12 min readConcept sheetSection A MCQ (1 mark) and fill in the blanks (2 marks, two parts); Section B very short answer (2 marks) or short answer numerical (3 marks)

Kinetic energy and potential energy

Kinetic energy is energy of motion, KE = ½mv². Potential energy is energy of height, PE = mgh. Both are measured in joules.

Kinetic energyKE = ½mv² (m in kg, v in m s⁻¹); doubles if the mass doubles, becomes 4 times if the speed doubles

Potential energyPE = mgh (m in kg, g = 9.8 m s⁻², h = height in m); doubles if the height or the mass doubles

UnitBoth are measured in joules (J)

Kinetic vs potential energy

Kinetic energy (KE)Energy a body has because it is moving. A moving hammer drives in a nail; flowing water turns a water mill. KE = ½mv². It depends on the mass, and even more on the speed.

Potential energy (PE)Energy a body has because of its position (height) or shape (a stretched spring). A raised hammer, when dropped, can break a lump of dry clay. PE = mgh. It depends on the weight (mg) and the height h.

Activity: a ball or cell rolling down a slope of books

You need two thick books, a hard-bound register to use as a slope, a pencil cell and a heavier torch cell (or a small and a large ball), and an empty matchbox.

1
Stack two thick books and lean the register on them to make a slope.
2
Place the matchbox on the table just below the slope.
3
Let the pencil cell roll down from the top and hit the matchbox. Measure how far the box moves.
4
Roll the heavier torch cell from the same height. The box moves farther: more mass, more KE.
5★
Add a book to raise the slope, and roll the pencil cell again. The box moves farther still: more height gives more speed and more KE.
6
Conclude: as the cell rolls down, its PE changes into KE. KE grows with both mass and speed.

★ key step

How KE and PE change

Change	Kinetic energy	Potential energy
Mass doubled	2 times	2 times
Speed doubled	4 times	No change
Speed made 3 times	9 times	No change
Height doubled	No change	2 times
Height halved	No change	Half

Worked example: kinetic energy of a scooter

Problem

A scooter and its rider have a total mass of 120 kg and move at 10 m s⁻¹. Find their kinetic energy. What is it if the speed doubles?

Working

KE = ½mv² = ½ × 120 kg × (10 m s⁻¹)².
KE = 60 × 100 = 6000 J.
At 20 m s⁻¹: KE = ½ × 120 × 20² = 60 × 400 = 24 000 J.

Answer

6000 J (6 kJ). Doubling the speed makes it 24 000 J, four times as much

Worked example: potential energy of a water tank

Problem

A rooftop tank holds 500 kg of water at a height of 12 m above the ground. Find the potential energy of the water. (g = 9.8 m s⁻²)

Working

PE = mgh.
PE = 500 kg × 9.8 m s⁻² × 12 m.
PE = 4900 × 12 = 58 800 J.

Answer

58 800 J, or about 58.8 kJ

Worked example: speed from kinetic energy

Problem

A ball of mass 0.4 kg has 20 J of kinetic energy. Find its speed.

Working

KE = ½mv², so v² = 2 × KE ÷ m.
v² = 2 × 20 J ÷ 0.4 kg = 100 m² s⁻².
v = √100 = 10 m s⁻¹.

Answer

10 m s⁻¹

In real life

Road safety signs ask drivers to slow down. KE grows with the square of the speed, so a crash at double the speed carries four times the energy. Water stored high in a dam has PE that power stations turn into electricity.

Exam angle

2 marks: “Define kinetic energy and write its formula. How does it change if the speed of a body is tripled?” Kinetic energy is the energy a body has because of its motion: KE = ½mv². Tripling v makes KE 3² = 9 times as large.

2 marks: “Find the potential energy of a 2 kg flower pot on a shelf 3 m high. (g = 9.8 m s⁻²)” PE = mgh = 2 × 9.8 × 3 = 58.8 J.

3 marks: “A 1000 kg car moves at 15 m s⁻¹. Find its kinetic energy. What is its kinetic energy at 30 m s⁻¹, and what does this mean for road safety?” KE = ½ × 1000 × 15² = 112 500 J. At 30 m s⁻¹: KE = ½ × 1000 × 30² = 450 000 J, four times as much. So a crash at double the speed releases four times the energy and does far more damage.

Remember it

Move it: half m v squared. Lift it: m g h.