Force and Pressure
Complete Notes & Free Quiz

A force is a push or a pull on an object. Forces are measured in newtons (N).

Forces always appear in pairs — one force acts in one direction and another force acts in the opposite direction.

Force is measured in newtons (N).

Yes, weight is a force — it is the downward pull of gravity on an object. It always acts downwards and is measured in newtons (N).

The downward force (its weight) is equal to the upward push (the normal force) from the table. The two forces are balanced, so the box stays stationary (for example, weight 50 N down = normal force 50 N up).

Balanced forces are forces that are equal in size but opposite in direction, so they cancel each other out. The object then behaves as if no force is acting on it.

With balanced forces, an object does not change its state of rest or motion — it stays stationary, or keeps moving at a steady (constant) speed in a straight line.

Examples: a box lying still on a table (weight = normal force); a tug of war where both teams pull with equal force, e.g. 300 N each, so there is no movement; and a skydiver falling at a steady speed (weight = air resistance).

The forces are balanced — his downward weight is exactly matched by the upward force of air resistance, so he falls at a steady speed.

If no external force acts on an object: if it is stationary it stays stationary; if it is moving it keeps moving at a steady speed in a straight line.

Unbalanced forces are two forces acting in opposite directions that are not equal in size, so they do not cancel out.

The resultant force is the single overall force left when unbalanced forces are combined. It is found by: greater force − smaller force = resultant (unbalanced) force.

Resultant force = weight − air resistance = 50 N − 20 N = 30 N downwards, so the box falls downwards.

(1) A stationary object starts to move in the direction of the resultant force. (2) A moving object speeds up (accelerates) in the direction of the resultant force.

The object moves or accelerates in the direction of the resultant force — a stationary object starts moving that way, and a moving object speeds up in that direction.

When one team pulls harder, the forces become unbalanced and there is a resultant force. The rope (a stationary object) starts to move in the direction of the resultant force — towards the stronger team.

No — balanced forces can also mean the object is moving at a steady speed in a straight line. Balanced forces only mean the motion does not change; the object may be at rest OR moving at constant speed.

A resultant force can make a stationary object start to move, make a moving object speed up (accelerate), slow it down (if it acts against the motion), or change its direction. It always acts in the direction of the resultant force.

When a skydiver reaches a steady speed and the forces on them are balanced, that speed is called the terminal speed or terminal velocity.

Balanced forces are equal in size and opposite in direction, so they cancel out and there is no resultant force — the motion does not change. Unbalanced forces are unequal, so they leave a resultant force that changes the object’s motion (starts it moving, speeds it up, slows it down, or changes its direction).

A resultant force of zero means the forces are balanced. The object stays stationary or keeps moving at a steady speed in a straight line — its motion does not change.

The two forces are the book’s weight acting downwards and the upward push (normal or reaction force) from the table. They are equal and opposite, so they are balanced.

Air resistance is a force that opposes the motion of an object moving through the air. It acts in the opposite direction to the object’s movement, so it tends to slow the object down.

Resultant force = greater − smaller = 800 N − 500 N = 300 N to the right.

Resultant force = 1200 N − 1200 N = 0 N. The forces are balanced, so the car stays still or moves at a steady (constant) speed.

The open parachute greatly increases the air resistance, so the upward force becomes larger than the skydiver’s weight. This gives a resultant force upwards, so the skydiver slows down until the forces balance again at a new, lower steady speed.

The only forces left act backwards (air resistance and friction), so there is a resultant force opposing the motion. The car slows down and eventually stops.

It is caused by balanced forces. When the forces balance, the resultant is zero, so a moving object keeps going at a steady speed in a straight line (and a stationary object stays still).

Resultant force = 300 N − 300 N = 0 N. The forces are balanced, so the rope does not move.

The object appears to lose weight because the water pushes up on it with a force called upthrust. It has not really lost weight — the upward upthrust reduces the reading on the forcemeter.

Upthrust is the upward push that a fluid exerts on an object in it. Archimedes discovered that the upthrust is equal to the weight of the fluid (water) displaced by the object.

Upthrust = weight of water displaced = 10 N. Apparent weight = 20 N − 10 N = 10 N, so the block appears to weigh only 10 N in water.

