Lesson 6: Forces

A force is a push or a pull. Forces are measured in newtons (N) with a spring balance (newton meter), and they are vectors — they have both magnitude (size) and direction. A force can change an object's speed, direction of motion, or shape. Whenever you walk, brake on a bicycle, or watch an MRT train leave the station, forces are at work; this lesson gives you the language and the calculations to describe them.

Types of forces and their effects

• Gravitational force (weight) — the pull of the Earth on a mass. Weight (N) = mass (kg) × gravitational field strength (g). Near Earth's surface g ≈ 10 N/kg, so a 50 kg student has a weight of 50 × 10 = 500 N. Mass (kilograms) never changes with place; weight does — on the Moon, g is about 1.6 N/kg, so the same student weighs only about 80 N there.
• Friction — opposes relative motion (or attempted motion) between two surfaces in contact. It is useful (grip between shoes and floor, brakes) and wasteful (heat and wear in engines). Friction increases with rougher surfaces and with the force pressing the surfaces together; lubricants such as oil reduce it; treads and spikes increase it.
• Normal contact force / reaction — the push of a surface on an object resting on it, perpendicular to the surface.
• Tension, air resistance (drag) and magnetic force — pulls through ropes and strings; a drag opposing motion through air or water, growing with speed; and the push or pull between magnets or on magnetic materials, acting without contact.

Balanced forces are equal in size and opposite in direction: the resultant (net) force is zero, so the object stays at rest or moves at constant velocity. Unbalanced forces give a non-zero resultant and the object accelerates in the direction of the resultant. Example: a cyclist pushes with 12 N of driving force east while drag and friction total 5 N west; resultant = 12 − 5 = 7 N east, so she accelerates eastwards. In a free-body diagram each force is an arrow drawn from the object, its length proportional to the force's size.

Pressure: force spread over area

Pressure = force / area, measured in pascals (Pa), where 1 Pa = 1 N/m². A student of weight 600 N standing on two feet with total sole area 0.03 m² exerts:

pressure = 600 N / 0.03 m² = 20 000 Pa (20 kPa)

Standing on one foot halves the area, doubling the pressure to 40 kPa. This is why wide tyres and tracks suit soft ground — they spread the load — while a sharp knife cuts: a small area concentrates the force into huge pressure.

Moments: turning effects

A force can turn an object about a pivot. Moment of a force = force × perpendicular distance from the pivot, in newton-metres (N·m). Opening a heavy door: 40 N applied 0.30 m from the hinge gives a moment of 40 × 0.30 = 12 N·m; the same force at 0.10 m gives only 4 N·m — hence door handles sit far from hinges. For a balanced beam, total clockwise moments = total anticlockwise moments (the principle of moments).

Practical focus: friction on different surfaces

A wooden block is dragged at steady speed across benches surfaced with wood, sandpaper, plastic and a wet tile; the steady-pull spring balance reading equals the friction force:

Sandpaper grips most; the wet tile grips less than dry wood because the water layer acts as a lubricant — exactly why Singapore's monsoon-slick roads demand longer braking distances. Steady speed matters: if the block accelerates, the reading is no longer equal to friction alone.

Singapore focus: the MRT and friction

An MRT train accelerates using friction between steel wheels and steel rails. Rain and fallen leaves lower friction on exposed track sections, so trains brake earlier and accelerate gently in wet weather. On the roads, the Land Transport Authority uses high-friction surfacing near junctions, and expressway signs warn of longer stopping distances in rain — a doubling of speed roughly quadruples braking distance, because both reaction distance and braking distance grow.

Common mistakes

• Treating mass and weight as the same quantity. Mass is in kilograms; weight is a force in newtons. On the Moon your mass is unchanged; your weight drops.
• Drawing friction in the direction of motion. Friction (except when it is the driving grip force, e.g. walking) opposes motion or slipping — state which surface and which motion.
• Saying a stationary object has "no forces". It has balanced forces: weight balanced by the normal contact force.
• Forgetting pressure units. Pa = N/m²; if area is measured in cm², convert to m² before calculating.

