Ciencias

Why a Heavy Object Falls No Faster Than a Light One

Twice the weight means twice the mass to move, so the two cancel: a = mg/m = g. Apollo 15 proved it with a hammer and a feather. Then air changes things.

Respuesta breve

Why does a heavy object fall at the same speed as a light one?

Because the extra weight pulling a heavy object down is exactly cancelled by the extra mass resisting that pull. In a vacuum everything accelerates at the same 9.8 m/s²; in air, shape decides.

La respuesta corta
A heavier object is pulled down harder, but it also has more mass to accelerate, and the two increases cancel exactly. Newton's second law gives a = F/m = mg/m = g, so mass drops out and everything falls at about 9.8 m/s² in a vacuum. Air resistance is what breaks the tie in practice.

Qué cambia la respuesta

Whether there is air: in a vacuum a hammer and a feather land together, and on the Moon in 1971 they did.
The shape and surface area rather than the weight — a sheet of paper flutters down, and the same sheet crumpled into a ball falls almost like a stone.
How far the object falls, because over a short drop air resistance barely matters and over a long one both objects settle at a terminal velocity that does depend on mass and shape.
Whether the object is dense enough for buoyancy to be ignored, since a helium balloon does not fall at all.

Two effects that cancel exactly

The intuition that heavy things fall faster is not stupid; it is half of a correct argument. Gravity does pull harder on a heavier object: a 10 kg mass weighs about 98 N and a 1 kg mass about 9.8 N, so the force on the heavier one is ten times greater. That much is true.

The half left out is that force does not determine acceleration on its own. Newton's second law says a = F ÷ m, and the heavier object has ten times the mass to shift as well as ten times the force shifting it. The force is the weight, W = mg, so a = mg ÷ m = g. The mass appears top and bottom and cancels completely.

Doubling the mass doubles the pull and doubles the resistance to being accelerated, in exactly the same proportion. That is why the answer comes out independent of mass — not approximately, but exactly, and it is the reason g is quoted as a single number for everything.

Galileo's argument, which needed no apparatus at all

Before any of this could be measured, Galileo demolished the heavier-falls-faster idea with nothing but reasoning, and the argument is still the most elegant thing in the topic.

Suppose heavy objects really do fall faster. Tie a heavy stone to a light one and drop the pair. The light stone falls more slowly, so it should hold the heavy one back and the combination should fall slower than the heavy stone alone. But the two together are heavier than the heavy stone by itself, so the same assumption says they should fall faster.

One assumption, two contradictory predictions: the assumption is wrong. No tower, no timing device, no experiment. It is worth showing students because it demonstrates that a physical claim can sometimes be tested for consistency before it is tested with equipment.

The demonstration on the Moon, 1971

At the end of the last Apollo 15 moonwalk, Commander David Scott held out a 1.32 kg aluminium geological hammer in one hand and a 0.03 kg falcon feather in the other, released them together from a height of about 1.6 m, and let the television cameras watch. They struck the surface at the same moment.

The hammer is roughly forty times the mass of the feather. On Earth this experiment does not work, and everybody knows it does not, which is exactly why the intuition persists. On the Moon it works, because there is no air to resist the feather.

One detail is worth checking with a calculator. Lunar gravity is about 1.62 m/s², so t = √(2h ÷ g) gives √(3.2 ÷ 1.62), roughly 1.4 seconds for that 1.6 m drop, against about 0.57 s on Earth. The two objects agreed with each other and both took nearly two and a half times as long as they would have here.

Where the rule stops holding: air

In air a second force acts upwards on the falling object, and it does not obey the same cancellation. Air resistance depends on speed, on cross-sectional area and on shape — and not on mass at all. That is why the neat result breaks.

The demonstration to run is a sheet of A4 paper against the same sheet crumpled into a ball. The mass is identical to the milligram. Dropped together, the ball reaches the floor while the flat sheet is still drifting. Nothing about the weight changed; only the area presented to the air did.

Drag also builds with speed until it equals the weight, and at that point the resultant force is zero, acceleration stops, and the object continues at a constant terminal velocity. A lighter object reaches that balance at a lower speed, because there is less weight for the drag to match. A skydiver falling flat reaches roughly 55 m/s, about 200 km/h; the same skydiver head-down goes considerably faster, and under an open parachute drops to a few metres per second — all at one body mass.

What the velocity–time graph shows

Almost every exam question on this topic is a velocity–time graph in disguise, and the graph tells the whole story if you can read the gradient.

At the instant of release the only force is weight, so the acceleration is the full 9.8 m/s² and the line is steepest. As speed builds, drag builds with it, the resultant shrinks, and the gradient gets shallower — the object is still speeding up, but by less each second. When drag equals weight the resultant is zero, the gradient is zero, and the line runs flat at terminal velocity.

Open a parachute and the area jumps, so drag suddenly exceeds weight. The resultant force now points upwards and the skydiver decelerates: the line drops steeply, then levels off at a new, much lower terminal velocity. Naming the forces at each of those four stages is what the marks are for, and the step most candidates miss is that a falling gradient still means speeding up.

Mass of the aluminium geological hammer dropped on the Moon, against 0.03 kg for the falcon feather: 1.32 kgMass of the aluminium geological hammer dropped on the Moon, against 0.03 kg for the falcon feather[1]
Acceleration of any object in free fall near the Earth's surface, whatever its mass: 9.8 m/s²Acceleration of any object in free fall near the Earth's surface, whatever its mass

Preguntas frecuentes

So does a hammer really fall at the same rate as a feather on Earth?

It would, if there were no air. In air it does not, and that is not a failure of the rule but the presence of a second force. Drop the same experiment in a vacuum tube, as physics departments do routinely with a coin and a feather, and the two land together every time.

Does terminal velocity depend on mass?

Yes, and this is where the answer flips. Terminal velocity is reached when drag equals weight, so a heavier object of the same shape needs more drag to balance it, and therefore has to be going faster before it stops accelerating. Heavier objects genuinely do fall faster in air over long drops — just not for the reason people assume.

Is g the same everywhere on Earth?

Very nearly, but not exactly. It is slightly smaller at the equator than at the poles, because of the Earth's rotation and its shape, and it decreases with altitude. School work uses 9.8 m/s² throughout, and some boards use 10 m/s² to simplify arithmetic — check which value your specification expects.

Why does a bowling ball beat a beach ball then?

Because they are the same size but wildly different masses. Both meet a similar amount of air resistance, but the beach ball has far less weight to overcome it, so it reaches terminal velocity almost immediately while the bowling ball is still accelerating hard. Match the masses or remove the air and the difference vanishes.

Fuentes

Apollo 15 Hammer-Feather Drop — NASA Space Science Data Coordinated Archive

Última actualización 21 de agosto de 2026