Pearson Edexcel International GCSE in Physics · 4PH1

Weight and Terminal Velocity

What weight actually is, why it is not the same as mass, and what happens to a falling object once the air starts pushing back.

Topic 1 · Forces and motion — one of 10 lessons in this topic, and one of 65 in Physics.

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

  • 1.18 — Use W = m × g
  • 1.21 — The forces on falling objects, and why they reach terminal velocity

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

In ordinary speech mass and weight are the same word, and in physics they are not even the same kind of quantity. Mass is how much matter there is in an object, measured in kilograms, and it is a property of the object itself — carry it to the Moon and it does not change, because none of the matter has gone anywhere. Weight is something being done TO that object: it is the force with which gravity pulls it, measured in newtons. Take the same object to the Moon and its weight falls to about a sixth, because the Moon pulls less hard. Same object, same mass, different weight.

The link between them is g, the gravitational field strength, and its unit tells you exactly what it means. On Earth g is about 10 N/kg — read that as 'ten newtons of pull for every kilogram of stuff'. So a 3 kg bag is pulled with 30 N, a 60 kg person with 600 N. That is the entire content of W = m × g: it is not a formula to memorise so much as a rate, applied to however many kilograms you happen to have.

What happens when you drop something — the four stages

  1. AT RELEASE the object is not yet moving, so there is no air resistance at all. The only force is its weight, the resultant is at its largest, and so the acceleration is at its largest.
  2. AS IT SPEEDS UP air resistance appears and grows, because air resistance increases with speed. It acts upwards, against the motion.
  3. SO THE RESULTANT SHRINKS: resultant = weight − air resistance, and the air resistance term is getting bigger. A smaller resultant on the same mass means a smaller acceleration. Read this carefully — the object is still speeding up, just less rapidly than before. Falling acceleration and falling speed are completely different claims.
  4. EVENTUALLY air resistance grows until it exactly equals the weight. The resultant force is now zero, so the acceleration is zero, so the speed stops changing. The object continues to fall at a steady speed, and that speed is its terminal velocity.
A velocity–time graph: gradient is acceleration, area is distancetime (s)velocity (m/s)acceleratingconstant velocitydeceleratingarea = distancegradient = acceleration · area under = distance travelled
A falling object's graph is steep at first and then bends, flattening into a horizontal line. The GRADIENT is the acceleration, so the curve flattening is the acceleration falling — while the line itself is still rising, meaning the object is still getting faster.

Notice that terminal velocity is not a property of gravity — it is where two forces happen to balance, so anything that changes either force changes it. A heavier object needs more air resistance before the forces balance, and more air resistance means more speed, so it falls faster. A larger or flatter object meets more air resistance at any given speed, so it balances sooner and falls more slowly. This is why a feather and a hammer fall at completely different rates in air, and at exactly the same rate on the Moon, where there is no air to resist either of them.

Opening a parachute — the sequence people get wrong

  1. Before opening, the skydiver is at terminal velocity: air resistance equals weight, resultant zero, steady speed.
  2. The parachute opens, hugely increasing the surface area, so air resistance jumps to a value much greater than the weight.
  3. The resultant force is now UPWARDS, so there is an upward acceleration — which, for something moving downwards, means it slows down.
  4. As it slows, the air resistance falls again, because air resistance depends on speed.
  5. It falls until it once more equals the weight. The resultant returns to zero and the skydiver descends at a new, much lower terminal velocity — which is the point of the parachute. He does NOT stop, and he does not go upwards.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

W = m × g

W is weight in newtons (N), m is mass in kilograms (kg), g is gravitational field strength in newtons per kilogram (N/kg). On Earth g ≈ 10 N/kg unless a question states otherwise

Units: N, kg, N/kg. Rearranged: m = W ÷ g and g = W ÷ m.

Learn this definition · Terminal velocity

The constant velocity reached by a falling object when the upward air resistance has grown to equal its downward weight, so that the resultant force is zero and there is no further acceleration.

Mass against weight — the distinction examiners test every year

A. MASS is the amount of matter in an object, measured in kilograms. It is a scalar and it is the same everywhere in the universe.

B. WEIGHT is the force of gravity acting on that mass, measured in newtons. It is a vector acting downwards, and it changes with the gravitational field strength where the object is.

