Force and Pressure

Every time you kick a football, open a stiff door, feel a shoulder-bag strap dig into your skin, or watch a nail sink into wood only when turned point-down, you are looking at the two ideas this chapter builds from the ground up: force and pressure. A force is nothing more mysterious than a push or a pull — but that simple idea, once sharpened, explains why a rolling ball slows down on its own, why a magnet can move a pin without touching it, why a stretched bow snaps an arrow forward, and why porters wrap their heads in a cloth pad before lifting a heavy sack. The chapter starts by showing that every push or pull, however it gets described in everyday speech — lifting, kicking, flicking, squeezing, drawing water from a well — is really just one of two actions, and that a force never appears out of nowhere: it always arises from an interaction between at least two objects. It then works through everything a force can do: start an object moving, speed it up, slow it down, turn it, or squash and stretch its shape, all gathered under a change in its state of motion (plus a possible change of shape). Forces are then sorted by how they act: contact forces, like the muscular force in your arm or the friction that slows a rolling ball, needing the two objects to touch; and non-contact forces — magnetic, electrostatic, gravitational — which act perfectly well from a distance. The second half turns to pressure, the discovery that the very same force feels utterly different depending on how much area it spreads over: a nail's flat head refuses to enter wood, but its sharp point sinks in easily, because pressure is force concentrated — or diluted — by area. That idea scales up to explain why liquids push outward on any container's walls, why a balloon must be tied shut to stay inflated, and why the invisible ocean of air above your head presses down with a force of roughly two and a quarter thousand newtons, without crushing you at all.

Key takeaways

A force is a push or a pull. Lifting, kicking, flicking, squeezing, pulling — every such action is, in science, a push, a pull, or both.
A force needs an interaction. At least two objects must interact for a force to exist; it always acts on one object due to another.
Forces combine. Forces in the same direction add; forces in opposite directions give a net force equal to their difference, as in a tug-of-war.
A force can change the state of motion of an object — start it moving, speed it up, slow it down, or change its direction.
A force can also change an object's shape, whether or not it is free to move — pressing dough, stretching a rubber band, bending a scale between bricks.
Contact forces need touching: muscular force (from muscles) and friction (opposing motion between touching surfaces).
Non-contact forces act without touching: magnetic force, electrostatic force (between charged bodies), and gravitational force (mutual attraction between any two objects).
Pressure is force per unit area, $P = F/A$ : the same force gives far more pressure over a smaller area — why a nail's point pierces wood but its flat head does not.
Liquids and gases exert pressure on the walls of their container, in every direction, growing with the depth of the column above.
Key idea: force is a push or a pull that arises only from an interaction between two objects and can change an object's state of motion or its shape, while pressure — force divided by the area it acts on, P = F/A — explains why the same force can pierce, crush, or gently support depending only on the area involved, including the roughly 2250 newton force the atmosphere presses on a head-sized patch of skin without crushing us.

The core insight

Force is a push or a pull that arises only from an interaction between two objects and can change an object's state of motion or its shape, while pressure — force divided by the area it acts over, $P = F/A$ — explains why the same force pierces, crushes or gently supports depending purely on how small or large that area is.

What this chapter covers

This article follows the chapter's own two-part path. The first half is about force: what counts as a push or a pull, why a force always needs two interacting objects, how forces combine when more than one acts at once, and what a force can do — change an object's state of motion (start, speed up, slow down, turn it) or change its shape. It then sorts forces into contact forces (muscular force, friction), needing the acting object to touch what it acts on, and non-contact forces (magnetic, electrostatic, gravitational), which act across a gap. The second half is about pressure: the same force spread over a small area presses far harder than over a large area. That relationship, pressure equals force over area, explains why liquids and gases push outward on every wall of their container, and why the atmosphere presses down on us with a real, measurable force.

The core ideas

Force: a push or a pull

Picking up a bag, opening a drawer, kicking a ball, drawing water from a well — everyday speech has separate verbs for each, but science collapses them into one idea. Every one of these actions is, at bottom, a push, a pull, or some combination. In science, a push or a pull exerted on an object is called a force. Kicking a ball is a push; drawing water is a pull; even a magnet's attraction of iron can be thought of as a pull, and repulsion between like magnetic poles as a push — force is the general word covering all of these.

