Force and Pressure

In everyday life we constantly push, pull, lift, and throw things. A force is simply a push or a pull acting on an object. We cannot see a force itself, but we can see what it does. Force is what starts an object moving, stops it, speeds it up, slows it down, changes its direction, or changes its shape. The SI unit of force is the newton (N), named after Sir Isaac Newton, and force is measured with a spring balance.

Forces are of two broad kinds, depending on whether the objects need to be touching. A contact force acts only when two objects are in physical contact — for example, the muscular force we use to push a box, the frictional force between surfaces, and the normal (support) force from a table. A non-contact force acts even without contact, across a distance — for example, the gravitational force that pulls objects toward the Earth, the magnetic force between magnets, and the electrostatic force between charged objects. These non-contact forces act through the space between objects.

When several forces act on an object at once, their combined effect is the net force (or resultant force). If two forces act in the same direction, they add up; if they act in opposite directions, the net force is their difference, in the direction of the larger force. Forces are called balanced when they cancel out, giving a net force of zero — then the object's motion does not change. Forces are unbalanced when they do not cancel, giving a non-zero net force — then the object's motion does change (it speeds up, slows down, or changes direction).

The effects of a force can therefore be summarised: a force can change the speed of an object (make it faster or slower), change its direction of motion, set a stationary object moving or bring a moving object to rest, and change the shape or size of an object (as when we squeeze a sponge or stretch a spring). Only an unbalanced force can change an object's state of motion. Understanding force — its types and effects — is the foundation for studying pressure, friction, motion, and gravitation in this grade.

When a force acts on a surface, its effect depends not only on how large the force is but also on the area over which it acts. Pressure is defined as the force acting per unit area on a surface. The same force spread over a small area produces a large pressure, while the same force spread over a large area produces a small pressure. This is why a sharp knife (small area) cuts easily, while lying on a wide bed of nails (large total area) does not pierce the skin.

Pressure is calculated using a simple formula: Pressure = Force ÷ Area, written as P = F / A, where F is the force (in newtons) acting perpendicular to the surface and A is the area (in square metres). The SI unit of pressure is the pascal (Pa), where 1 pascal = 1 newton per square metre (1 Pa = 1 N/m²). From the formula we see that for a fixed force, pressure is larger when the area is smaller, and smaller when the area is larger.

This relationship explains many everyday observations. The sharp edge of a knife, the pointed tip of a nail, and the fine point of a pin all have a very small area, so even a moderate force produces a very high pressure that lets them cut or pierce. On the other hand, the wide straps of a heavy school bag, the broad feet of a camel, the large area of a tractor's tyres, and the wide foundations of buildings all spread the force over a large area to give low pressure, preventing sinking or damage.

To work with pressure, we rearrange the formula as needed: P = F/A, F = P × A, and A = F/P. Using these, we can calculate the pressure exerted by an object, the force needed for a certain pressure, or the area required. Understanding pressure as force per unit area, and how it depends on area, is essential for studying the pressure in fluids and the atmosphere that follow.

Liquids and gases are together called fluids, because they can flow. Fluids also exert pressure, but in a special way: a fluid presses in all directions — not just downward, but sideways and upward too — on the walls of its container and on any object placed in it. This is different from a solid, which presses only on the surface directly beneath it. A simple demonstration is a plastic bottle filled with water and pierced with holes at different heights: water spurts out of every hole, showing that the liquid pushes outward in all directions.

An important feature of liquid pressure is that it increases with depth. The deeper you go in a liquid, the greater the pressure, because there is more liquid above pressing down. This is why the water spurts out farther and faster from a lower hole than from a higher one, and why a dam is built much thicker at the bottom than at the top. The pressure at a depth in a liquid is given by the formula P = h ρ g, where h is the depth, ρ (rho) is the density of the liquid, and g is the acceleration due to gravity. The formula shows pressure depends on depth and density, but not on the shape or width of the container.

