Forces

A bridge, a brake, a bungee cord, a planet in orbit: engineers analyse them all with forces. This reference covers AQA GCSE Physics 8463, topic 4.5 Forces — the largest topic of Paper 2.

How the exam treats this topic:

• Paper 2 (4.5–4.8) carries this topic, and it may also draw on energy and electricity ideas. The equations $W = mg$, $W = Fs$, $F = ke$, $M = Fd$, $p = F/A$, $s = vt$, $a = \Delta v/t$, $v^2 - u^2 = 2as$, $F = ma$ and $p = mv$ are on the enclosed sheet.
• Moments, levers and gears, pressure in fluids, terminal-velocity graphs and momentum calculations are physics only; momentum itself is Higher Tier.
• Free-body diagrams, vector diagrams (scale drawing) and resolution of forces are HT only.
• Required practicals: RP6 (force–extension of a spring) and RP7 (force and mass effect on acceleration).

Scalar 标量: magnitude only — distance, speed, mass, energy. Vector 矢量: magnitude and direction — displacement, velocity, force, weight, momentum. A vector is drawn as an arrow: length = magnitude, direction = direction.

A force is a push or pull from the interaction with another object:

• contact 接触 forces (touching): friction, air resistance, tension, normal contact force;
• non-contact 非接触 forces (separated): gravitational, electrostatic, magnetic.

Gravity: weight 重力 is the force on an object due to gravity; it acts at the centre of mass 质心 and is measured with a calibrated spring-balance (newtonmeter):

• $W$ weight in N; $m$ mass in kg; $g$ gravitational field strength in N/kg (given, usually 9.8 near Earth).
• Weight and mass are directly proportional ($W \propto m$).

Resultant force 合力: the single force replacing several forces with the same effect. Collinear: add same-direction forces, subtract opposite ones. (HT) Use free-body diagrams 自由体图 (only the forces on the chosen object), resolve a force into perpendicular components, and find resultants by scale drawing.

Worked example. A 65 kg person stands on Mars where $g = 3.7$ N/kg.

A force does work when it moves its point of application through a distance:

• $W$ work done in J; $F$ force in N; $s$ distance moved along the line of action of the force, in m.
• 1 J = 1 N·m: one joule is the work of one newton over one metre.
• Work done against friction raises the object's temperature — the energy transfers to thermal stores.

Worked example. A child pushes a baby walker 2.8 m with a horizontal force of 25 N.

More than one force is needed to stretch, bend or compress a stationary object (a single force would just move it). Elastic deformation 弹性形变 is recovered when the forces are removed; inelastic 非弹性 is not.

Below the limit of proportionality:

• $k$ spring constant in N/m (stiff spring → large $k$); $e$ extension = stretched length − original length (or compression).
• Work done on the spring = elastic energy stored (if not inelastically deformed).

Required practical 6: hang masses on a spring, measure extension for each (ruler at eye level), plot force against extension. The linear section's gradient is $k$; beyond the limit of proportionality the line curves. Hooke's-law reasoning: doubling the force doubles the extension only below the limit.

• $M$ moment 力矩 in N·m; $d$ is the perpendicular distance from the pivot to the line of action of the force.
• Balance: total clockwise moment = total anticlockwise moment.

Levers and gears transmit the rotational effect of a force: a long lever or a large gear multiplies the moment — force × distance trade-off (small force, long arm → big moment).

• $p$ pressure in Pa; $F$ force normal to the surface; $A$ area in m².
• (HT) $h$ column height in m, $\rho$ liquid density in kg/m³. Pressure grows with depth and density.
• A submerged object feels greater pressure on its bottom than its top → a resultant upthrust 浮力. Floating: upthrust = weight; sinking: upthrust < weight (density-dependent).
• Atmospheric pressure decreases with height: fewer air molecules above a surface as you climb, so less weight of air; the atmosphere gets less dense with altitude.

• Distance 路程 (scalar): how far. Displacement 位移 (vector): straight-line distance and direction.
• Speed 速率 (scalar) — typical values: walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s, sound in air ≈ 330 m/s. Velocity 速度 (vector): speed in a given direction.
• $s = vt$ (constant speed); average speed = total distance ÷ total time.
• Distance–time graph: gradient = speed; (HT) a tangent gives instantaneous speed of an accelerating object.
• Acceleration 加速度: $a = \Delta v / t$, in m/s²; deceleration = negative acceleration. Estimate everyday accelerations.
• Velocity–time graph: gradient = acceleration; (HT) area under = distance (count squares).
• Uniform acceleration: $v^2 - u^2 = 2as$. Free fall near Earth: $a \approx 9.8$ m/s².

