Potential and Kinetic Energy – JSS2 Basic Science Lesson Note (Second Term)

Potential energy is the energy a body has because of its position, and kinetic energy is the energy a body has because it is moving.

Behavioural objectives

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

1. define potential energy and kinetic energy and give examples of each;
2. state the formulas for potential energy and kinetic energy;
3. calculate potential energy, kinetic energy and work done;
4. explain how potential energy changes to kinetic energy when an object falls;
5. define power and calculate it.

What is mechanical energy?

Mechanical energy is the energy a body has because of its position or its motion.

• Potential energy: stored energy due to position, for example a stone on a table.
• Kinetic energy: energy of motion, for example a rolling ball.
• Unit: both are measured in joules (J).
• Kilojoule: 1 kJ = 1000 J.

What is potential energy?

Potential energy is the energy stored in a body because of its position (its height above the ground).

• On the ground: a stone lying on the ground has no potential energy, so it cannot do work by falling.
• On a table: the same stone has stored energy because of its height.
• When it falls: it can break a lamp on which it lands, so it can do work.
• Effect of height: the energy increases as the height increases.
• Falling: the energy decreases as the stone falls towards the ground.
• At the ground: the potential energy is zero.

Examples of potential energy

• Fruit on a tree: a mango hanging high up can fall and do work.
• Water in a tank: water in a raised tank can flow down a pipe.
• Stretched rubber band: it stores energy because of its shape and returns to its length when released.
• Compressed spring: it stores energy because it is squeezed.

What is kinetic energy?

Kinetic energy is the energy possessed by a moving body, also called movement energy.

• Moving car: a car on the road has kinetic energy.
• Running man: a runner has kinetic energy.
• Falling orange: it gains kinetic energy as it falls.
• Fired bullet: it moves very fast, so it has a large kinetic energy.
• Rolling ball: it has kinetic energy while it rolls.

What are the formulas for potential and kinetic energy?

Potential energy is P.E = mgh and kinetic energy is K.E = ½mv².

Kinetic energy

• Formula: K.E = ½ × m × v².
• m: the mass of the moving object, in kilograms (kg).
• v: the velocity of the object, in metres per second (m/s).
• Effect of speed: doubling the velocity makes the kinetic energy four times larger.

Potential energy

• Formula: P.E = m × g × h.
• m: the mass of the object, in kilograms (kg).
• g: the acceleration due to gravity, in m/s².
• h: the height of the object above the ground, in metres (m).

Comparing potential and kinetic energy

Worked example 1: potential energy

An object of mass 6 kg is at a height of 5 m. Calculate its potential energy. (g = 10 m/s².)

1. Write the formula: P.E = m × g × h.
2. Write the values: m = 6 kg, g = 10 m/s², h = 5 m.
3. Substitute: P.E = 6 × 10 × 5.
4. Answer: P.E = 300 J.

Worked example 2: mass from kinetic energy

A ball moving at 10 m/s has a kinetic energy of 50 kJ. Find its mass.

1. Write the formula: K.E = ½mv².
2. Convert the energy: 50 kJ = 50,000 J.
3. Substitute: 50,000 = ½ × m × 10².
4. Simplify: 50,000 = ½ × 100 × m = 50m.
5. Divide both sides by 50: m = 50,000 / 50.
6. Answer: m = 1000 kg.

How does potential energy change to kinetic energy?

When an object falls, its potential energy changes to kinetic energy as work is done by gravity.

• Energy is not lost: energy cannot be created or destroyed, it only changes from one form to another.
• Equal amounts: the potential energy lost equals the kinetic energy gained, if air resistance is ignored.
• Work and energy change: when energy changes from one form to another, work is done.

What happens as an object falls?

What is work done?

Work is done when a force moves a body through a distance, and it is measured in joules.

• Formula: Work done = force × distance moved in the direction of the force.
• Force of a weight: force = mass × g, so lifting a mass gives W = m × g × h.
• Unit: the joule (J).

Worked example: work done in raising a mass

What work is done when a mass of 6 kg is raised through a vertical height of 3.5 m? (g = 10 m/s².)

1. Write the formula: W = m × g × h.
2. Substitute: W = 6 × 10 × 3.5.
3. Answer: W = 210 J.

What is power?

Power is the rate of doing work, found by dividing work done by the time taken.

• Formula: Power = Work done / Time taken.
• Unit: the watt (W), which is one joule per second.
• Kilowatt: 1 kW = 1000 W.
• Meaning: a machine with more power does the same work in less time.

Worked example 1: power of a child

What is the power of a child who does 60 J of work in 20 seconds?

1. Write the formula: P = Work / Time.
2. Substitute: P = 60 / 20.
3. Answer: P = 3 W.

Worked example 2: power of a pump

Calculate the power of a pump that lifts 500 kg of water through a vertical height of 12 m in 0.3 minutes. (g = 9.8 m/s².)

1. Find the force: F = 500 × 9.8 = 4900 N.
2. Find the work done: W = 4900 × 12 = 58,800 J.
3. Convert the time to seconds: 0.3 × 60 = 18 s.
4. Find the power: P = 58,800 / 18 = 3266.67 W.
5. Convert to kilowatts: 3266.67 / 1000 = 3.27 kW.

Evaluation

1. Define potential energy and give one example.
2. Define kinetic energy and give two examples.
3. What is the potential energy of a stone when it reaches the ground?
4. Calculate the potential energy of a 4 kg object at a height of 10 m. (g = 10 m/s².)
5. Define power and state its unit.

Assignment

1. Calculate the kinetic energy of a ball of mass 2 kg moving at a velocity of 5 m/s.
2. What work is done when a mass of 4 kg is raised through a vertical height of 2.5 m? (g = 10 m/s².)
3. Calculate the power of a boy who does work of 120 J in 30 seconds.