OCR GCSE Physics A: Deformation, springs and Hooke's law (J249) – Revision Notes

These notes condense statements P2.3a to P2.3f of the OCR GCSE (9-1) Gateway Science Physics A (J249) specification, Version 5.0 (July 2026), for first assessment in 2018. All six statements are assessed in both tiers. The study guide has the full explanations and longer examples. To test yourself, use the practice questions, the OCR GCSE Physics hub, the printable checklist and the free 10-minute diagnostics.

Key ideas at a glance

Statement	One-line summary
P2.3a	Stretching, bending or compressing needs more than one force, acting in opposite senses
P2.3b	Elastic: returns to original shape. Plastic: permanent change of shape
P2.3c	Spring: force against extension is a straight line through the origin, then it curves
P2.3d	Linear: straight line through origin. Non-linear: anything else
P2.3e	k = F / e in the linear region, in N/m
P2.3f	Work done = area under the graph; for a spring, E = ½ke²

P2.3a: forces that deform

• One force on a free object changes its motion, not its shape.
• Deformation needs forces on different parts of the object that squeeze or stretch it.
• Stretch: spring between clamp and weight.
• Compress: foam block between two hands, or between a hand and a table.
• Bend: plank across two supports with a person standing in the middle (three forces).
• The tension in a spring pulled by two equal forces is the size of one force, not the sum.

Reminder: each end of a spring is pulled with 6.0 N. The spring is stretched by 6.0 N, not 12.0 N.

P2.3b: elastic and plastic

	Elastic deformation	Plastic deformation
After forces removed	Returns to original shape and size	Stays deformed
Examples	Spring within its limit, gently stretched rubber band	Modelling clay, a paper clip bent open, an over-stretched spring
Test	Load, unload, measure length again	Length after unloading is greater than the natural length

An object can be elastic for small forces and plastic for large ones.

P2.3c and P2.3d: force-extension graphs

Extension = stretched length − natural length. Measure both in the same unit.

Method in steps for the spring investigation (PAG P2 suggestion):

1. Measure the natural length with a ruler next to the spring.
2. Add a known weight to the hanger. Let it settle.
3. Measure the new length at eye level, then work out the extension.
4. Repeat with more weights. Take care not to overload the spring.
5. Plot force (vertical) against extension (horizontal).
6. Draw a straight line through the linear points. Mark where the points leave it.
7. To test elasticity, unload and check that the length returns.

Feature on the graph	Meaning
Straight line through the origin	Linear. Force is directly proportional to extension
Where the line starts to bend	Limit of proportionality
Curve	Non-linear. No single spring constant applies
Steeper straight line	Stiffer spring (larger k)

Other simple systems are an elastic band, a rubber cord and a wire. A band gives a curved graph over most of its range, and its unloading curve usually sits below its loading curve.

Must-know distinction: linear and non-linear describe the graph shape. Elastic and plastic describe whether the object recovers. A graph can be curved while the object is still elastic.

P2.3e: spring constant

Quantity	Symbol	Unit
Force	F	newton, N
Spring constant	k	newton per metre, N/m
Extension	e	metre, m

F = ke, so k = F / e and e = F / k.

The spring constant is the gradient of the straight part of a force-extension graph.

Method in steps:

1. Work out the extension (stretched length minus natural length).
2. Convert to metres.
3. Write the equation, rearrange if needed, then substitute.
4. Give the unit.

Reminder: a force of 9.0 N produces a 4.5 cm extension. e = 0.045 m. k = 9.0 / 0.045 = 200 N/m.

Reminder: a graph line passes through the origin and the point (0.12 m, 9.0 N). Gradient = 9.0 / 0.12 = 75 N/m.

Valid for compression too, within the linear range. Use the compression as e.

P2.3f: work done and stored energy

• Work done stretching = energy transferred to the object.
• Elastic behaviour: that energy is stored and can be released.
• Spring in linear region: E = ½ke² (e squared, then multiplied).
• Also E = ½Fe for a straight-line graph, because the area is a triangle.
• Non-linear: E = area under the curve. Count squares, or add up trapezium strips.
• Doubling e quadruples E. Tripling e multiplies E by 9.

Graph	How to find work done
Straight line through origin	½ × base × height, or ½ke²
Curve	Count squares, scale using the grid, or split into strips

Reminder (counting squares): if one small square represents 0.5 N by 0.5 cm, one square is 0.25 N cm, which is 0.0025 J.

