AQA GCSE Physics 8463: Forces – Study Guide

This guide teaches section 4.5 Forces of the AQA GCSE Physics (8463) specification, Version 1.1 (30 September 2019), for teaching from September 2016 and exams from 2018 onwards. It covers 4.5.1 to 4.5.7, including required practicals 6 and 7. Forces is assessed on Paper 2 (topics 5 to 8), set at Foundation and Higher Tier; Paper 2 may also draw on energy ideas from topics 1 and 2. Content the specification marks (HT only), including all of 4.5.7 Momentum, is labelled Higher tier only.

For quick recall, use the Forces revision notes. To test yourself, use the Forces practice questions. The course hub is AQA GCSE Physics, the printable checklist lists every point, and the free diagnostics show your gaps. In every calculation, the value of g will be given.

What this unit covers

Spec point	What you must be able to do	Tier
4.5.1 Forces and interactions	Scalars and vectors; contact and non-contact forces; W = mg; resultant of forces in a line	Both
4.5.1.4 Resultant forces	Free body diagrams; resolve forces; vector (scale) diagrams	Higher tier only
4.5.2 Work done	W = Fs; newton-metres and joules; heating by friction	Both
4.5.3 Elasticity	Elastic and inelastic deformation; F = ke; Eₑ = ½ke²; required practical 6	Both
4.5.4 Moments, levers and gears	M = Fd; principle of moments; how levers and gears transmit turning effects	Both
4.5.5 Pressure in fluids	p = F/A; atmospheric pressure	Both
4.5.5.1.2 Pressure in a fluid 2	p = hρg; pressure differences with depth; upthrust; floating and sinking	Higher tier only
4.5.6 Forces and motion	Speed, velocity, graphs, acceleration, v² − u² = 2as, terminal velocity, Newton’s laws, stopping distances; required practical 7	Both
4.5.6 (parts)	Circular motion; tangents; area under v–t graphs; inertia; inertial mass; estimating braking forces	Higher tier only
4.5.7 Momentum	p = mv; conservation; F = mΔv/Δt; safety features	Higher tier only

4.5.1 Forces and their interactions

Scalars have magnitude only (distance, speed, mass). Vectors have magnitude and direction (displacement, velocity, force). An arrow represents a vector: its length shows the size, its direction the direction.

A force is a push or pull from an interaction between two objects. Contact forces need touching: friction, air resistance, tension, normal contact force. Non-contact forces act at a distance: gravitational, electrostatic, magnetic. An interaction always produces a force on each object.

Weight is the force on an object due to gravity. It depends on the gravitational field strength where the object is, and acts at the object’s centre of mass. Weight ∝ mass. It is measured with a calibrated spring-balance (newtonmeter).

W = m g      (W in N, m in kg, g in N/kg)
A 65 kg person where g = 9.8 N/kg:  W = 65 × 9.8 = 637 N
Same person where g = 1.6 N/kg:     W = 65 × 1.6 = 104 N  (mass is still 65 kg)

The resultant force is the single force with the same effect as all the forces acting. For forces in a line, add those in one direction and subtract the others: 350 N forwards and 120 N backwards give 230 N forwards.

Higher tier only. Draw free body diagrams showing every force on an isolated object; if the forces are balanced the resultant is zero. A single force can be resolved into two components at right angles with the same combined effect. Use scale drawings for resolution, equilibrium and the resultant of two forces (size and direction). A 50 N force at 30° above the horizontal, drawn at 1 cm = 10 N, gives components of about 43 N horizontally and 25 N vertically.

4.5.2 Work done and energy transfer

Work is done when a force causes a displacement of an object.

W = F s   (W in J, F in N, s in m, along the line of action of the force)
Pushing a box with 40 N for 12 m:  W = 40 × 12 = 480 J

1 J is the work done when 1 N moves an object 1 m, so 1 J = 1 N m. Doing work transfers energy between stores. Work done against friction raises the object’s temperature.

4.5.3 Forces and elasticity

Changing the shape of a stationary object (stretching, bending, compressing) needs more than one force. Elastic deformation: the object returns to its original shape when the forces are removed. Inelastic deformation: it does not.

Up to the limit of proportionality, extension is directly proportional to force (a linear relationship). Beyond it, the graph curves (non-linear). The same applies to compression.

F = k e              (k in N/m, e in m)          recall
Eₑ = ½ k e²          (on the equation sheet)
A 6.0 N load stretches a spring by 0.15 m:
k = F / e = 6.0 / 0.15 = 40 N/m
Eₑ = 0.5 × 40 × 0.15² = 0.45 J

Provided the spring is not inelastically deformed, the work done stretching it equals the elastic potential energy stored.

Required practical 6. Hang a spring beside a vertical ruler. Record the unstretched length, then add masses one at a time and record the new length. Extension = new length − original length. Plot force (y) against extension (x). The straight section’s gradient is k.

4.5.4 Moments, levers and gears

A force can make an object rotate. Its turning effect is its moment:

M = F d   (M in N m; d = perpendicular distance from pivot to line of action, in m)

When an object is balanced, total clockwise moment = total anticlockwise moment about the pivot.

A 400 N person sits 1.5 m left of a seesaw pivot. Where must a 250 N child sit?
400 × 1.5 = 250 × d   →   d = 600 / 250 = 2.4 m right of the pivot

A lever transmits a turning effect: a small force far from the pivot gives a large moment, which can lift a large load close to the pivot. In gears, a small gear driving a larger one gives a larger moment at the output, but the larger gear turns more slowly.

