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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)