# Mechanical Energy It corresponds to the sum of the kinetic energy (Ec) produced by the movement of bodies with the potential elastic energy (Epe) or gravitational (Epg) produced by the interaction of bodies related to their position.

To illustrate, let's think of an object launched from a certain distance from the ground that has kinetic energy. This is because it is moving and acquires speed. In addition to kinetic energy, it has gravitational potential energy, mediated by the force of gravity acting on the object.

The mechanical energy (Em) corresponds to the resultant of both energies. Remember that according to the SI (International System) the unit of measurement for mechanical energy is the Joule (J).

## Mechanical Energy Formula

To calculate mechanical energy, use the formula below:

Em = Ec + Ep

Where:

In : mechanical energy
Ec : kinetic energy
Ep : potential energy

Therefore, it is worth remembering that the equations for calculating the kinetic and potential energies are:

Kinetic Energy : Ec = mv 2 / 2

Where:

Ec: energia cinética
m: massa (Kg)

Elastic potential energy : Epe = kx 2 / 2
Gravitational potential energy : Epg = m. g. H

Where:

Epe : Elastic Potential Energy
Epg : Gravitational Potential Energy
K : Elastic Constant
m : mass (Kg)
g : gravity acceleration of approximately 10m / s 2
h : height (m)

• Kinetic Energy
• Potential Energy
• Elastic Potential Energy
• Gravitational Potential Energy

## Principle of Mechanical Energy Conservation

When mechanical energy comes from a isolated system (one where there is no friction) based on conservative forces (which conserves the mechanical energy of the system), its resultant will remain constant.

In other words, the energy of this body will be constant, since the change will occur only in the energy mode (kinetic, mechanical, potential) and not its value:

Em = Ec + Ep = constante

• Frictional Strength
• Mechanical Waves

## Resolved Exercises

To better understand mechanical energy, here are some college entrance exercises:

1 . (UEM-2012 / Adapted) Below are some issues involving mechanical energy and energy conservation. In this way, check the incorrect alternative.

a) Kinetic energy is the energy that a body has because it is in motion.
b) Gravitational potential energy can be called the energy that a body possesses by being situated at a certain height above the earth's surface.
c) The total mechanical energy of a body is conserved even with the occurrence of friction.
d) The total energy of the universe is always constant and can be transformed from one form to another; however, it cannot be created nor destroyed.
e) When a body has kinetic energy, it is capable of doing work.

Correct alternative c) The total mechanical energy of a body is conserved even with the occurrence of friction.

2 . (UFSM-2013) A mass bus m walks down a mountain road and goes down a height h. The driver keeps the brakes on so that the speed is kept constant in module throughout the ride. Considering the following statements, indicate whether they are true (V) or false (F).

() The kinetic energy range of the bus is zero.
() The mechanical energy of the bus-to-land system is conserved as the bus speed is constant.
() The total energy of the Earth bus system is conserved, although part of the mechanical energy becomes internal energy.

The correct sequence is:

a) V, V, F
b) V, F, V
c) F, F, V
d) V, V, V
e) F, F, V

Alternativa correta: b) V, F, V

3 . (Enem-2012) Toy cars can be of various types. Among them are the rope-powered ones, where a spring inside is compressed when the child pulls the stroller backwards. When released, the cart moves while the spring returns to its initial shape. The energy conversion process that occurs in the described cart is also verified at:

a) a dynamo.
b) an automobile brake.
c) a combustion engine.
d) a hydroelectric power plant.
e) a slingshot.

Alternativa correta: e) uma atiradeira (estilingue).

## Curiosity: Did You Know?

Potential energy can also be electrical, that is, produced by the interaction of particles in a given electric field. It can also be nuclear, generated by the work gained from nuclear reactions, for example the atomic bomb. 