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## Mechanical energy

Definition 1: Mechanical energy

Mechanical energy is the sum of the gravitational potential energy and the kinetic energy of a system.

Quantity: Mechanical energy ($E M$)         Unit name: Joule         Unit symbol: J

Mechanical energy, $E M$, is simply the sum of gravitational potential energy ($E P$) and the kinetic energy ($E K$). Mechanical energy is defined as:

$E M =E P +E K$(1)
$E M =mgh+1 2mv 2$(2)

## Tip:

You may see mechanical energy written as U. We will not use this notation in this book, but you should be aware that this notation is sometimes used.

## Example 1: Mechanical energy

### Question

Calculate the total mechanical energy for a ball of mass 0,15 kg which has a kinetic energy of 20 J and is 2 m above the ground.

### Answer

#### Analyse the question to determine what information is provided

• The ball has a mass $m=0,15$ kg

• The ball is at a height $h=2$ m

• The ball has a kinetic energy $E K =20$ J

#### Analyse the question to determine what is being asked

We need to find the total mechanical energy of the ball

#### Use the definition to calculate the total mechanical energy

$E M =E P +E K =mgh+1 2mv 2 =mgh+20=(0,15kg)(9,8m·s -1 )(2m)+20J=2,94J+20J=22,94J$(3)