Work, Energy and Power – SS1 Physics Lesson Note (Second Term)

Work is done when a force moves a body through a distance in the direction of the force. Energy is the ability to do work, and power is the rate of doing work. All three are scalar quantities. Work and energy are measured in joules, and power is measured in watts.

Behavioural objectives

By the end of the lesson, students should be able to:

• define work, energy and power and state their units;
• calculate work done, potential energy, kinetic energy and power using the correct formulae;
• list the forms of energy and the two types of mechanical energy;
• state the law of conservation of energy and give examples of energy conversion;
• classify energy resources as renewable or non-renewable.

What is work?

Work is done whenever a force moves a body through a certain distance in the direction of the force. Mathematically, work done is the product of the force and the displacement. It is a scalar quantity and is measured in joules (J).

W = F × d

W = mgh

Work done by a force applied at an angle

If a force F is applied on a body at an angle θ to the horizontal:

• Work done to move the body on the horizontal plane = F cos θ × d
• Work done to raise the body to an appreciable height = F sin θ × d

Worked example: work done against gravity

A boy of mass 50 kg runs up a set of steps of total height 3.0 m. Find the work done against gravity.

Solution

m = 50 kg, h = 3 m, g = 10 m/s²

Work done = mgh = 50 × 10 × 3 = 1500 J

What is energy?

Energy is the ability to do work. It is a scalar quantity and is measured in joules. There are many forms of energy. These include:

1. Mechanical energy
2. Thermal energy
3. Chemical energy
4. Electrical energy
5. Nuclear/atomic energy
6. Solar/light energy
7. Sound energy

What are the types of mechanical energy?

Mechanical energy is classified as potential energy and kinetic energy.

• Potential energy is stored energy, that is, energy possessed by a body by virtue of its position or state. P.E = mgh
• Kinetic energy is the energy possessed by a body by virtue of its motion. Examples are a student running a race, wind or air in motion, electrical charges in motion and a moving bullet. K.E = ½mv²

Worked example: kinetic energy

An object of mass 5 kg is moving at a constant velocity of 15 m/s. Calculate its kinetic energy.

Solution

K.E = ½mv² = ½ × 5 × 15 × 15 = 562.5 J

Worked example: potential energy

Find the potential energy of a boy of mass 10 kg standing on a building floor 10 m above the ground level. g = 10 m/s²

Solution

P.E = mgh = 10 × 10 × 10 = 1000 J

What is power?

Power is the rate of doing work or the rate of transfer of energy. It is a scalar quantity and is measured in watts (W).

Power = work done ÷ time

P = (F × d)/t = F × (d/t) = Fv

Worked example: power of a boy climbing steps

A boy of mass 10 kg climbs up 10 steps, each of height 0.2 m, in 20 seconds. Calculate the power of the boy.

Solution

Height climbed = 10 × 0.2 = 2 m

Work done = mgh = 10 × 10 × 2 = 200 J

Power = work done ÷ time = (10 × 10 × 2) ÷ 20 = 10 W

How is work done in lifting a body and in falling bodies?

The work done in lifting a body is given by:

Work = force × distance = mg × h = mgh

The work done on a falling body is given by the same expression:

Work = force × distance = mg × h = mgh

What is the law of conservation of energy?

Energy can be converted from one form to another in a closed system. The law of conservation of energy states that in an enclosed system, energy can neither be created nor destroyed during transformation.

Examples of such conversions include:

1. A motor converts electrical energy to mechanical energy.
2. A generator converts mechanical energy to electrical energy.
3. An electric pressing iron converts electrical energy to heat energy.

What are the world energy resources?

World energy resources are classified as:

1. Renewable energy resources: energy that can be replaced as it is used, for example solar energy, wind energy, water energy and biomass.
2. Non-renewable energy resources: energy that cannot be replaced after use, for example nuclear energy, petroleum and natural gas.

Evaluation

1. Define work, energy and power, and state the unit of each.
2. Write the formulae for potential energy and kinetic energy.
3. A girl of mass 40 kg climbs a flight of stairs of total height 5 m. Calculate the work done against gravity. (g = 10 m/s²)
4. State the law of conservation of energy and give two examples of energy conversion.
5. Give two examples each of renewable and non-renewable energy resources.

Assignment

1. An object of mass 4 kg is moving at a constant velocity of 10 m/s. Calculate its kinetic energy.
2. Find the potential energy of a box of mass 20 kg placed on a shelf 3 m above the ground. (g = 10 m/s²)
3. A boy of mass 20 kg climbs up 10 steps, each of height 0.2 m, in 10 seconds. Calculate his power. (g = 10 m/s²)