Exam Experience

Question 1 (structured, data-based). A student pulls a loaded trolley with a horizontal force of 30 N. Friction and air resistance together exert 18 N in the opposite direction. The trolley's mass is 6 kg. (a) Calculate the resultant force on the trolley. [2] (b) State and explain what happens to the trolley's motion. [2] (c) The student stops pulling, but the trolley keeps moving. Describe and explain how the trolley's motion changes now. [3]

Question 2. A box of mass 4 kg rests on a table. Taking g = 10 N/kg, the normal contact force from the table on the box is: [1] A. 0 N B. 4 N C. 40 N D. 400 N

Question 3. A spanner 0.25 m long is used to undo a tight nut. A force of 60 N is applied at the end of the spanner, perpendicular to it. (a) Calculate the moment of the force about the nut. [2] (b) Explain why a longer spanner makes the nut easier to undo with the same force. [2]

Marking scheme. Q1(a) Resultant = 30 − 18 = 12 N [1] in the direction of the pull [1]. Q1(b) Resultant force is non-zero / forces are unbalanced [1]; so the trolley accelerates in the direction of the pull [1]. Q1(c) Only friction/air resistance (18 N) acts, opposing motion [1]; resultant force acts opposite to motion [1]; trolley decelerates / slows down and stops [1]. Q2 C [1]. (Weight = 4 × 10 = 40 N, balanced by the normal contact force.) Q3(a) Moment = 60 × 0.25 = 15 N·m [1 method, 1 answer with unit]. Q3(b) Moment = force × perpendicular distance from pivot [1]; a longer spanner increases the distance, so the same force produces a larger turning effect / moment [1].

Going deeper: stopping distances and balanced beams

Braking splits into two distances. Thinking distance — travelled while the driver reacts — grows in direct proportion to speed. Braking distance — travelled while friction between tyres and road removes the kinetic energy — grows with the SQUARE of speed, because kinetic energy does. Double the speed and total stopping distance becomes roughly four times the braking part plus twice the thinking part: a powerful reason wet-weather speed discipline in Singapore is not mere advice. Examiners often present a stopping-distance table and ask you to spot the non-linear pattern — always check whether the increase per step is constant (linear) or growing (quadratic).

Moments in balance. A uniform beam pivots at its centre. A 30 N weight hangs 0.40 m to the left of the pivot (moment = 30 × 0.40 = 12 N·m clockwise). A 60 N weight at 0.20 m to the right gives 60 × 0.20 = 12 N·m anticlockwise. Equal moments: the beam balances. This principle runs everything from playground see-saws to the counterweights on the tower cranes over Singapore construction sites — and the quickest check in any moments question is: is the bigger force on the SHORTER side? If not, something is wrong.

A see-saw puzzle in exam form: a 400 N child sits 1.5 m from the pivot; where must a 600 N adult sit to balance? Adult moment must equal 400 × 1.5 = 600 N·m, so distance = 600/600 = 1.0 m. Two steps, two marks — the pattern of every moments calculation.

Exam-style extra

Question. A wheelbarrow is used to carry a load of 300 N whose centre of mass is 0.50 m from the wheel axle. The handles are 1.5 m from the axle. (a) Calculate the moment of the load about the axle. [2] (b) Calculate the upward force the gardener must apply at the handles to just lift the load. [2]

Marking points. (a) Moment = 300 × 0.50 = 150 N·m [1 method, 1 answer with unit]. (b) Force × 1.5 = 150, so force = 150/1.5 = 100 N [1 method, 1 answer]; the barrow acts as a lever giving a mechanical advantage of 3.

Workshop: pressure you can feel

Stand on one heel and the floor notices. A 500 N person balanced on a stiletto heel tip of area 1 cm² (0.0001 m²) applies a pressure of 500/0.0001 = 5 000 000 Pa. The same person in trainers, sole area about 200 cm² (0.02 m²), applies 500/0.02 = 25 000 Pa — two hundred times less. That ratio explains stiletto dents in wooden floors, why elephants (huge mass, huge feet) tread softer than dancers, and why tracked vehicles cross mud that stops wheeled trucks.

Pressure thinking also solves the drawing pin (sharp end concentrates force), the snowshoe (spreads it), and the MRT viaduct pier (wide footing spreads a train's load into soft reclaimed soil — Lesson 6's geography of Singapore again). One formula, P = F/A, two directions of travel: ask "is this problem making A bigger or smaller?" before calculating anything, and you will never again invert the relationship.