The stages of a fall — the sequence to reproduce

  1. At release: no air resistance, so the resultant equals the weight and the acceleration is at its maximum.
  2. As speed increases: air resistance increases and acts upwards, so the resultant force decreases.
  3. A smaller resultant on the same mass means a smaller acceleration — the object is still speeding up, but less quickly.
  4. When air resistance equals weight: the resultant is zero, the acceleration is zero, and the object falls at a constant terminal velocity.

What changes an object's terminal velocity

  • Greater weight → more air resistance is needed to balance it → higher terminal velocity
  • Greater surface area or a flatter shape → more air resistance at any given speed → lower terminal velocity
  • Denser air → more air resistance at any given speed → lower terminal velocity
  • No air at all, as on the Moon → no air resistance ever → no terminal velocity, and everything falls at the same rate whatever its mass

Model answer [4 marks]

Explain why a skydiver's acceleration decreases as she falls, even though she is still speeding up. [4]

Her weight is constant, but air resistance increases as her speed increases. The resultant force is her weight minus the air resistance, so as air resistance grows the resultant force gets smaller. Her mass does not change, so by F = m × a a smaller resultant force produces a smaller acceleration. She is still accelerating, so she is still speeding up — just at an ever-decreasing rate.

Model answer [4 marks]

A skydiver falling at terminal velocity opens her parachute. Describe and explain what happens to her motion. [4]

Opening the parachute greatly increases her surface area, so air resistance increases sharply and becomes larger than her weight. The resultant force is now upwards, so she decelerates. As she slows, air resistance decreases, until it equals her weight again. The resultant force is then zero and she falls at a new, lower terminal velocity — she does not stop.

Mark-losing trap. At terminal velocity the forces are balanced, so the object is NOT slowing down. It is falling at a steady speed.

Mark-losing trap. A decreasing acceleration still means speeding up. Only a negative resultant force makes something slow down.

Mark-losing trap. Weight is in newtons, mass in kilograms. Writing 'a weight of 70 kg' is marked wrong however good the rest of the answer is.

Mark-losing trap. A parachute gives a NEW lower terminal velocity. It never brings the skydiver to a stop in mid-air.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 · Calculate [2 marks] — Calculate the weight of a 60 kg student on Earth, where the gravitational field strength is 10 N/kg.
  2. Grade 7 · Identify [2 marks] — An astronaut travels from Earth to the Moon, where the gravitational field strength is about 1.6 N/kg. What happens to her mass and her weight?
  3. Grade 8 · Explain [4 marks] — A ball bearing is dropped into a tall tube of oil. It speeds up at first, then falls at a constant speed for the rest of the tube. Select every statement that belongs in a full-mark explanation.
  4. Grade 9 · Calculate [4 marks] — A hailstone of mass 5.0 g is falling. At one instant the air resistance acting on it is 0.021 N. Taking g as 10 N/kg, calculate its acceleration at that instant.
  5. 9+ · Analyse [5 marks] — On the Moon, an astronaut drops a hammer and a feather from the same height at the same moment. They land together. On Earth the same two objects, dropped in the same way, land many seconds apart. The Moon's gravitational field strength is about a sixth of Earth's. Select every statement that belongs in a full-mark explanation.

The people behind this science

Two ways into the same idea — the one who said heavier things fall faster, and the one who separated how much matter from how hard it is pulled. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Aristotle — the one who said heavier things fall faster

Aristotle taught that an object's speed of fall is proportional to its weight, and for two thousand years nobody seriously disputed it — because in air, with a stone and a feather, it looks exactly right. This lesson explains what he was actually observing: not gravity, but air resistance. Arguing with him is the fastest way to see why the everyday evidence is so misleading.

  • “Why were you so certain that a heavier object must fall faster?”
  • “What would you say to someone who dropped two stones of different weights together?”
  • “How much of what you saw was caused by the air rather than the falling?”
  • “What experiment would have changed your mind?”

Isaac Newton — the one who separated how much matter from how hard it is pulled

Newton was the first to treat the amount of matter in a body and the gravitational pull on it as two distinct quantities linked by the strength of the field — which is exactly what W = m × g says. Before that separation there was no way to explain how the same object could be pulled differently in different places while remaining the same object.

  • “Why is the amount of matter in an object not the same thing as its weight?”
  • “What does it mean to say gravity is stronger in one place than another?”
  • “Why does gravity give every object the same acceleration if there is no air?”
  • “How does the same law describe both a falling stone and the orbiting Moon?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against Robert Boyle in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course