A floating boat displaces a large volume of water. This displaced water provides enough upthrust to balance the boat’s weight pushing down. Because the upward upthrust equals the downward weight, the forces are balanced and the boat floats.

Density is the mass per unit volume of a substance — how much mass is packed into the space (volume) that an object takes up.

A block of lead has much more mass in each cm³ than a block of wood, so lead has a higher density than wood — it is denser.

Density = mass ÷ volume (density = mass / volume).

Density is commonly measured in grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³).

Water has a density of about 1 g/cm³ (about 1000 kg/m³). Objects with a density less than water float; objects with a density greater than water sink.

Sea water is denser than fresh water. The denser a liquid is, the greater the upthrust it gives, so a ship floats higher in sea water.

The high salt content makes the Dead Sea water much denser than fresh water. Denser water gives greater upthrust, so it supports the swimmer’s weight more easily, making it easier to float.

Archimedes’ principle states that the upthrust on an object in a fluid is equal to the weight of the fluid displaced by the object.

A ship is hollow and shaped so that it pushes aside (displaces) a very large volume of water. This large volume of displaced water provides enough upthrust to balance the ship’s weight, so it floats — even though a solid lump of steel, which displaces little water, would sink.

A floating boat has its downward weight balanced by the equal upward upthrust from the water it displaces. Because these two forces are equal and opposite (balanced), there is no resultant force and the boat floats steadily.

Density = mass ÷ volume = 200 ÷ 100 = 2 g/cm³. This is greater than water’s 1 g/cm³, so the object sinks.

Density = 90 ÷ 100 = 0.9 g/cm³. This is less than water’s 1 g/cm³, so the object floats.

Mass = density × volume = 8 × 5 = 40 g.

Volume = mass ÷ density = 240 ÷ 12 = 20 cm³.

Upthrust = weight in air − weight in water = 30 N − 18 N = 12 N.

Upthrust = weight of water displaced = 15 N. Apparent weight = 50 N − 15 N = 35 N.

Petrol has a density of about 800 kg/m³, which is less than water’s 1000 kg/m³. A liquid or object less dense than water floats on it, so petrol floats on top.

Aluminium sinks. Its density (2700 kg/m³) is greater than water’s (1000 kg/m³), and anything denser than water sinks.

Gold sinks. Its density (19 300 kg/m³) is far greater than water’s (1000 kg/m³), so it sinks.

Displaced water is the water pushed aside (moved out of the way) by an object placed in it. The weight of this displaced water equals the upthrust on the object.

Pressure is the force acting on a surface per unit area — the amount of force pressing on each unit of area of a surface.

The sharp end gives a high pressure because the force acts on a very small area; the blunt end gives a low pressure because the same force is spread over a larger area.

For the same force, pressure is large when the surface area is small and small when the area is large — pressure increases as the area decreases.

For the same area, pressure is larger when the force is larger. Increasing the force increases the pressure.

The person’s weight is spread over thousands of nails, so the total surface area is large. This makes the pressure low, so the nails do not penetrate the skin.

Studs reduce the surface area in contact with the ground, so the force is more concentrated (higher pressure). This makes the studs cut more deeply into the ground, giving grip and stopping skidding.

A stiletto heel has a very small area of contact, so the force (the person’s weight) acts on a tiny area. This gives a very high pressure, which can dent or damage the floor.

The blade has a very small area, so the pressure under it is very high. This high pressure melts the ice, forming a thin film of water on which the skater slides; the water refreezes after the skater passes.

Pressure = force ÷ area (pressure = force / area).

The unit of pressure is the pascal (Pa). When a force of 1 N acts on an area of 1 m², the pressure is 1 pascal (1 Pa = 1 N/m²).

Pressure = force ÷ area = 100 N ÷ 2 m² = 50 N/m² = 50 Pa. (If the same 100 N acts on 1 m², the pressure = 100 Pa.)

The blunt (flat) end gives the lowest pressure, because its larger area spreads the same force over more surface, reducing the pressure.

Pressure = force ÷ area = 200 ÷ 4 = 50 Pa.

Pressure = 500 ÷ 0.5 = 1000 Pa.

Force = pressure × area = 20 × 3 = 60 N.

Area = force ÷ pressure = 100 ÷ 25 = 4 m².

Wide tyres give a large contact area, so the truck’s heavy weight is spread out. This lowers the pressure on the road, stopping the tyres from sinking in or damaging the surface.

