Gravitation

Why does an apple fall to the ground, the Moon go round the Earth, and the Earth go round the Sun? The answer is gravitation — a force of attraction that acts between all objects in the universe. According to a famous story, Sir Isaac Newton was inspired by a falling apple to realise that the same force that pulls an apple down also keeps the Moon and planets in their orbits. He stated this as the Universal Law of Gravitation.

The Universal Law of Gravitation states that every object in the universe attracts every other object with a force. This force of attraction is called the gravitational force. The law tells us exactly how strong this force is: the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In a formula, this is written as F = G m₁ m₂ / r², where m₁ and m₂ are the masses of the two objects, r is the distance between their centres, and G is a constant called the universal gravitational constant.

From the formula we can understand how the force behaves. Because the force is proportional to the masses, objects with larger masses attract each other more strongly — this is why the very massive Earth pulls objects to it noticeably, while the tiny gravitational pull between two ordinary objects is too small to notice. Because the force is inversely proportional to the square of the distance, the gravitational force becomes weaker as the objects move farther apart — doubling the distance makes the force one-fourth as strong.

The constant G has a fixed, very small value, about 6.67 × 10⁻¹¹ in SI units, and it is the same everywhere in the universe (which is why the law is called "universal"). Because G is so small, gravitational forces between everyday objects are extremely weak; the force is significant only when at least one of the objects is very massive, like a planet or a star. The universal law of gravitation explains a huge range of phenomena — the falling of objects, the weight we feel, the orbits of the Moon and planets, and the tides — all from a single rule of attraction between masses.

When any object near the Earth's surface is dropped, it falls downward, pulled by the Earth's gravitational force. This pull gives the falling object an acceleration, called the acceleration due to gravity, represented by the symbol g. It is the acceleration that any freely falling object gains because of the Earth's gravity. A very important fact is that g does not depend on the mass of the falling object — in the absence of air resistance, a heavy stone and a light feather would fall with exactly the same acceleration and reach the ground together.

The value of the acceleration due to gravity near the Earth's surface is about g = 9.8 m/s² (sometimes rounded to 10 m/s² for easy calculation). This means that as an object falls freely, its downward velocity increases by about 9.8 m/s every second. So after 1 second a freely falling object has a velocity of about 9.8 m/s, after 2 seconds about 19.6 m/s, and so on, steadily speeding up as it falls.

Although g is roughly constant near the surface, its value is not exactly the same everywhere on the Earth. The Earth is not a perfect sphere — it is slightly flattened at the poles and bulging at the equator. As a result, a place at the poles is slightly closer to the centre of the Earth than a place at the equator. Since gravity is stronger when closer to the centre, the value of g is slightly greater at the poles than at the equator. The value of g also decreases slightly as we go to very high altitudes, far above the surface, because we move farther from the centre.

The acceleration due to gravity g is the link between the universal law of gravitation and the everyday falling of objects: it is the acceleration the Earth's gravity gives to objects near its surface. Because g does not depend on the object's mass, all objects fall at the same rate (ignoring air resistance) — a fact famously demonstrated and one of the surprising truths of physics. Understanding g prepares us to study the difference between mass and weight, and the motion of freely falling objects.

Two quantities that are often confused in everyday language but are quite different in science are mass and weight. Mass is the amount of matter (material) contained in an object. It is a measure of how much "stuff" the object is made of, and it is a scalar quantity. The SI unit of mass is the kilogram (kg), and mass is measured with a beam balance. A crucial point is that the mass of an object is constant — it stays the same everywhere in the universe, whether on Earth, on the Moon, or in space, because the amount of matter does not change.

Weight, on the other hand, is the force with which the Earth (or any planet) attracts an object toward its centre. In other words, weight is the gravitational force on the object. Since weight is a force, it is a vector quantity (it acts downward), and its SI unit is the newton (N), like all forces. Weight is measured with a spring balance. The weight of an object is given by the formula Weight = mass × acceleration due to gravity, or W = m g.

