Force and its effects
A force is a push or a pull, measured in newtons (N).
A force can change an object's speed, direction or shape.
Balanced forces: equal and opposite. The object stays still, or continues at constant speed.
Unbalanced forces: the object accelerates in the direction of the larger force.
This is why a car at constant speed still needs its engine running: the driving force is balancing friction and air resistance, not producing acceleration.
Pressure
Pressure is force spread over an area.
P = F ÷ AForce in newtons, area in m², pressure in pascals (Pa). One pascal is one newton per square metre.
The key relationship: for the same force, smaller area means greater pressure. Halve the area and you double the pressure.
This one formula explains knives, nails, snowshoes, tractor tyres and why a stiletto heel damages a floor more than an elephant.
Weight is not mass
Used interchangeably in daily speech; genuinely different in physics.
- Mass: the amount of matter, in kilograms. It never changes.
- Weight: the force of gravity on that mass, in newtons. It changes with location.
on Earth, g ≈ 10 N/kg
Worked: a 60 kg person has a weight of 600 N on Earth.
On the Moon, where g is about 1.6 N/kg, the same person still has a mass of 60 kg but weighs only about 96 N.
So an astronaut is not "weightless" because they lost mass, gravity is simply much weaker, or they are in free fall.
A worked pressure calculation
Question. A 60 kg person stands on snow. Compare the pressure with boots (total contact area 0.04 m²) and with snowshoes (0.4 m²).
Step 1: find the force, which is weight.
W = 60 × 10 = 600 NStep 2: pressure in boots.
P = 600 ÷ 0.04 = 15,000 PaStep 3: pressure in snowshoes.
P = 600 ÷ 0.4 = 1,500 PaThe result: ten times the area gives one tenth the pressure. The force is identical, only how it is spread has changed.
That is why snowshoes work, and why camels have wide feet for sand.
Pressure in liquids and gases
In a liquid, pressure increases with depth, because there is more liquid above pressing down.
This is why dam walls are built thicker at the bottom, and why divers must ascend slowly.
Liquid pressure acts in all directions, not just downwards, which is why water squirts sideways from a hole in a container.
Atmospheric pressure is the weight of air above us, about 100,000 Pa at sea level. It decreases with altitude, which is why aircraft cabins are pressurised and why cooking takes longer in the mountains, water boils below 100°C.
A drinking straw does not "suck". You lower the pressure in your mouth, and atmospheric pressure pushes the liquid up. Without an atmosphere, straws would not work.
Designing for pressure
Engineers deliberately choose area to get the pressure they want.
Want HIGH pressure, make the area small:
- Knife blades sharpened to a very thin edge, so a modest force cuts.
- Nails and pins with fine points.
- Studs on boots to grip by pressing into ground.
Want LOW pressure, make the area large:
- Tractor tyres wide, so they do not sink into soft soil.
- Building foundations spread wide, so the ground is not crushed.
- Backpack straps broad, so they do not cut into shoulders.
- Skis and snowshoes.
The design question is always the same: do I want this force concentrated or spread? Then choose the area accordingly.
Pressure in daily life
Blood pressure. Measured because consistently high pressure damages vessels over years, a genuine and common health issue.
Tyres. Under-inflated tyres have a larger contact area, which increases friction and fuel consumption, and they wear unevenly.
Weather. Air moves from high to low pressure. That movement is wind. Falling pressure usually means unsettled weather.
Pressure cookers. Sealing raises the internal pressure, which raises water's boiling point above 100°C, so food cooks faster.
Hydraulics. Because liquids transmit pressure and barely compress, a small force on a small piston produces a large force on a large one, which is how car brakes and jacks work.
Where it usually goes wrong
- "Weight and mass are the same." Mass in kg, weight in newtons.
- "A sharp knife applies more force." Same force, smaller area.
- "Liquid pressure acts only downwards." All directions.
- "A straw sucks liquid up." Air pressure pushes it.
- "Constant speed means no forces." It means balanced forces.
What to remember
- P = F ÷ A: smaller area, greater pressure.
- Mass kg, unchanging · weight newtons, W = mg.
- Liquid pressure rises with depth and acts in all directions.
- Balanced forces → constant speed, not necessarily stillness.
Watch one worked through
Here is one done slowly, with the reason for every move. Then one for you.
A box weighing 600 N rests on the floor. Its base is 2 m by 1.5 m. Find the pressure. Then explain why a drawing pin pierces wood easily.
- Work out the area of the base.area = 2 × 1.5 = 3 m²Pressure always needs an area, so find it before anything else. Watch the units: metres give m².
- Apply the formula.pressure = force ÷ area = 600 ÷ 3 = 200 PaA pascal is one newton per square metre. The unit is built from the formula, so it is never something to memorise separately.
- For the drawing pin, the force is small but the tip area is tiny.small force ÷ very small area = very large pressurePressure depends on both. Dividing by a very small number gives a very large answer, which is the whole point of a sharp tip.
- Compare with the opposite case.camel's foot: big area → low pressure drawing pin: tiny area → high pressureSame idea run backwards. Wide feet, skis and tractor tyres all spread a force out to avoid sinking.
Answer: 200 Pa, and the pin works because its tiny tip area makes the pressure enormous
A force of 100 N acts on 0.5 m². What is the pressure in Pa?
Show the answer
200
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