Ene**rgy Calculations**

Energy involves doing calculations and the skill of being able to manipulate formula and solve problems by using formula.

The following examples show how to manipulate formula to solve numerical problems:

**Formulae**

W = F. d work = force x distance

E_{p} = mgΔh potential energy = mass x gravity x change in height

Ek = ^{1}/_{2}mv^{2} kinetic energy = 1/2 x mass x (velocity)^{2}

Using these formulae calculate and determine the unknowns from the following problems.

**Example 1: Work**

W=Fxd

Work (J) Force (N) Distance (m)

Use the formula triangle to help manipulate the formula:

NB: WD means work done.

Calculate the force required when 500J of work are done lifting a box 20m.

F = W

d

F = 500

20

F = 25 N (Newtons)

**Example 2: Potential Energy**

Ep = m.g.Δh

Gravitational Potential Energy (J) mass (kg) Gravity (10 ms^{-2}) Change in height (m).

Calculate the gravitational potential energy when a 5009 bag of tomatoes is lifted 2 metres

E_{p} = m.g.Δh

E_{p} = 0.5 x 10 x 2

= 10 J (Joules)

Note that g always equals 10 ms^{-2}.

Example 3

E_{k }= ^{1}/_{2 m. v}^{2}

Where:

E_{k } = kinetic energy in Joules (J)

m = mass (kg)

v = velocity (ms^{-1})

Calculate the mass of a motorcycle which is moving at 10ms^{-1} (36 kn h^{-1}) and has a kinetic energy of 20 000 Joules(J).

E_{k }= ^{1}/_{2 m. v}^{2}

20 000 = ^{1}/_{2 m.} (10)^{2}

20 000 . (2) = m(100)

40 000 = 100 . m

m = 40 000

100

m = 400 kg