the free falling object will accelerate due to gravity, the instant before hitting the ground, the object will reach maximum kinetic energy (potential energy converted into kinetic energy), after the object impact the ground, the velocity become zero, because kinetic energy is converted into other energy (heat energy, light energy, sound energy), the energy is still conserved!

note that when a object come to stop, its kinetic energy would not always converted into potential energy, in that case that is when the object was thrown up, the conversion of energy not always same for different motion