Mass, Weight and Free Fall

Mass and weight are used interchangeably in ordinary speech and mean quite different things in physics. The distinction is worth pinning down carefully, because it underlies free fall, gravity and a good number of questions whose wrong options are built entirely on the confusion.

Mass is how much matter; weight is a force

Mass is the amount of matter in something, measured in kilograms, and it does not change when you move the object. Take a 2 kilogram mass to the Moon and it is still 2 kilograms, because the amount of stuff has not altered. Weight is different: it is the force that gravity exerts on that mass, so it is measured in newtons like any other force, and it depends on where you are.

That same g appears as an acceleration of 9.8 metres per second squared, and the two readings are equivalent — newtons per kilogram and metres per second squared are the same combination of units, which you can verify by substituting the newton's definition from the units lesson. Because 9.8 makes arithmetic tedious, questions designed for mental calculation routinely use 10 instead, and the question will normally tell you when it does. The physics bank does this in several items, so a weight of 20 N for a 2 kg mass is a deliberate simplification rather than an error.

Free fall

Drop something with air resistance small enough to ignore and gravity is the only force acting, so by Newton's second law it accelerates at g regardless of its mass. This is the result that feels wrong: a heavy object and a light one, released together, land together. The reason is visible in F = ma — the heavier object has more weight pulling it down, but it also has proportionally more mass resisting the acceleration, and the two effects cancel exactly. Every falling object gains about 10 metres per second of speed for each second it falls.

That cancellation is worth seeing in numbers rather than taking on trust. Take a 1 kilogram mass and a 10 kilogram mass with g = 10. The lighter one has a weight of 10 newtons and a mass of 1 kilogram, so its acceleration is $\frac{F}{m} = \frac{10}{1} = 10$ metres per second squared. The heavier one has ten times the weight at 100 newtons, but also ten times the mass, so its acceleration is $\frac{100}{10}$ — which is the same 10 metres per second squared. The extra pull is exactly used up moving the extra matter, and that is the whole explanation.

A detail that occasionally appears: g is not perfectly constant across the Earth. It is slightly larger at the poles than at the equator, because the Earth is not a perfect sphere and because rotation has a small effect, and it falls off gradually with altitude. The variation is under one per cent at the surface, which is why treating it as a fixed 9.8 is safe for everything in this course. The gravitation lesson at the end of this module returns to why it falls off with height at all.

The place candidates most often come unstuck is a ball thrown straight up. At the very top of its flight the ball is momentarily stationary, so its velocity is genuinely zero — but gravity has not switched off, so the acceleration there is still the full g downwards. Zero velocity and zero acceleration are different claims, and an object can have the first without the second. If the acceleration really were zero at the top, the ball would stay there.

When air resistance cannot be ignored

Real falls in air are not free falls for long. Air resistance, or drag, pushes back against the motion, and unlike weight it grows as the object speeds up. So the net downward force shrinks as the fall continues, the acceleration tails off, and eventually drag grows until it exactly matches the weight. At that point the net force is zero, and by Newton's first law the velocity stops changing — the object keeps falling, but at a steady speed called the terminal velocity.

This is why a parachute works: opening it multiplies the drag at a given speed, so the forces balance at a far lower terminal velocity. It is also why a feather and a hammer fall differently in air and identically on the Moon, where there is no air to resist either.

Putting it to work

Mass measures two things at once

There is a quiet coincidence buried in this lesson worth naming, because it explains why the same letter does two jobs. Mass appears in W = mg as the thing gravity pulls on, and it appears in F = ma as the thing that resists being accelerated. Those are logically separate roles — how strongly gravity grips something, and how stubbornly it refuses to speed up — and there is no obvious reason they should be measured by the same number. Experimentally they are, to extraordinary precision, and that is exactly why every object falls at the same rate: the quantity being pulled and the quantity resisting are identical, so they cancel for every object equally.

For this course you do not need that idea beyond recognising it, but it does make the free-fall result less arbitrary. It is not a coincidence that heavy and light objects fall together — it follows from mass playing both parts, and it is the reason the mass cancels out of the arithmetic every time you try to include it.

Why it matters in aviation

Aviation keeps mass and weight formally apart because an aircraft's weight changes throughout every flight. Fuel is burned continuously, so an airframe that left the gate heavy arrives measurably lighter, and the speeds a crew flies are not fixed numbers but figures worked out for the weight at the time. A lighter aircraft can be flown more slowly before the wing stops supporting it, so its approach speed on landing is lower than the same aircraft would have used at the start of the flight, and its takeoff speeds were higher when it was full of fuel.

The other half of the distinction shows up in manoeuvring. Pulling into a turn or a climb does not alter the amount of matter in the aircraft, but it does alter the force the wings must supply, and the apparent weight of the airframe and everything in it rises in proportion. That ratio is called load factor and is quoted in multiples of g: one g in steady level flight, and more whenever the lift exceeds the weight. Structural limits are written in those terms rather than in newtons precisely because the mass is fixed while the apparent weight is not — the same reasoning that keeps the ball at the top of its throw accelerating even with zero velocity.

What the test asks

Weight quoted in kilograms is the commonest error, and it will appear as an answer option that looks reassuringly like the mass you were given. Expect at least one item asking what changes when an object is moved to the Moon, where the correct answer is the weight alone. And expect the thrown-ball question about the top of the flight, where the tempting option is that both velocity and acceleration are zero — the velocity is, the acceleration is not.