Every force needs an interaction

A man standing quietly behind a parked car does not make it move — nothing happens until he actually pushes it. This is the second key fact: a force never appears by itself. It arises only when one object interacts with another, as when two teams pull on a tug-of-war rope. At least two objects must be involved for a force to come into play — one object cannot generate a force acting on itself alone.

Magnitude, direction, and combining forces

A force has a magnitude (how large) and a direction (which way), and more than one force often acts on an object at once, combining into a single net force.

F_{net} = F_1 + F_2 \quad \text{(same direction)}, \qquad F_{net} = F_1 - F_2 \quad \text{(opposite directions, } F_1 > F_2\text{)}

where: $F_1$ and $F_2$ are the two force magnitudes and $F_{net}$ decides what actually happens. Two friends pushing a box the same way add their forces; pushing from opposite sides, the net force is the difference, moving the box (if at all) toward the larger push. In a tug-of-war with equal teams, $F_1 = F_2$ , so $F_{net} = 0$ and the rope does not move — not because no force acts, but because the two forces exactly cancel.

What a force can do: change of motion, and change of shape

Pushing a resting ball makes it start moving. Pushing it again along its motion speeds it up; catching it with your palm slows it to a stop — a force changes an object's speed, increasing it along the direction of motion and decreasing it against that direction. Placing a ruler in a rolling ball's path deflects it into a new direction — a force can change direction of motion too. Any change in speed, direction, or both, is a change in the object's state of motion; an object at rest is simply in a state of motion with zero speed. A force can also change an object's shape even when it cannot move at all — pressing dough flat, stretching a rubber band, bending a scale between two bricks. A force may start motion, change speed, change direction, change shape, or cause several of these together — but none of these changes can happen without a force.

Figure

Four panels showing what a force can do to an object: starting a resting ball moving, changing the speed of a moving ball, changing the direction of a moving ball at a ruler, and pressing a lump of dough flatter to change its shape

Contact forces: muscular force and friction

Forces also sort by whether the object exerting the force must touch the object it acts on. A contact force can only be applied when the two objects are touching, directly or through a connector such as a rope. The most familiar is muscular force: the force caused by the action of muscles, in humans or animals. It lets us push a bag or lift a bucket, and lets bullocks, horses, donkeys and camels work for us; inside the body, it pushes food along the alimentary canal during digestion and expands and contracts the lungs during breathing. A second contact force is friction. A rolling ball, a coasting bicycle, and a drifting boat all slow down and stop with no person pushing — the force responsible is friction, arising between two touching surfaces and always acting opposite to the direction of motion.

Non-contact forces: magnetic, electrostatic, gravitational

A non-contact force can act between two objects without them ever touching. Magnetic force is the force a magnet exerts on another magnet or on iron; like poles repel and unlike poles attract, and a magnet on rollers moves when another magnet is merely brought near, never touching. Electrostatic force is the force a charged body exerts on another charged or uncharged body — a straw rubbed with paper attracts (or, if both are charged, repels) another straw held nearby, again without contact. Gravitational force is the mutual attraction between any two objects in the universe; the Earth's pull, usually just called gravity, is why a coin or a leaf falls and why water flows downhill. Gravity acts on every object, all the time, with no contact at all.

Pressure: force concentrated, or spread out, over an area

Pushing a nail into wood by its flat head almost never works, however hard you press; turned point-down, the same nail slides in easily. The applied force can be identical in both attempts — what changes is the tiny area it acts over. This is the chapter's second big idea: the effect of a force depends not just on the force itself but on the area it acts on, a quantity called pressure.

P = \dfrac{F}{A}. \qquad (1)

where: $P$ is pressure, $F$ is the force acting perpendicular to a surface, and $A$ is that surface's area. The SI unit of pressure is the pascal (Pa), $1\ \text{Pa} = 1\ \text{N/m}^2$ . Because $A$ sits in the denominator, a smaller area gives a larger pressure for the same force. This is why a nail's tiny-area point pierces wood while its broad-area head does not; why a porter places a round cloth pad on his head before carrying a load, spreading the same weight over more area; why shoulder-bag straps are made broad rather than thin; and why knives and scissors are kept sharp.