Another key principle of fluids is Pascal's law, which states that pressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid, without being weakened. In other words, if you press on a trapped fluid at one point, that pressure is passed on undiminished to every part of the fluid. This may seem surprising, but it is the basis of many powerful machines.

Pascal's law makes possible hydraulic machines, which use an enclosed liquid to multiply force. In a hydraulic system, a small force applied on a small piston creates a pressure that is transmitted through the liquid to a larger piston, producing a much larger force. This is how hydraulic lifts, hydraulic brakes in cars, and hydraulic jacks work, lifting heavy loads with a small effort. Thus the pressure in fluids — increasing with depth and obeying Pascal's law — explains everything from why dams are thick at the base to how a car's brakes stop a heavy vehicle.

The Earth is surrounded by a thick blanket of air called the atmosphere, which extends many kilometres upward. Although air is very light, the atmosphere is so deep that the air has considerable weight, and this weight presses down on everything on the Earth's surface. The pressure exerted by the weight of the air (the atmosphere) on the Earth's surface and on all objects is called atmospheric pressure. Like other fluid pressure, atmospheric pressure acts in all directions.

Atmospheric pressure is surprisingly large — at sea level it is about 100,000 pascals (10⁵ Pa), which means the air pushes on every square metre with a force of about 100,000 newtons. We do not feel crushed by it because the pressure of the fluids inside our bodies pushes outward and balances the atmospheric pressure pushing inward. The presence and strength of atmospheric pressure can be shown by simple experiments.

One famous demonstration is the crushing can experiment: a small amount of water is boiled inside a metal can to fill it with steam, driving out the air; the can is then sealed and cooled. As the steam condenses, the pressure inside drops, and the much greater atmospheric pressure outside crushes the can inward. This dramatically shows how strong atmospheric pressure is. Other everyday effects include drinking through a straw (we lower the pressure inside, and atmospheric pressure pushes the drink up) and the working of suction cups and rubber suckers, which stick because atmospheric pressure presses them against a surface.

Atmospheric pressure is not the same everywhere; it decreases with altitude (height above sea level). This is because, as we go higher, there is less air above us pressing down, so the pressure is lower. That is why atmospheric pressure is high at sea level but low at the top of a tall mountain — and why mountaineers may carry oxygen and why food is harder to cook at high altitudes. The instrument used to measure atmospheric pressure is the barometer. Understanding atmospheric pressure completes our study of how fluids — both liquids and the air — exert pressure all around us.

When an object is placed in a fluid (a liquid or gas), the fluid pushes it upward. This upward force exerted by a fluid on an object placed in it is called the buoyant force or upthrust, and the tendency of a fluid to push objects up is called buoyancy. Upthrust is the reason a heavy iron ship floats, a swimmer feels lighter in water, and a bucket of water feels lighter to lift while it is still under water. Buoyancy arises because fluid pressure increases with depth, so the fluid pushes up on the bottom of the object more strongly than it pushes down on the top.

The amount of this upthrust is given by a famous rule, Archimedes' principle, which states that when an object is wholly or partly immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced (pushed aside) by the object. In other words, the upward buoyant force equals the weight of the fluid that the object pushes out of the way. This is why an object seems to lose weight when placed in water: the upthrust supports part of its weight. The apparent weight of a submerged object equals its real weight minus the upthrust.

Whether an object floats or sinks in a fluid depends on a comparison of its density with the density of the fluid. If the object's density is less than that of the fluid, the upthrust can support its weight and it floats; if its density is greater than that of the fluid, the upthrust is not enough and it sinks. This is why a piece of wood (low density) floats on water while a stone (high density) sinks, and why oil floats on water.

This principle explains how huge ships made of iron, which is denser than water, can float. A ship is built hollow, with a large shape that displaces a great volume of water; this makes the ship's overall (average) density less than that of water, so it floats. Submarines, life jackets, hot-air balloons (which float in air using the buoyancy of the atmosphere), and the floating of fish all rely on buoyancy and Archimedes' principle. Understanding buoyancy completes this chapter on force and pressure by showing how fluids push objects upward.