Do heavier objects fall faster? Free fall and air resistance

Take a book and a scrap of paper and drop them at the same moment. The book hits the floor; the paper drifts and flutters down. The result seems clear: the heavier one falls faster. But is that really so? For centuries people thought it was; then a thought experiment, a few measurements and a demonstration on the surface of the Moon showed why the idea is incomplete. In this post we tell the story, the physics and an experiment you can do safely at home.

What did Aristotle think?

In the physics of the ancient Greek philosopher Aristotle, heavier objects fell faster; the speed of fall was proportional to the object’s weight. According to him, motion also depended on the “density” of the medium an object moves through. This idea matched everyday observation (a stone falls faster than a leaf) and was taught for centuries.

Galileo’s thought experiment

In his Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the Italian scientist Galileo Galilei described a thought experiment showing that Aristotle’s view contradicts itself. Think of it like this: there is a heavy stone and a light stone. According to Aristotle the heavy one falls fast and the light one falls slowly. Now tie the two together with a string. The light stone should slow the heavy one, so the tied pair should fall more slowly than the heavy stone alone. But the tied pair is also a heavier object, so it should fall faster than the heavy stone. The two results cancel each other. The only way out of the contradiction is for everything to fall at the same rate.

The story of him dropping cannonballs from the Leaning Tower of Pisa is well known. But there is no evidence for it in Galileo’s own writings; it comes from a biography written years later by his student Vincenzo Viviani, and historians do not take the event as real. What is well documented is Galileo’s measurements with balls rolling down inclined planes; because the ball moved slowly, it was possible to measure the time.

Air resistance enters the picture

So why does paper fall more slowly than a book in daily life? The answer is air resistance. Two forces act on a falling object:

• Weight (downward): $F = m \cdot g$. Here $g$ is the acceleration due to gravity, about 9.8 m/s² at Earth’s surface.
• Air resistance (upward): It grows with speed, and it also depends on the object’s shape and surface area.

By Newton’s second law, acceleration is the net force divided by the mass. If only weight acted: $a = \frac{m \cdot g}{m} = g$. The mass cancels; every object falls with the same acceleration. This is the reason “heavier objects do not fall faster”: a larger force acts on a larger mass, but that force has to accelerate that larger mass.

Air resistance spoils the pattern. For a wide, light sheet of paper, the resistance is very large compared with the weight and quickly reduces the net force; the paper falls slowly. For a compact stone, the resistance is small next to the weight, and the stone moves almost like “free fall”. So the hidden factor is not mass but the ratio of air resistance to weight. Given enough height, the resistance becomes equal to the weight and the object reaches a steady speed (terminal velocity); this speed depends on both shape and surface area and on the object’s weight: for the same shape, a heavier object must reach a higher speed before the resistance equals its weight, so it falls faster.

A small nuance: looked at very precisely, a heavier object pulls Earth very slightly towards itself. For everyday objects this effect is negligible.

Falling in a vacuum: the Apollo 15 hammer-and-feather drop

What happens if we find a place without air resistance? On 2 August 1971, David Scott, commander of Apollo 15, let go of a hammer and a feather at the same moment on the surface of the Moon. The Moon has almost no atmosphere. The hammer and the feather fell side by side and reached the surface at the same time. According to NASA records, the hammer’s mass was about 1.32 kg and the feather’s about 0.03 kg. The footage sits in NASA’s archives for anyone to watch. Two objects with very different masses fell with the same acceleration.

The physicist Brian Cox dropped an object and feathers at the same moment in a vacuum chamber at NASA’s Space Power Facility for the 2014 BBC documentary Human Universe.

Try it at home: paper and a book

A safe and cheap experiment. Drop objects from no higher than table height, over a flat, clear area of floor, with nobody nearby.

1. Take a book and a piece of paper slightly smaller than the book’s cover.
2. Predict: If you lay the paper flat on top of the book and drop the book, what happens to the paper?
3. Drop the book held flat. The paper falls together with the book: the book pushes the air in front of it aside, and the paper, sitting just above the book, hardly meets the air at all.
4. Now crumple one of two identical sheets into a ball and leave the other flat. Drop both from the same height. The crumpled ball falls noticeably faster. The mass is the same, the shape is different: the difference comes from air resistance.
5. Drop the paper ball together with the book as well and compare.

If you do this experiment with the predict-observe-explain method, writing the prediction first and asking for a reason strengthens learning. Safety: drop hard objects like the book so that they cannot land on your foot, and never drop anything near other people, from a balcony or from a staircase.

Why does this idea matter?

Free fall is the foundation of the topic of force and motion. To understand how an object’s acceleration depends on net force and mass, see our balanced and unbalanced forces lesson, and to see that air applies a kind of friction against motion, see our friction force lesson. You can find similar misconceptions in other science topics in our misconceptions post.

Summary

• Aristotle said heavier objects fall faster; Galileo showed with a thought experiment that this view contradicts itself.
• Without air, all objects fall with the same acceleration ($a = g$); the mass cancels.
• In daily life the difference comes from air resistance, and what decides the fall is the ratio of air resistance to weight; the resistance depends on shape and surface area.
• On the Moon during Apollo 15 a hammer and a feather fell together; you can see it on a small scale at home with paper and a book.