Because weight depends on g, and g changes from place to place, the weight of an object can change even though its mass stays the same. The most striking example is on the Moon: the Moon's gravity is only about one-sixth (1/6) of the Earth's, so g on the Moon is about one-sixth of its value on Earth. This means an object weighs only about one-sixth as much on the Moon as on Earth, even though its mass is exactly the same on both. This is why astronauts can jump high and lift heavy objects easily on the Moon.

The differences between mass and weight can now be summarised. Mass is the amount of matter (kilograms), is constant everywhere, and is a scalar measured by a beam balance. Weight is the gravitational force (newtons), changes with location (with g), and is a vector measured by a spring balance. The relationship between them is W = mg. Understanding this distinction clears up much everyday confusion and is essential for studying free fall and gravitation.

When an object falls under the influence of gravity alone, with no other force (such as a push or air resistance) acting on it, its motion is called free fall. During free fall, the only force acting is the Earth's gravity, so the object falls with the acceleration due to gravity, g (about 9.8 m/s²). An object in free fall speeds up steadily as it falls, gaining about 9.8 m/s of downward velocity each second. A freely falling object is sometimes said to be "weightless" in the sense that it and everything with it fall together — which is why astronauts in orbit, in continuous free fall, appear to float.

Because free fall is motion with a constant acceleration (g), we can describe it using the equations of motion, with the acceleration taken as g. The two most useful equations for free fall are:

• v = u + g t — gives the velocity (v) after time t, where u is the initial velocity.
• h = u t + ½ g t² — gives the height fallen (h) in time t. Here u is the initial velocity (often 0 if the object is simply dropped), v is the final velocity, t is the time, and h is the distance fallen. These let us calculate how fast an object is moving and how far it has fallen at any time.

Let us see how to use them. If an object is dropped from rest, its initial velocity u = 0, so the equations simplify to v = g t and h = ½ g t². For example, taking g = 10 m/s², after 2 seconds a dropped object has a velocity v = 10 × 2 = 20 m/s, and has fallen a height h = ½ × 10 × 2² = ½ × 10 × 4 = 20 m. In this way we can predict the speed and the distance of fall at any time.

It is important to remember that these simple results assume free fall — gravity acting alone, without air resistance. In real life, air resistance affects light objects, so they do not exactly follow these equations. But for compact, heavy objects falling short distances, the equations work very well. Understanding free fall and its equations connects the acceleration due to gravity to real calculations, letting us work out the motion of falling objects, completing the practical side of gravitation.

Gravity gives objects weight, and this weight is a force that presses down on whatever supports the object. The force acting on a surface in a direction perpendicular (at right angles) to it is called thrust. For an object resting on a surface, the thrust is simply its weight, pressing down on the surface. Thrust, being a force, is measured in newtons (N). The effect of this thrust on a surface, however, depends on the area over which it acts — which brings us back to pressure.

As we learned earlier, pressure is the thrust (force) acting per unit area: Pressure = Thrust ÷ Area, or P = F / A, measured in pascals (Pa). The same thrust produces a larger pressure on a smaller area and a smaller pressure on a larger area. This is why the connection between thrust and pressure explains so many things: a person standing on soft snow with flat shoes may sink (small area, high pressure), but with wide snowshoes does not sink (large area, low pressure), even though the thrust (their weight) is the same.

The pressure in enclosed fluids obeys Pascal's law, which (as we saw with fluids) states that pressure applied to an enclosed fluid is transmitted equally in all directions. This principle is the basis of hydraulic systems — machines that use a trapped liquid to transmit and multiply force. In a hydraulic system, a small thrust applied on a small piston creates a pressure that is transmitted through the liquid to a large piston, where the same pressure acting over a larger area produces a much larger thrust. This allows a small force to lift a very heavy load.

Hydraulic systems are used in many important machines. Hydraulic lifts raise cars in service stations and lift heavy loads; hydraulic brakes in cars and trucks use the pressure in a fluid to press the brake pads against all the wheels at once; hydraulic jacks lift heavy vehicles to change tyres; and hydraulic presses are used in industry to shape metals and compress materials. By combining the ideas of thrust, pressure, and Pascal's law, these systems turn a small effort into a large force — a powerful application of the physics of pressure that completes our study of force, pressure, and gravitation in Grade 8.