Wide feet give a larger contact area, spreading the camel’s weight over more surface. This lowers the pressure on the sand, so the camel does not sink into it.

A sharp knife has a very thin edge (small area), so the same force produces a much higher pressure. This high pressure cuts through the material easily.

The pointed tip has a very small area, so pushing it creates a very high pressure at the point. This high pressure lets the nail or pin pierce the surface easily.

Wide tyres increase the contact area and lower the pressure on the soft ground, so the tractor does not sink into the mud or soil.

A large area spreads the person’s weight over more surface, lowering the pressure on the snow. This stops them from sinking into it.

Wide foundations spread the building’s huge weight over a large area, lowering the pressure on the ground so it does not sink or crack.

Standing on one foot gives a higher pressure. Your whole weight now acts on a smaller area (one foot instead of two), and a smaller area means a greater pressure.

In a gas: the molecules are not arranged in any particular order; they are far apart; they are not strongly held together; and they move very fast in all directions.

Air can be squashed easily because its molecules are far apart with lots of empty space between them, so they can be pushed closer together.

Atmospheric (air) pressure is the force exerted on the surface of the Earth by the weight of the air above it, caused by the Earth’s gravity pulling on the air. The air has weight and presses against everything it touches.

At sea level, atmospheric pressure is about 100 kilopascals (kPa) — roughly equal to the weight of ten cars pressing on every square metre.

We are not crushed because the pressure inside our lungs and blood system pushes outwards and exactly balances the atmospheric pressure pushing inwards.

When you suck, you remove air from the straw, lowering the air pressure inside it. The higher atmospheric pressure outside then pushes the liquid up the straw and into your mouth.

If a gas is squashed into a smaller volume, its pressure rises. If the volume is halved, the pressure is doubled, and pressure × volume stays the same. (This inverse relationship is known as Boyle’s Law.)

Compressing a gas makes its molecules move faster, and faster-moving molecules mean a higher temperature — so the gas heats up.

Compressing a gas heats it up. Doing it slowly gives the gas time to lose that heat to the surroundings, so it can keep a steady temperature during the experiment.

When the volume is halved, the pressure doubles. The product pressure × volume stays the same (for example, 10 000 in the experiment).

As air is blown in, the increased pressure makes the balloon inflate. When fully inflated, the pressure inside is higher than outside because the tension (stretching) forces of the rubber pull inwards against the inflation.

Aircraft create artificial cabin pressure so passengers stay comfortable; steam engines use compressed gases to drive pistons in cylinders; and spray aerosols use compressed gas as a propellant to push the contents out.

Pressure × volume stays constant: 200 × 50 = 10 000. New pressure = 10 000 ÷ 25 = 400 kPa. (Halving the volume doubles the pressure.)

The pressure is halved. Because pressure × volume stays constant, doubling the volume makes the pressure half as big.

Pumping compresses the air, making its molecules move faster. Faster-moving molecules mean a higher temperature, so the pump warms up.

The molecules of a gas are far apart and move very fast in all directions with nothing holding them together, so they spread out until they fill the whole container.

No. A gas can be squashed because its molecules are far apart with lots of space, but in a liquid the particles are already very close together, so a liquid can hardly be compressed.

Blowing in more air keeps increasing the pressure inside the balloon. Eventually the pressure is too great for the stretched rubber to hold, so the balloon bursts.

A propellant is the compressed gas inside an aerosol can. When the button is pressed, the high-pressure gas pushes the contents out as a spray.

It is lower at the top of a mountain. Higher up there is less air above pushing down, so the atmospheric pressure is smaller than the roughly 100 kPa found at sea level.

When a liquid is poured into a container, the weight of the liquid pushes down on the base, creating a pressure.

The deeper you go, the more liquid there is above pressing down, so the pressure is greater. Pressure is high at the bottom and gradually decreases nearer the top.

Water from the lowest hole travels furthest because the pressure is greatest at the bottom. The top jet does not travel as far because the pressure there is smaller. This shows pressure increases with depth.

Pressure in a liquid acts in all directions, not just downwards. The jets of water squirt outwards, showing the pressure pushes sideways too.

Denser liquids have a greater weight for the same volume, so they press down with greater pressure. For example, at the same depth mercury (13 600 kg/m³) gives 13 600 Pa while water (1000 kg/m³) gives only 1000 Pa.

