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Energy, Work and Power

Energy 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

Ep = mgΔh potential energy = mass x gravity x change in height

Ek = 1/2mv2 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

Ep = m.g.Δh

Ep = 0.5 x 10 x 2

= 10 J (Joules)


Note that g always equals 10 ms-2.

Example 3

Ek = 1/2 m. v2

Where:

Ek = 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).

Ek = 1/2 m. v2

20 000 = 1/2 m. (10)2

20 000 . (2) = m(100)

40 000 = 100 . m

m = 40 000
100

m = 400 kg