Figure

A nail pushed by its flat head fails to enter a wooden plank while the same force applied through its sharp pointed tip drives it straight in, because the tip has a far smaller area and therefore produces a far larger pressure for the same force

Pressure exerted by liquids and gases

Fill a vertical pipe fitted with a stretched rubber sheet with water, and the sheet bulges outward, more so as the water rises — a liquid pushes down on the base of its container. Fix the same sheet over a hole on the side of a bottle instead, and it still bulges once water is poured in: a liquid pushes sideways on the walls too, harder the deeper the point considered. Gases behave the same way: air escaping through a punctured bicycle tube, water spraying equally from holes drilled at the same height around a bottle, and a balloon that must be tied shut to stay inflated all show a confined gas pushing outward on every part of its container, in every direction.

Atmospheric pressure

Air surrounds the Earth for many kilometres, forming the atmosphere, and this air has weight. The pressure it exerts, simply from being stacked above a point, is called atmospheric pressure — pictured as the force of gravity on all the air inside a tall imaginary column of unit area, standing on that point and reaching to the top of the atmosphere. It is large enough to hold a rubber sucker firmly on a smooth surface once the air between them is pressed out. We do not notice this huge, continuous push because the pressure inside our bodies matches the pressure pushing in from outside, and the two balance.

Two derivations

Derivation AWhy the same force pierces wood at a nail's point but not at its head

The chapter states, without working the numbers, that a nail goes into wood through its point but not its head, because the point has a much smaller area. The goal here is to turn that into a numeric comparison using $P = F/A$ , so "smaller area gives larger pressure" becomes something you can compute rather than only recite.

Step 1. Fix the force. A firm hammer blow delivers roughly the same push whichever way the nail is turned, so take $F = 50\ \text{N}$ in both attempts — the one quantity held fixed, isolating the effect of area alone.

Step 2. Estimate the two areas. The flat head is a few millimetres across; take $A_{\text{head}} = 25\ \text{mm}^2 = 2.5\times10^{-5}\ \text{m}^2$ . The tapered point is far finer; take $A_{\text{tip}} = 0.05\ \text{mm}^2 = 5\times10^{-8}\ \text{m}^2$ , about five hundred times smaller.

Step 3. Apply $P = F/A$ to each. At the head, $P_{\text{head}} = \dfrac{50}{2.5\times10^{-5}} = 2.0\times10^{6}\ \text{Pa}$ . At the point, $P_{\text{tip}} = \dfrac{50}{5\times10^{-8}} = 1.0\times10^{9}\ \text{Pa}$ — five hundred times larger, exactly matching the five-hundred-fold gap in area, since pressure is inversely proportional to area for a fixed force.

Step 4. Interpret. The identical hammer blow produces a pressure at the tip five hundred times higher than at the head; it is this concentrated pressure, not any change in force, that pushes wood fibres apart. The same reasoning, run in reverse, explains the porter's cloth pad and the broad shoulder strap: spreading a weight over a larger area lowers pressure exactly as concentrating it over a smaller one raises it. Check: $A_{\text{head}}/A_{\text{tip}} = 500$ and $P_{\text{tip}}/P_{\text{head}} = 500$ — the pressure ratio matches the inverse area ratio, as $P = F/A$ requires.

Go deeper · Derivation B · 1 minHow large a force the atmosphere presses on your head

Derivation BHow large a force the atmosphere presses on your head

The chapter poses this directly: if your head's area is about $15\ \text{cm}\times15\ \text{cm}$ , how much force does the surrounding air exert on it — and states the answer, nearly the weight of a $225\ \text{kg}$ mass, about $2250\ \text{N}$ , without showing the working. The goal is to reproduce that exact number using $P = F/A$ rearranged for force, so this invisible everyday force becomes a calculation rather than an assertion.

