## Mechanical Energy Conservation

The mechanical energy of a body is equal to the sum of its potential and kinetic energies.

So:

Any movement is accomplished through energy transformation, for example, when you run, it turns your body's chemical energy into kinetic energy. The same goes for the conservation of mechanical energy.

We can solve many mechanical problems by knowing the principles of energy conservation.

For example, a stone that is abandoned from a cliff. At first, before being abandoned, the stone has zero kinetic energy (since it is not in motion) and total potential energy. When the stone reaches the ground, its kinetic energy will be total and potential energy zero (since the height will be zero).

We say that the potential energy has become or has become kinetic energy.

When dissipative forces (friction, drag force, etc.) are not considered, mechanical energy is conserved, then:

For the case of gravitational potential energy converted to kinetic energy, or vice versa:

For the case of elastic potential energy converted to kinetic energy, or vice versa:

Examples:

1) An apple stuck in an apple tree at 3 m height comes off. How fast will it reach the ground?

2) A block of mass equal to 10kg travels with constant speed equal to 12m / s, when it finds a spring of elastic constant equal to 2000N / m it decreases its speed until it stops, what is the compression in the spring at this moment?