OxfordAQA International GCSE Physics: Forces, Hooke's law, vectors and distance-time motion (9203) – Revision Notes

These revision notes are aligned to the OxfordAQA International GCSE Physics (9203) specification, version 5.2, for exams May/June 2018 onwards, sections 3.1.1 and 3.1.2. They condense the full study guide, which has the explanations and longer worked examples. Test yourself afterwards with the practice questions.

Related pages: course hub, printable checklist, forces revision notes and the free 10-minute diagnostics.

Key terms

Term	Meaning
Contact force	Needs the objects to touch: friction, air resistance, tension, normal contact force
Non-contact (field) force	Acts across a gap: gravity, electrostatic, magnetic
Friction	Force between two surfaces that impedes motion; may result in heating
Air resistance	A form of friction, for motion through air
Scalar	Magnitude only
Vector	Magnitude and direction; drawn as an arrow
Weight	The pull of gravity on an object
Elastic distortion	Object goes back to its first shape once the forces stop
Inelastic distortion	Object stays out of shape afterwards
Limit of proportionality	Point beyond which extension is no longer directly proportional to force
Velocity	Speed in a given direction, v = s ÷ t

Scalar or vector?

Scalar	Vector
distance	displacement
speed	velocity
time	acceleration
	force
	momentum

Arrow rule: length = magnitude, head = direction. With a scale of 1 cm to 4 N, a 14 N force is 3.5 cm long.

Force pairs

• When two objects interact, each exerts a force on the other.
• The two forces are vectors: equal in size, opposite in direction.
• They act on different objects, so they never cancel each other.
• Example: a boot pushes the ground backwards; the ground pushes the boot forwards.

Equations

Equation	Symbols and units
W = m × g	W weight (N), m mass (kg), g gravitational field strength (N/kg)
F = k × e	F force (N), k spring constant (N/m), e extension (m)
v = s ÷ t	v velocity or average speed (m/s), s displacement or distance (m), t time (s)
speed = gradient of distance-time graph	change in distance ÷ change in time

The value of g is given in the question. Use that value.

Method boxes

Weight calculation

1. Write W = m × g.
2. Check mass is in kg (divide grams by 1000).
3. Substitute the g value supplied.
4. Give the answer in N with a sensible number of significant figures.

Hooke’s law calculation

1. Work out extension = new length − original length.
2. Convert cm to m.
3. Use F = k × e, or rearrange to k = F ÷ e or e = F ÷ k.
4. Check the force is within the limit of proportionality.

Reading a distance-time graph

1. Flat line: stationary.
2. Straight slope: constant speed. Speed = rise ÷ run, with units from the axes.
3. Curve: speed changing. Use a tangent for the speed at one instant.
4. Average speed: total distance ÷ total time, including any rests.

Worked reminders

Spring. A spring of original length 20.0 cm is 26.0 cm long under 3.0 N. Extension = 6.0 cm = 0.060 m. k = 3.0 ÷ 0.060 = 50 N/m. A 5.0 N load then gives e = 5.0 ÷ 50 = 0.10 m, so the length is 30.0 cm (if the limit is not exceeded).

Weight. A 2.0 kg bag where g = 1.6 N/kg: W = 2.0 × 1.6 = 3.2 N. Its mass is still 2.0 kg.

Distance-time. A runner covers 100 m in the first 20 s, rests for 10 s, then covers 100 m in 30 s. Average speed = 200 ÷ 60 = 3.3 m/s (2 significant figures).

Displacement. A cat walks 6 m north then 2 m south in 8 s: distance 8 m, speed 1.0 m/s; displacement 4 m north, velocity 0.50 m/s north.

Friction, heating and field forces

• Friction acts against the motion, or against the tendency to move.
• Rubbing surfaces warm up: brakes, hands, a rope sliding through a fist.
• Air resistance grows with speed and falls with a more streamlined shape.
• Field forces act without contact because each object sits in a field: a falling apple is in the Earth’s gravitational field, a paper clip near a magnet is in its magnetic field, and a charged comb near scraps of paper is in an electric field.
• A force changes the shape of an object only when other forces also act. A spring needs a pull at each end.