Step 1. Take the standard sea-level atmospheric pressure, $P_{\text{atm}} \approx 1.0\times10^{5}\ \text{Pa}$ .

Step 2. Convert the head's dimensions to metres and find the area: $15\ \text{cm} = 0.15\ \text{m}$ , so $A = 0.15 \times 0.15 = 0.0225\ \text{m}^2$ .

Step 3. Rearrange $P = F/A$ to $F = P \times A$ : $F = (1.0\times10^{5})(0.0225) = 2250\ \text{N}$ .

Step 4. Convert to an equivalent mass to check against the chapter's figure, using $F = mg$ with $g \approx 10\ \text{m/s}^2$ : $m = F/g = 2250/10 = 225\ \text{kg}$ — matching the chapter exactly.

Step 5. Resolve the puzzle: if this force is real and constant, why are we not crushed? Because the push is not one-sided — the pressure inside our own bodies matches the atmosphere pushing in, so the two balance. Check: $F = PA = 2250\ \text{N}$ and $m = F/g = 225\ \text{kg}$ — both match the chapter's stated result.

Worked examples

Board level - Classifying the forces in an archer shooting an arrow

An archer stretches her bow while taking aim, then releases the arrow, which flies toward the target. Identify (a) the force used to stretch the bow, and its effect; (b) whether the force starting the arrow's motion is contact or non-contact; (c) the two forces acting on the arrow in flight.

Step 1. Stretching the bow: the archer's hands touch the bowstring, so this is a muscular, contact force, and its effect is to change the bow's shape (it bends), not to move it.

Step 2. Releasing the arrow: the snapping bowstring pushes the arrow while still touching it, so the force starting the arrow's motion is a contact force.

Step 3. In flight: the arrow feels gravity (a non-contact, gravitational pull downward) and friction due to air (a contact force opposing its motion).

The archer's pull is a muscular contact force that changes the bow's shape; the string's push is a contact force that starts the arrow's motion; in flight, gravity (non-contact) and air friction (contact) act on it.

Board level - Comparing the pressure a book exerts flat versus on its edge

A book weighing 6 N rests flat on a table over an area of 0.03 m². Stood upright on its spine, it touches the table over only 0.003 m². Find the pressure in each position, and state which way it presses harder.

Step 1. Flat: $P_{\text{flat}} = \dfrac{6}{0.03} = 200\ \text{Pa}$ .

Step 2. Upright: $P_{\text{upright}} = \dfrac{6}{0.003} = 2000\ \text{Pa}$ .

Step 3. The weight, $F = 6\ \text{N}$ , is unchanged in both positions; only the area shrank tenfold, and pressure grew by the same factor of ten.

Lying flat, the book presses with 200 Pa; standing on its spine, it presses with 2000 Pa — ten times harder — purely from a tenfold smaller contact area.

Higher-order thinking (HOTS / olympiad-style) - A porter's cloth pad, and a heavier sack

A porter carries a 300 N sack directly on his head over an area of 30 cm². A round cloth pad spreads this to 150 cm². Find the pressure with and without the pad, and the reduction factor. Then, on the same pad, he carries a heavier 450 N sack — find the new pressure, and check it against the original no-pad pressure.

Step 1. Convert areas: $30\ \text{cm}^2 = 0.0030\ \text{m}^2$ ; $150\ \text{cm}^2 = 0.0150\ \text{m}^2$ .

Step 2. No pad: $P_{\text{no pad}} = \dfrac{300}{0.0030} = 1.0\times10^{5}\ \text{Pa}$ .

Step 3. With pad: $P_{\text{pad}} = \dfrac{300}{0.0150} = 2.0\times10^{4}\ \text{Pa}$ , a reduction factor of $5$ , matching the fivefold increase in area.

Step 4. Heavier 450 N sack on the same pad: $P_{\text{heavy}} = \dfrac{450}{0.0150} = 3.0\times10^{4}\ \text{Pa}$ — still well under a third of the original $1.0\times10^{5}\ \text{Pa}$ , despite the sack being 1.5 times heavier.

