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.

Behavioural objectives

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

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

What is work?

Work is the product of a force and the distance moved by the body in the direction of the force.

• Formula: W = F × d, where F is the force in newtons (N) and d is the distance in metres (m).
• Unit: the joule (J). One joule is the work done when a force of 1 N moves a body through 1 m.
• Type: work is a scalar quantity.
• No movement, no work: a person pushing a fixed wall does no work, because the wall does not move.
• Lifting a body: the force needed is the weight mg, so W = mgh, where h is the height raised.

How is work done by a force applied at an angle?

When a force F acts at an angle θ to the horizontal, only its component along the movement does work.

• Horizontal component: F cos θ acts along the surface.
• Vertical component: F sin θ acts upwards and helps to lift the body slightly.
• Work done along the horizontal plane: W = F cos θ × d.
• Special case: when θ = 0°, cos θ = 1 and W = F × d.
• No work from the vertical component: F sin θ does no work when the body moves only along the horizontal.

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

Worked example: force at an angle

A force of 20 N pulls a box 5 m along a horizontal floor. The force makes an angle of 60° with the floor. Find the work done.

Solution

Work done = F cos θ × d = 20 × cos 60° × 5 = 20 × 0.5 × 5 = 50 J

What is energy?

Energy is the ability to do work, and it is measured in joules (J).

What are the forms of energy?

There are seven common forms of energy: mechanical, thermal, chemical, electrical, nuclear, solar (light) and sound.

1. Mechanical energy: energy of a body due to its position or motion, such as a moving car.
2. Thermal energy: heat energy, as in a hot stove.
3. Chemical energy: energy stored in food, fuel and batteries.
4. Electrical energy: energy of moving charges, as in a circuit.
5. Nuclear (atomic) energy: energy stored in the nucleus of an atom and released in a nuclear reactor.
6. Solar (light) energy: energy from the sun.
7. Sound energy: energy given out by vibrating bodies, such as a drum.

What are the types of mechanical energy?

There are two types of mechanical energy: potential energy and kinetic energy.

• Potential energy: stored energy a body has because of its position or state. P.E = mgh.
• Kinetic energy: energy a body has because of its motion. K.E = ½mv².

Examples of potential energy

• Water in a tank: water in a tank on a high tower has energy due to its height.
• Stretched spring: a stretched or compressed spring stores energy due to its state.

Examples of kinetic energy

• Runner: a student running a race.
• Moving air: wind or air in motion.
• Moving charges: electrical charges in motion.
• Moving bullet: a bullet in flight.

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, and it is measured in watts (W).

• Formula: Power = work done ÷ time, or P = W ÷ t.
• Unit: 1 watt is 1 joule per second (1 W = 1 J/s).
• Kilowatt: 1 kW = 1000 W.
• Type: power is a scalar quantity.
• Power and velocity: 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

Worked example: power from work and time

A machine does 3000 J of work in 60 s. Find its power.

Solution

Power = work done ÷ time = 3000 ÷ 60 = 50 W

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

Work done in lifting a body or in the fall of a body is found with the same expression, mgh.

• Lifting a body: work = force × distance = mg × h = mgh. The work is done against gravity and is stored as potential energy.
• Falling body: work = force × distance = mg × h = mgh. The work is done by gravity and appears as kinetic energy.

What is the law of conservation of energy?

The law of conservation of energy states that in an enclosed system, energy can neither be created nor destroyed, but can only be changed from one form to another.

What are examples of energy conversion?

How does energy change in a falling body?

• At the top: the body has maximum potential energy and no kinetic energy.
• While falling: potential energy decreases and kinetic energy increases.
• Just before landing: kinetic energy equals the potential energy at the top, if air resistance is ignored.

Worked example: energy of a falling ball

A ball of mass 2 kg is dropped from a height of 5 m. Find its kinetic energy and speed just before it hits the ground. Ignore air resistance. g = 10 m/s²

Solution

P.E at the top = mgh = 2 × 10 × 5 = 100 J

K.E just before the ground = 100 J

½ × 2 × v² = 100, so v² = 100 and v = 10 m/s

What are the world energy resources?

World energy resources are classified into two groups: renewable and non-renewable.

• Renewable energy resources: energy sources that can be replaced as they are used.
• Non-renewable energy resources: energy sources that cannot be replaced after use.

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

Solve the three calculations below, showing the formula, substitution and answer with unit.

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)