Model answers to learn

• Stretching. “The extension is directly proportional to the force, so the graph is a straight line through the origin, until the limit of proportionality.”
• Past the limit. “The line curves, so extension is no longer proportional to force. The spring may not return to its original length.”
• Gradient. “The gradient of a force-extension graph is the spring constant. The gradient of a distance-time graph is the speed.”
• Weight. “Weight is the pull of gravity on the object. It is different on different planets because g is different, but the mass is the same.”

Force-extension graph

• A straight line from the origin that stays straight until the limit of proportionality. Gradient = k.
• Beyond the limit the line curves: extension grows faster than force.
• A stiffer spring has a larger k, so a steeper force-extension line.
• A spring stretched elastically stores elastic potential energy, and releases it when it returns to its original length.

Required practical: force and extension

Step	Detail
Set up	Spring hung from a clamped stand, vertical rule alongside
Measure	Original length, then length after each added mass
Force	Weight of the masses, found with W = m × g
Process	Extension = length − original length; plot force against extension
Conclude	Straight line through the origin, so extension is proportional to force within the limit
Reduce error	Eye level with the pointer (parallax), repeat readings, check the zero error, small mass steps
Safety	Eye protection, stable stand, feet clear of falling masses

Unloading the spring and re-measuring checks whether the distortion was elastic.

Must-know distinctions

• Mass and weight: mass is a scalar in kg and does not change with place. Weight is a vector in N and depends on g.
• Distance and displacement: distance is the path length. Displacement is the straight-line separation with a direction.
• Speed and velocity: speed is a scalar. Velocity includes direction.
• Length and extension: extension is the increase in length.
• Elastic and inelastic: elastic recovers fully; inelastic does not.

Quick self-test

1. Is tension a contact or a non-contact force?
2. Calculate the weight of a 0.25 kg object where g = 9.8 N/kg.
3. An object weighs 49 N where g = 9.8 N/kg. What is its mass?
4. A force of 1.8 N gives a spring an extension of 12 cm. Find the spring constant in N/m.
5. Using the same spring, find the extension for 4.5 N (assume the limit is not exceeded).
6. On a distance-time graph an object is at 20 m when t = 10 s and at 80 m when t = 30 s. What is its speed?
7. Convert 90 km/h to m/s.
8. A bird flies 360 m in 45 s. Find its average speed.
9. A trolley moves 120 m in 15 s, stops for 5 s, then moves 60 m in 10 s. Find its average speed.
10. Name two scalars and two vectors from this unit.
11. Explain what inelastic distortion means.

Answers

1. Contact.
2. W = 0.25 × 9.8 = 2.45 N, so 2.5 N (2 significant figures).
3. m = 49 ÷ 9.8 = 5.0 kg.
4. k = 1.8 ÷ 0.12 = 15 N/m.
5. e = 4.5 ÷ 15 = 0.30 m = 30 cm.
6. Speed = (80 − 20) ÷ (30 − 10) = 60 ÷ 20 = 3.0 m/s.
7. 90 ÷ 3.6 = 25 m/s.
8. 360 ÷ 45 = 8.0 m/s.
9. Total distance 180 m, total time 30 s: 180 ÷ 30 = 6.0 m/s.
10. Scalars: any two of distance, speed, time. Vectors: any two of displacement, velocity, acceleration, force, momentum.
11. Once the forces stop, the object stays out of shape.

Where marks are usually lost

• Giving the new length of a spring where the extension is needed.
• Forgetting to convert cm to m before using a spring constant in N/m.
• Writing a weight in kg, or a mass in N.
• Missing units, or giving too many significant figures.
• Describing a flat distance-time line as steady movement instead of stationary.
• Averaging speeds instead of using total distance over total time.
• Writing “the forces cancel” for a force pair, without noting they act on different objects.
• In the practical, forgetting to read at eye level, or saying “repeat” without saying what is then averaged.
• Calling a graph proportional when it does not pass through the origin.

Official syllabus

OxfordAQA International GCSE Physics (9203) specification, version 5.2, for exams May/June 2018 onwards, published by Oxford International AQA Examinations. Sections 3.1.1 and 3.1.2.