Pressure falls from 1.0 x 10^5 Pa to 2.0 x 10^4 Pa with the pad (a fivefold drop), and even a 50 per cent heavier sack on the same pad presses with only 3.0 x 10^4 Pa — under a third of the unpadded pressure. Timing note: budget four to five minutes. The main trap is dividing by an area still in cm² — always convert to m² first. Do not stop after Step 3: the question asks you to re-check with the heavier sack too.

Common traps

Thinking "no motion" means "no force." A box that will not budge still has a force acting on it, simply balanced by another force such as friction; net force, not one force alone, decides motion.
Assuming opposite forces always cancel to exactly zero. They cancel only when equal in magnitude; otherwise the net force is their difference, toward the larger force — as in a tug-of-war.
Believing every force needs touching. Muscular force and friction do; magnetic, electrostatic and gravitational forces act across empty space.
Calling gravity only "the Earth's force." Gravity is mutual: every object attracts every other; the Earth's pull feels dominant only because the Earth is so much more massive.
Treating force and pressure as the same quantity. Force alone never predicts piercing, crushing, or sinking — area matters equally, exactly why $P = F/A$ has area in it.
Forgetting gases exert pressure too. A balloon needs its mouth tied precisely because trapped air pushes outward on every part of its inner wall.
Thinking atmospheric pressure is too small to feel. It pushes on a head-sized area with over two thousand newtons; we are not crushed only because internal body pressure pushes back equally.

You should be able to…

Explain what a force is, with two everyday examples each of a push and a pull.
Explain why a force can never act without an interaction between at least two objects.
State how forces combine in the same and opposite directions, using the tug-of-war as an example.
List the effects a force can have: starting motion, changing speed, changing direction, changing shape.
Distinguish contact from non-contact forces, and classify muscular force, friction, magnetic, electrostatic and gravitational force correctly.
State the pressure formula $P = F/A$ and explain why the same force gives more pressure over a smaller area.
Solve numeric pressure problems, converting areas from square centimetres to square metres first.
Explain that liquids and gases exert pressure on their container's walls, in every direction.
Explain what atmospheric pressure is, and why it does not crush us despite its large magnitude.

Ask the tutor: if you are unsure whether a described scenario, like the archer's bow or the porter's sack, calls for a force answer or a pressure calculation, ask the tutor to walk through how to spot which one the question is really asking for.

If I push against a wall with all my strength and it does not move at all, am I actually applying a force?

Yes, you are — the wall simply pushes back with an equal and opposite resisting force, so the net force is zero and nothing moves. A force is present the moment you push, whether or not anything happens as a result; motion depends on the net force after every force on the object is counted. The same reasoning explains a heavy box that will not budge alone: your force is real, just matched by friction between the box and the floor.

How can a magnet move a pin without ever touching it? Does not every force need contact?

Not every force needs contact — that is exactly the contact versus non-contact split the chapter draws. Muscular force and friction genuinely require touching, but magnetic, electrostatic and gravitational forces all act perfectly well across a gap. A magnet exerts a real pull on nearby iron with empty space between them, in the same way the Earth pulls a falling coin toward it before it ever touches the ground. Contact simply is not a requirement for every force, only for some kinds.

Why does the huge force of the atmosphere pressing on us all the time not crush us flat?

Because the push is not one-sided. Air really does press inward with a large force — on a head-sized patch of skin, roughly 2250 newtons — but the fluids inside our own bodies are under a matching internal pressure, pushing outward with essentially equal strength. The two balance, so we feel no net crushing effect. You can see the unbalanced version in a rubber sucker: once most of the air between it and a surface is pressed out, nothing inside pushes back, and the full outside atmospheric pressure holds it firmly in place.

Force and pressure both seem to be about pushing on something — what is actually different between them?

Force is simply the push or pull itself, in newtons, and it does not care how large or small the area it acts on is. Pressure is that same force divided by area, $P = F/A$ , in pascals, and it very much cares about area. The same force can give wildly different pressures: a person's weight spread across two feet gives a modest pressure, but the same weight balanced on one stiletto heel concentrates onto a tiny area and gives an enormous pressure, enough to dent a soft floor. A question about piercing, cutting, sinking or crushing is really asking about pressure, not force alone.