The pressure in a liquid does not depend on the shape of the container. In a teapot the tea reaches the same level in the pot and in the spout, showing the pressure at the same depth is equal in both parts, whatever the shape.

When you dive into water, the water pushes on your body with a pressure called hydrostatic pressure. It increases with depth, which is why you feel it on your ear drums.

Deep under water the pressure is very high (pressure increases with depth), so a submarine needs strong, thick walls to withstand the huge water pressure without being crushed.

The pressure is greater at the deep end. Pressure in a liquid increases with depth because there is more water above pressing down.

Water pressure increases with depth, so it is greatest at the bottom of the dam. The wall is built thicker there so it is strong enough to hold back the much larger pressure of the deep water.

The greater the height (depth) of water above the taps, the greater the pressure at the bottom. Placing the tank high up gives more pressure to push the water strongly through the pipes and out of the taps.

Mercury exerts the greater pressure. It is much denser than water (13 600 kg/m³ compared with 1000 kg/m³), and denser liquids press down with greater pressure.

The pressure at the bottom is the same in both. Liquid pressure depends on depth (and density), not on the width or shape of the container.

The deeper you go, the greater the water (hydrostatic) pressure, because more water presses down from above. This increasing pressure pushes on your ear drums, so your ears hurt.

Pressure in a liquid acts in all directions, not just downwards. This is shown by water squirting outwards from holes made at the sides of a container.

Hydraulic machines are machines that use liquids to transmit (pass on) forces. This use of a liquid to transmit force is called hydraulic pressure.

(1) Liquids are very difficult to compress because their particles are very close together. (2) If a trapped liquid is put under pressure, the pressure is transmitted throughout the whole liquid.

Pressure applied to the small (narrow) cylinder is transmitted by the liquid to the larger (wide) piston. Because the output piston has a bigger area, the same pressure produces a larger output force than the input force — so the jack multiplies force.

A force multiplier is a device that gives out a larger force than the force put in. A hydraulic jack is a force multiplier because a small input force produces a much larger output force.

Pressure = 12 ÷ 0.01 = 1200 Pa. This pressure is transmitted to the output piston: output force = pressure × area = 1200 × 0.1 = 120 N. So 12 N in gives 120 N out.

When the brake pedal is pressed, a piston puts pressure on the brake fluid in a cylinder. This pressure is transmitted through the fluid to another piston, which pushes a brake pad onto the disc, slowing the wheel. There are two brake pads, one on each side of the disc.

Gases can be compressed (squashed) easily, so instead of passing on the force they would just squash. Liquids are almost impossible to compress, so they transmit the pressure and force properly — that is why hydraulics use liquids.

Pressure = 10 ÷ 0.02 = 500 Pa. Output force = pressure × area = 500 × 0.2 = 100 N. So 10 N in gives 100 N out.

Examples include the hydraulic jack used to lift heavy loads and a car’s hydraulic braking system. (Diggers and lifting platforms also use hydraulics.)

Air is a gas and can be compressed, so an air bubble squashes instead of passing on the pressure. Less pressure reaches the brake pads, so the brakes feel spongy and work poorly. The fluid must be an incompressible liquid with no air in it.

Yes. When a trapped liquid is put under pressure, the pressure is transmitted equally throughout the whole liquid, so it is the same everywhere in the system.

It is the pressure that is transmitted equally through the liquid. Because the output piston has a larger area, the same pressure acting on it (force = pressure × area) produces a larger output force than the input force.

Correct answer: (d) staying still in one place. Balanced forces cannot change motion, so the object stays still (or moves at a steady speed in a straight line). Moving in circles or speeding up both need an unbalanced (resultant) force.

Correct answer: (b) Objects with a density lower than 1 g/cm³ will float. Objects denser than water sink.

Correct answer: (c) It increases. Since pressure = force ÷ area, a bigger force on the same area gives a bigger pressure.

Correct answer: (b) 30 Pa. Area = 2 × 1 = 2 m²; pressure = 60 ÷ 2 = 30 Pa.

Correct answer: (d) Its pressure increases and it heats up. Compressing a gas raises its pressure and makes the molecules move faster, so it gets hotter.

True. The upthrust from the displaced water balances the boat’s weight, keeping it afloat.