Worked example (graph). A v–t graph rises straight from 0 to 20 m/s in 8 s, then stays flat for 12 s.

• Acceleration (gradient): $a = 20/8 = 2.5$ m/s².
• (HT) Distance (area): $\tfrac12 \times 8 \times 20 + 12 \times 20 = 80 + 240 = 320$ m.

Terminal velocity 末速度: a falling object accelerates (weight > drag 空气阻力); as speed grows, drag grows until resultant force = 0 — constant speed = terminal velocity. Skydiver: fast terminal before the chute, slow after; interpret the v–t curve shape.

• First law: zero resultant force → stationary stays stationary; moving keeps the same velocity. Steady speed means driving force = resistive forces. (HT) Inertia 惯性: the tendency to keep the state of motion.
• Second law: $a \propto F$, $a \propto 1/m$, so:

(HT) Inertial mass = force ÷ acceleration — resistance to change of velocity.

Required practical 7: trolley on a runway — vary the force (masses on a hanger over a pulley) at constant trolley mass, then vary the trolley mass at constant force; measure acceleration with light gates; plot $a$ against $F$ (linear) and $a$ against $1/m$.

• Third law: two interacting objects exert equal and opposite forces on each other — same type, opposite directions, on different objects.

Stopping distance = thinking distance + braking distance.

• Thinking (reaction) distance = reaction time × speed. Reaction time 0.2–0.9 s typically; affected by tiredness, drugs, alcohol, distractions. Measure it: drop a ruler between a partner's fingers — distance fallen → time from $s = \tfrac12 at^2$ (or electronic timers).
• Braking distance: grows with speed (for a given braking force); wet or icy roads, worn brakes or tyres lengthen it.
• Braking physics: friction between brake and wheel does work on the kinetic energy store; the brakes' temperature rises; a higher speed or shorter stop → larger force needed → larger deceleration → overheating brakes, loss of control. (HT) Estimate deceleration forces with $F = ma$.

Worked example. A 1500 kg car brakes from 30 m/s to rest in 60 m.

• Deceleration from $v^2 - u^2 = 2as$: $0 - 30^2 = 2a(60)$ → $a = -7.5$ m/s².
• Braking force: $F = ma = 1500 \times 7.5 = 11\,250 \approx 11\,000$ N.

• $p$ momentum in kg m/s (a vector); conservation: in a closed system, total momentum before = total momentum after an event (collisions).
• $F = m\Delta v/\Delta t$: force = rate of change of momentum (this is $F = ma$ restated).
• Safety features explained by it: air bags, seat belts, crash mats, cycle helmets, cushioned playgrounds — all increase the time over which momentum changes, so $\Delta v/\Delta t$ falls and the force falls.

Worked example. A 1000 kg car at 20 m/s hits a barrier and stops in 0.25 s.

• Momentum change: $\Delta p = m\Delta v = 1000 \times 20 = 20\,000$ kg m/s.
• Force: $F = \Delta p / \Delta t = 20\,000/0.25 = 80\,000$ N. With a crumple zone ($t = 0.5$ s) the force halves to 40 000 N.

• Classify scalar/vector, contact/non-contact; compute $W = mg$; find collinear resultants; (HT) draw free-body and scale-diagram resultants.
• $W = Fs$ with energy transfer story; $F = ke$, $E_e = \tfrac12 ke^2$; RP6 with gradient = $k$.
• (physics only) Moments balance; levers and gears trade force for distance; $p = F/A$, (HT) $p = h\rho g$; upthrust and floating; atmospheric pressure vs height.
• Distance vs displacement; typical speeds; read d–t and v–t graphs (gradient, tangent, area); $v^2 - u^2 = 2as$; terminal velocity story.
• Newton's three laws with examples; RP7 method and graphs.
• Stopping distance split; reaction-time measurement; braking energy and deceleration dangers.
• (HT) $p = mv$, conservation in collisions, $F = m\Delta v/\Delta t$, safety features via longer $\Delta t$.