# How kinetic energy changes

We have already talked about that. Kinetic energy has any moving body: a ball that rolls on a smooth surface, a flying plane or an athlete jumping from a springboard. calculated by the formula E_K = (mv ^ 2) / 2, where m is the mass of the body, and v is its speed.

Does the kinetic energy change as it moves, or does it remain constant all the time? It can be seen from the above formula that the kinetic energy of the bodies changes as the velocity or mass of the moving body changes. Consider both cases.

## Example 1

On a country road with a constant speed tank rides with water. She was worn out, and water flows out of the hole. What happens to the kinetic energy of the tank in two hours, if during this time its mass decreases by half?

To determine how the kinetic energy of a tank changes, let's recall the kinetic energy formula:

- E_K = (mv ^ 2) / 2

We know that the speed of the tank does not change:

- v2 = v1,

but its mass in two hours will decrease by 2 times:

- m2 = m½.

So, the kinetic energy of the tank in two hours will be equal to:

- E2 = (m2 × 〖(v2)〗 ^ 2) / 2 = (m1 × (v1) ^ 2) / 2 = (m1 × 〖v1〗 ^ 2) / 4 = E1

## Example 2

Skater, pushing off, gliding on the ice. At the beginning of the movement its speed v_start is maximum, and then gradually decreases and equals zero 〖at the moment of stopping (v〗 _stop = 0. At the same time, its mass remains constant. formula for calculating the kinetic energy:

- E = (mv ^ 2) ⁄2.

At the beginning of the movement, the kinetic energy of the skater was equal to

- E_Kstart = (m × 〖(v_start)〗 ^ 2) / 2

At the time of stopping the kinetic energy of a skater

- E_Kstop = (m × 〖(v_stop)〗 ^ 2) / 2 = (m × 0 ^ 2) / 2 = 0

We see that, since the speed of the skater at the moment of stopping is zero, his kinetic energy is also zeroed. The change in the kinetic energy of a skater was:

- ∆E_K = E_Kstart-E_Kstop = E_Kstart-0 = E_Kstart

In this case, the change in the kinetic energy of the skater was due to the work done by the force of sliding friction:

- Atr. = ∆E_K

## Theorem on the change in the kinetic energy of the body

The equality A = ΔE_K is called the kinetic energy change theorem and is decoded as follows:

The change in the kinetic energy of the body for a certain period of time is equal to the work done during this time by the force acting on the body.

This work is considered positive if, when it is done, the kinetic energy of the body increases. Such work is produced by the force of elasticity of the bowstring, which accelerates the arrow during archery.

Work is considered negative if at its performance the kinetic energy of the body decreases. For example, the force of gravity acting on a ball reduces its kinetic energy when bouncing off the floor.

If several forces act on the body, then the change in kinetic energy is equal to the sum of the work of all these forces.

### A task:

Determine what kinetic energy will have a bullet ejected from a gun. Its speed at departure from a gun is 600 m / s, and its mass is 7.5 g.