# Examples of Mechanical Energy

We explain that what are some examples of mechanical energy? The **mechanical energy** is the ability to **perform mechanical work** . Systems such as motors, which **transmit movement** between their components, use this energy to function. The mechanical energy of a body is the sum of its kinetic and potential energies. It depends on both the movement and the position of the body.

## How is mechanical energy calculated?

Mechanical energy is the sum of the kinetic and potential energies. The general formula to calculate it is:

**Em = Ec + Ep**

However, to understand it better, it can also be written by substituting the formulas for each of the energies.

The equation is in two ways:

**Em = ½ mv ^{2} + mgh**

In this, the kinetic energy (first term: **½ mv ^{2}** ) and the

**gravitational**potential

**energy**(second term:

**mgh**) are added.

**Em = ****½ mv ^{2}** +

**½ kx**

^{2}Here the kinetic energy (first term: **½ mv ^{2}** ) and the

**elastic**potential

**energy**(second term:

**½ kx**) are added.

^{2}## Units of mechanical energy

Mechanical energy, like all forms of energy, is measured in Joules (J), which are the units of energy for the International System of Units (SI). It is equal to Newton-meters (Nm).

**Joules (J) = Newton-meter (Nm)**

## Conservation of mechanical energy

The **first Law of Thermodynamics** , also called the Principle of Conservation of Energy, indicates that “Energy is neither created nor destroyed, it only transforms.” This is true for mechanical energy: in a body, this is always in equal measure, only that it is formed by **different portions** of kinetic energy and potential energy at each moment of the event.

It can be understood with the example of a **toy car that is supported by a spring** , which will give it momentum to travel a track. While the spring is compressed, the mechanical energy (Em) is concentrated there. It is its elastic potential energy (Ep _{e} ), plus the gravitational potential energy (Ep _{g} ) that the cart at rest has due to its position on the track.

When the spring is released, it quickly delivers kinetic energy to the cart, so that it reaches another point on the track, or until it collides with an obstacle. The forces acting in the event keep the mechanical energy constant. From the spring, through the wheels of the cart, to the obstacle or the end of the track, there is mechanical energy that maintains its value.

## Examples of mechanical energy

**Example 1**

A 1.5Kg ball is rolled at a speed of 20m / s through a channel that is 4m high. What is its mechanical energy?

Em =?

Ec =?

Ep =?

m = 1.5Kg

v = 20m / s

h = 4m

**Em = Ec + Ep**

**Em = ½ mv ^{2} + mgh**

**Ec = ****½ mv ^{2}** = ½ (1.5Kg) * (20m / s)

^{2}= 300 J

**Ep = ****mgh** = (1.5Kg) * (9.81m / s ^{2} ) * (4m) = 58.86 J

**Em =** 300 J + 58.86 J = 358.86 J

**Em = 358.86 Joules**

**Example 2**

A 4.2Kg ball is rolled at a speed of 5.5m / s through a channel that is 2m high. What is its mechanical energy?

Em =?

Ec =?

Ep =?

m = 4.2Kg

v = 5.5m / s

h = 2m

**Em = Ec + Ep**

**Em = ½ mv ^{2} + mgh**

**Ec = ****½ mv ^{2}** = ½ (4.2Kg) * (5.5m / s)

^{2}= 63.525 J

**Ep = ****mgh** = (4.2Kg) * (9.81m / s ^{2} ) * (2m) = 82.404 J

**Em =** 63.525 J + 82.404 J = 145.929 J

**Em = 145.929 Joules**

**Example 3**

A 2.3Kg ball is rolled at a speed of 6.2m / s through a channel that is 6.5m high. What is its mechanical energy?

Em =?

Ec =?

Ep =?

m = 2.3Kg

v = 6.2m / s

h = 6.5m

**Em = Ec + Ep**

**Em = ½ mv ^{2} + mgh**

**Ec = ****½ mv ^{2}** = ½ (2.3Kg) * (6.2m / s)

^{2}= 44.206 J

**Ep = ****mgh** = (2.3Kg) * (9.81m / s ^{2} ) * (6.5m) = 146.6595 J

**Em =** 44.206 J + 146.6595 J = 190.8655 J

**Em = 190.8655 Joules**

**Example 4**

A 6Kg ball is rolled at a speed of 16m / s through a channel that is 10m high. What is its mechanical energy?

Em =?

Ec =?

Ep =?

m = 6Kg

v = 16m / s

h = 10m

**Em = Ec + Ep**

**Em = ½ mv ^{2} + mgh**

**Ec = ****½ mv ^{2}** = ½ (6Kg) * (16m / s)

^{2}= 768 J

**Ep = ****mgh** = (6Kg) * (9.81m / s ^{2} ) * (10m) = 588.6 J

**Em =** 768 J + 588.6 J = 1356.6 J

**Em = 1356.6 Joules**

**Example 5**

A spring that has a constant of 2.5Kg / s ^{2} is compressed . The compression is 0.2m, and it is released to move a 0.5Kg body at 20m / s. What is the mechanical energy?

Em =?

Ec =?

Ep =?

m = 0.5Kg

v = 20m / s

k = 2.5kg / s ^{2}

x = 0.2m

**Em = Ec + Ep**

**Em = ****½ mv ^{2}** +

**½ kx**

^{2}**Ec = ****½ mv ^{2}** = ½ (0.5Kg) * (20m / s)

^{2}= 100 J

**Ep = ****½ kx ^{2}** = ½ (2.5Kg / s

^{2}) * (0.2m)

^{2}= 0.05 J

**Em =** 100 J + 0.05 J = 100.05 J

**Em = 100.05 Joules**