True. Sea water is denser, so it gives more upthrust and ships float higher.

True. A small area means a very high pressure, which can damage the floor.

False. Compressing a gas makes the molecules move faster, so the gas heats up (gets hotter), not colder.

False. The tea reaches the same level in the pot and the spout — liquid pressure does not depend on the shape or width of the container.

Unbalanced. On each car the two opposite forces are not equal, so there is a resultant force.

Car A gains speed (accelerates). Its forward force (1500 N) is greater than the backward force (1000 N), giving a resultant force of 500 N forwards, so it speeds up in the direction of motion.

Car B loses speed (slows down). Its forward force (800 N) is less than the backward force (1000 N), giving a resultant of 200 N backwards, so it decelerates.

Car A would accelerate more — it would gain speed faster (a greater acceleration).

The forces would be balanced, so there is no resultant force. The car would either stay stationary or keep moving at a steady (constant) speed in a straight line — its speed would not change.

Density is the mass of a material per unit volume — how much mass is contained in a given volume. It is calculated as density = mass ÷ volume.

1 g/cm³ (equal to 1000 kg/m³).

(a) a liquid less dense than water: petrol (800 kg/m³). (b) two solids denser than steel (7800): gold (19 300) and lead (11 300). (c) a low-density gas: air (1.3 kg/m³). (d) a solid that floats on water: wood (900 kg/m³, less than water’s 1000).

Wood’s density (900 kg/m³) is greater than air’s (1.3 kg/m³), so it sinks in air. But wood’s density is less than water’s (1000 kg/m³), so it floats on water.

Two forces act: the weight of the boat acting downwards, and the upthrust from the water acting upwards. They are equal and opposite.

The boat floats because the upthrust from the water (equal to the weight of water displaced) exactly balances the boat’s weight. Equal and opposite forces mean the forces are balanced.

A loaded boat weighs more, so it needs more upthrust to balance the extra weight. To get more upthrust it must displace more water, so it sinks lower until the larger upthrust equals its greater weight.

Highest pressure: standing on its smallest face (2 cm × 3 cm = 6 cm²). Lowest pressure: lying on its largest face (3 cm × 4 cm = 12 cm²).

Smallest face: 6 cm² = 0.0006 m², P = 600 ÷ 0.0006 = 1 000 000 Pa (1000 kPa). Largest face: 12 cm² = 0.0012 m², P = 600 ÷ 0.0012 = 500 000 Pa (500 kPa).

The block is most stable lying on its largest face (3 cm × 4 cm). This gives the widest base and the lowest centre of gravity, so it is least likely to topple — and it also gives the lowest pressure.

Pressure = force ÷ area = 20 ÷ 0.1 = 200 Pa.

Output force = pressure × area = 200 × 0.5 = 100 N.

The output force = pressure × output area, so (a) a smaller output cylinder gives a smaller output force, and (b) a bigger output cylinder gives a bigger output force.

It would work much less well. Air is a gas and can be compressed (squashed) easily, whereas oil (a liquid) cannot. If air were used, pushing the input would mostly just squash the air instead of transmitting the pressure to the output piston, so the output force would be much smaller and the system would feel spongy. Hydraulic machines need an almost incompressible liquid to transmit force properly.

(a) Air resistance 1000 N equals the forward force, so the forces are balanced with no resultant — the car moves at a steady (constant) speed. (b) Air resistance 3800 N is greater than 1000 N, giving a resultant of 2800 N backwards, so the car slows down (decelerates).

It means every 1 cm³ of water has a mass of 1 gram. Anything with a density less than this floats on water, and anything denser sinks.

Pressure = force ÷ area. Water: 4500 ÷ 1.5 = 3000 Pa. Oil: 6000 ÷ 1.5 = 4000 Pa.

Taking the weight on one heel: stiletto — area 1 cm² = 0.0001 m², P = 550 ÷ 0.0001 = 5 500 000 Pa. Flat heel — area 10 cm² = 0.001 m², P = 550 ÷ 0.001 = 550 000 Pa. The flat heel gives a far lower pressure, so it is less likely to damage a wooden floor (larger area → lower pressure).

Use a container with sections of different shapes joined at the bottom (like a teapot with a pot and a spout). Pour in liquid and it settles to the same level in every section, showing that the pressure at a given depth is the same regardless of the shape.