OxfordAQA International GCSE Physics: Work, kinetic, gravitational and elastic energy, and power (9203) – Revision Notes

These notes condense section 3.2.1, Forces and energy (statements a to f), of the OxfordAQA International GCSE Physics (9203) specification, for exams from May/June 2018. The qualification is untiered. For full explanations and worked examples use the study guide, and for exam-style questions use the practice set.

Related pages: the OxfordAQA International GCSE Physics hub, the printable checklist, the Energy revision notes and the free diagnostics.

Equations to learn

Spec	Quantity	Equation	Units
3.2.1 a	Work done	W = F × d	J, N, m
3.2.1 c	Elastic potential energy of a stretched spring	Ee = ½ × k × e²	J, N/m, m
3.2.1 d	Gravitational potential energy	Ep = m × g × h	J, kg, N/kg, m
3.2.1 e	Kinetic energy	Ek = ½ × m × v²	J, kg, m/s
3.2.1 f	Power	P = E / t and P = W / t	W, J, s

Rearranged forms you will need:

To find	Use
Force	F = W / d
Distance	d = W / F
Extension	e = √(2 × Ee / k)
Spring constant	k = 2 × Ee / e²
Height	h = Ep / (m × g)
Speed	v = √(2 × Ek / m)
Mass (from Ek)	m = 2 × Ek / v²
Energy	E = P × t
Time	t = E / P

Work done (3.2.1 a)

• Work is done when a force makes an object move through a distance.
• Only movement along the line of the force counts. Holding something still does no work on it.
• The work done equals the energy transferred. 1 J = 1 N m.
• Convert cm to m, and kJ to J, before substituting.

Method in steps:

1. Write the equation, W = F × d.
2. Put in values with units in J, N and m.
3. Calculate and give the unit.

Reminder: 250 kg is lifted 6.0 m. The force is the weight, 250 × 10 = 2500 N, so W = 2500 × 6.0 = 15 000 J. That equals m × g × h.

Work against friction and heating (3.2.1 b)

• Friction opposes motion. Work done against it is transferred by heating.
• The energy is not lost. It becomes thermal energy in the surfaces and the surroundings, and spreads out.
• Brakes: friction between pads and discs turns the vehicle’s kinetic energy into thermal energy in the brakes. Braking force × braking distance = Ek lost.
• Shuttle re-entry: very high speed means air resistance does a lot of work. Kinetic energy is transferred by heating to the surface and the air. Heat-resistant tiles protect the craft.
• Meteorites: a small object moving very fast through the atmosphere is heated by air resistance until it glows and burns up. It is a meteor while it glows.

Reminder: an 800 kg van at 10 m/s has Ek = ½ × 800 × 10² = 40 000 J. A braking force of 4000 N stops it in 40 000 / 4000 = 10 m.

Elastic potential energy (3.2.1 c)

• Ee = ½ × k × e², where e is extension, not total length.
• Valid only below the limit of proportionality, where the spring obeys Hooke’s law.
• Area under a straight force-extension graph gives the same energy.
• Double the extension, four times the energy.

Reminder: a spring with k = 120 N/m is stretched from 0.30 m to 0.45 m. The extension is 0.15 m, so Ee = ½ × 120 × 0.15² = 1.35 J.

Method in steps:

1. Work out the extension: new length minus original length, in metres.
2. Square the extension first.
3. Multiply by k, then by one half.

Gravitational potential energy (3.2.1 d)

• Ep = m × g × h with h the vertical height gained.
• Take g as the value given in the question, such as 10 N/kg.
• On a ramp, use how far the object rises, not how far it travels along the ramp.
• A smaller g gives a smaller Ep for the same lift.

Kinetic energy (3.2.1 e)

• Ek = ½ × m × v². Square only the speed.
• To change km/h into m/s, divide by 3.6.