4.5.5 Pressure and pressure differences in fluids

A fluid is a liquid or a gas. Fluid pressure acts at right angles (normal) to any surface.

p = F / A    (p in Pa, F in N, A in m²)
600 N spread over 0.020 m²:  p = 600 / 0.020 = 30 000 Pa

Higher tier only. Pressure due to a column of liquid is p = hρg (equation sheet). Pressure increases with depth, because there is a taller column of liquid above, and with density.

Water, ρ = 1000 kg/m³, g = 9.8 N/kg, depth 2.5 m:  p = 2.5 × 1000 × 9.8 = 24 500 Pa
Difference between 1.0 m and 3.0 m:              Δp = 2.0 × 1000 × 9.8 = 19 600 Pa

A submerged object has more pressure on its bottom surface than its top, giving a resultant upward force: upthrust. An object floats if the upthrust can equal its weight before it is fully submerged, which depends on its density compared with the fluid’s; otherwise it sinks.

Atmospheric pressure is caused by air molecules colliding with a surface. The atmosphere is a thin layer that gets less dense with height. Higher up, there is less air (less weight of air) above a surface, so atmospheric pressure decreases with height.

4.5.6 Forces and motion

Describing motion

Distance is a scalar; displacement is distance in a straight line from start to finish plus direction. Speed is a scalar; velocity is speed in a given direction. Higher tier only: an object moving in a circle at constant speed has a changing velocity, because its direction keeps changing.

Typical speeds: walking about 1.5 m/s, running about 3 m/s, cycling about 6 m/s; sound in air about 330 m/s.

s = v t   (constant speed)          average speed = total distance / total time
1200 m in 400 s:  v = 1200 / 400 = 3.0 m/s

On a distance–time graph, gradient = speed. Higher tier only: for an accelerating object, draw a tangent and find its gradient.

a = Δv / t                                  recall
0 to 24 m/s in 8.0 s:  a = 24 / 8.0 = 3.0 m/s²
v² − u² = 2 a s                              equation sheet
30 m/s to rest in 45 m:  0 − 30² = 2 × a × 45  →  a = −10 m/s² (deceleration 10 m/s²)

On a velocity–time graph, gradient = acceleration. Higher tier only: area under the graph = distance travelled; count squares for curved lines. For example, 0 to 10 m/s in 5 s then 10 s at 10 m/s covers ½ × 5 × 10 + 10 × 10 = 125 m.

An object falling freely near the Earth accelerates at about 9.8 m/s². Falling through a fluid, it first accelerates; air resistance grows with speed until it equals the weight, the resultant force is zero and it moves at terminal velocity.

Newton’s laws

First law. If the resultant force is zero, a stationary object stays stationary and a moving object keeps the same velocity. A car at steady speed has driving force = resistive forces. Higher tier only: the tendency to stay at rest or in uniform motion is inertia.

Second law. Acceleration ∝ resultant force, and inversely proportional to mass: F = m a. A 1200 kg car accelerating at 3.0 m/s² needs 1200 × 3.0 = 3600 N. Higher tier only: inertial mass measures how hard it is to change an object’s velocity; it is the ratio F/a.

Required practical 7. Pull a trolley with a string over a pulley to a hanging mass; measure acceleration with light gates. To vary force at constant mass, move masses from the trolley to the hanger. To vary mass, add masses to the trolley with the same hanging force.

Third law. When two objects interact, the forces they exert on each other are equal and opposite. A book on a table pushes down on the table; the table pushes up on the book with an equal force.

Stopping distances

Stopping distance = thinking distance (during reaction time) + braking distance. Reaction times are typically 0.2 s to 0.9 s, and get longer with tiredness, drugs, alcohol and distractions. You can measure reaction time with a falling-ruler catch. Braking distance increases with speed, wet or icy roads, and worn brakes or tyres.

20 m/s, reaction time 0.7 s:  thinking distance = 20 × 0.7 = 14 m
Deceleration 5.0 m/s²:        braking distance = 20² / (2 × 5.0) = 40 m
Stopping distance = 14 + 40 = 54 m
Higher tier only, 1200 kg car:  braking force = 1200 × 5.0 = 6000 N

Braking: friction between brakes and wheel does work, reducing kinetic energy and heating the brakes. Large decelerations can overheat brakes and cause loss of control.

4.5.7 Momentum (Higher tier only)

p = m v    (kg m/s)       1500 kg at 12 m/s:  p = 18 000 kg m/s

In a closed system, total momentum before an event = total momentum after (conservation of momentum). A 2.0 kg trolley at 3.0 m/s hits a stationary 1.0 kg trolley and they stick: 2.0 × 3.0 = 3.0 × v, so v = 2.0 m/s.

Force = rate of change of momentum: F = mΔv/Δt (equation sheet). A 70 kg person stopping from 8.0 m/s in 0.05 s feels 11 200 N; in 0.40 s, only 1400 N. Air bags, seat belts, crash mats, cycle helmets and soft playground surfaces increase the stopping time, so they reduce the force.

Common errors

• Confusing mass (kg) and weight (N).
• Using the extension in cm in F = ke.
• Using the distance along the beam rather than the perpendicular distance in M = Fd.
• Reading speed off a velocity–time graph gradient.
• Forgetting to square both velocities in v² − u² = 2as.
• Naming weight and the normal force on the same book as a Newton’s third law pair.

Official syllabus

AQA GCSE Physics (8463) specification, Version 1.1, 30 September 2019, for teaching from September 2016 and exams from 2018 onwards (AQA), section 4.5 Forces.