Reminder (linear): k = 90 N/m and e = 0.10 m. E = ½ × 90 × 0.10² = 0.45 J.

Reminder (finding extension): a spring with k = 60 N/m must store 0.075 J. e² = 2 × 0.075 / 60 = 0.0025, so e = 0.050 m.

Worked reminder: reading a results table

A spring has a natural length of 10.0 cm. Loads of 1.0 N, 2.0 N, 3.0 N and 4.0 N give lengths of 12.0 cm, 14.0 cm, 16.0 cm and 19.0 cm.

1. Extensions: 2.0 cm, 4.0 cm, 6.0 cm and 9.0 cm.
2. The first three rise by 2.0 cm per newton, so they are linear. The fourth rises by 3.0 cm, so the line has bent.
3. Use a linear point: k = 3.0 / 0.060 = 50 N/m.
4. Energy stored at 3.0 N: E = ½ × 50 × 0.060² = 0.090 J.

State the limit of proportionality as lying between 3.0 N and 4.0 N, and say how you know: the extra extension per newton changes.

Where the ideas show up

• A rope, bungee cord or climbing harness is stretched by the weight of a person and the anchor point.
• A mattress, trampoline or car seat is compressed or bent by a load and its supports.
• A toy launcher stores energy in a compressed spring. The larger the compression, the more energy is stored.

Mixed-up pairs to keep apart

• Extension and length: extension is the change.
• Limit of proportionality and breaking point: the first is where the straight line ends. The spring is not broken there.
• Force and energy: F = ke gives newtons. E = ½ke² gives joules.
• Spring constant and extension: a bigger k means a smaller extension for the same force.
• Compression and extension: both use the same equations, both measured as a change in length.

Quick self-test

1. State why a single force cannot stretch a free spring.
2. Define plastic deformation.
3. A force of 12 N stretches a spring by 0.15 m, within its linear range. Calculate k.
4. A spring has k = 150 N/m. Calculate the extension produced by 6.0 N.
5. Calculate the energy stored when a spring of k = 90 N/m is stretched by 0.10 m.
6. A straight-line graph shows 8.0 N at an extension of 0.050 m. Find the energy stored using the area under the graph.
7. The extension of a spring is tripled. By what factor does the stored energy change?
8. Name the point on a force-extension graph where the straight line ends.
9. True or false: any object whose force-extension graph is curved has been plastically deformed.
10. Describe how to estimate the work done on an elastic band from a curved graph.
11. A spring with k = 60 N/m is compressed by 5.0 cm. Calculate the energy stored.
12. A student measures a spring that is 28.5 cm long under a 3.0 N load. Its natural length is 24.0 cm. Calculate k.

Answers

1. A free spring would simply accelerate. A second force in the opposite sense is needed for the parts to move apart.
2. A permanent change of shape that remains after the forces are removed.
3. k = F / e = 12 / 0.15 = 80 N/m.
4. e = F / k = 6.0 / 150 = 0.040 m (4.0 cm).
5. E = ½ × 90 × 0.10² = 0.45 J.
6. Area = ½ × 0.050 × 8.0 = 0.20 J.
7. It increases by a factor of 9, because E is proportional to e².
8. The limit of proportionality.
9. False. A curved graph means non-linear. The object can still be elastic.
10. Count the squares under the curve, or split it into strips and add their areas. Use the axis scales to turn the total into joules.
11. E = ½ × 60 × 0.050² = 0.075 J.
12. Extension = 28.5 − 24.0 = 4.5 cm = 0.045 m. k = 3.0 / 0.045 = 67 N/m (66.7 N/m to 3 significant figures).

Where marks are usually lost

• Writing the stretched length where the extension is needed.
• Forgetting to change centimetres or millimetres to metres.
• Quoting E = ½ke² without squaring the extension.
• Answering “elastic” or “plastic” from the shape of the graph alone, without saying what happens when the load is removed.
• Calculating k from a point beyond the limit of proportionality.
• Leaving out units, or giving newtons for an energy.
• Describing a graph as “proportional” without saying it is a straight line through the origin.
• Saying a spring “breaks” at the limit of proportionality.
• Not showing the substitution step in a calculation, which makes a slip harder to credit.

Official syllabus

OCR, GCSE (9-1) Gateway Science Physics A (J249), Version 5.0 (July 2026), first assessment 2018. Statements P2.3a to P2.3f.