Change	Effect on Ek
Mass doubled, same speed	Doubles
Speed doubled, same mass	Four times
Speed tripled, same mass	Nine times

Road safety link: stopping needs braking force × distance = Ek. With the same braking force, doubling the speed makes the braking distance four times as long. Higher speed also means more energy to transfer in a collision.

Power (3.2.1 f)

• Power measures how quickly energy is transferred, or how quickly work is done.
• P = E / t and P = W / t. 1 W = 1 J/s.
• Convert minutes and hours to seconds.
• A bigger power means the same job finished sooner, or more done in the same time.

Reminder: a hoist does 15 000 J of work in 20 s. P = 15 000 / 20 = 750 W.

Reminder: a 20 W lamp transferring energy for 5.0 minutes: t = 300 s, E = 20 × 300 = 6000 J.

Must-know distinctions

• Work done is energy transferred. Power is how fast it is transferred.
• Extension is not length. Height is not slope length.
• Mass doubled gives twice Ek. Speed doubled gives four times Ek.
• Heating by friction is energy transferred to the surroundings, not energy destroyed.
• J is energy and W is power. A watt is a joule per second.

Quick self-test

Take g = 10 N/kg where needed.

1. A force of 60 N moves a box 9.0 m in the direction of the force. How much work is done?
2. A force moves a trolley 18 m and does 900 J of work. What is the force?
3. A spring with spring constant 200 N/m is stretched by 0.10 m. How much elastic potential energy does it store?
4. A spring with spring constant 50 N/m stores 0.36 J. What is its extension?
5. A 3.0 kg bag is lifted through 1.5 m. What gravitational potential energy does it gain?
6. Find the kinetic energy of a 3.0 kg cart moving at 4.0 m/s.
7. A 5.0 kg object moves at 3.0 m/s. Its speed increases to 9.0 m/s. By what factor does its kinetic energy increase, and what is the new kinetic energy?
8. A machine transfers 4500 J in 30 s. What is its power?
9. A 1.5 kW heater transfers 90 000 J. How long does that take?
10. A car of mass 1000 kg travels at 72 km/h. What is its kinetic energy?
11. Explain why a meteorite gets hot as it falls through the atmosphere.

Answers

1. W = F × d = 60 × 9.0 = 540 J
2. F = W / d = 900 / 18 = 50 N
3. Ee = ½ × 200 × 0.10² = 1.0 J
4. e² = 2 × 0.36 / 50 = 0.0144, so e = 0.12 m
5. Ep = 3.0 × 10 × 1.5 = 45 J
6. Ek = ½ × 3.0 × 4.0² = 24 J
7. Speed is three times as big, so Ek is 3² = 9 times as big. Original Ek = ½ × 5.0 × 3.0² = 22.5 J. New Ek = ½ × 5.0 × 9.0² = 202.5 J, and 202.5 / 22.5 = 9.
8. P = E / t = 4500 / 30 = 150 W
9. 1.5 kW = 1500 W. t = E / P = 90 000 / 1500 = 60 s
10. 72 km/h = 72 / 3.6 = 20 m/s. Ek = ½ × 1000 × 20² = 200 000 J
11. It moves very fast, so air resistance does work against its motion. The work is transferred by heating and its kinetic energy decreases, warming the surface and the air around it, so it can glow and burn up.

Where marks are usually lost

• Substituting the whole spring length where the extension belongs.
• Squaring the wrong thing, for example (½ × v)² instead of ½ × v².
• Saying that doubling speed doubles the kinetic energy.
• Forgetting to convert km/h to m/s, minutes to seconds, or cm to m.
• Taking height along a ramp rather than the vertical rise in Ep = m × g × h.
• Describing friction as “using up” energy, with no mention of heating or the surroundings.
• Giving a meteorite or brake explanation with no mention of kinetic energy, or with no mention of work done against a force.
• Giving the answer with no unit, or a joule when the quantity is a watt.
• Leaving out working. Writing the equation, the substitution and the answer makes your method clear to the reader.

Official syllabus

These notes are aligned to section 3.2.1 of the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, published by OxfordAQA.