Take two identical sheets of paper. Leave one flat, crumple the other, and release them from the same height. The crumpled one will usually reach the ground first. Does Earth somehow pull more strongly on paper after crumpling it, even though its mass has not changed?
Objects fall because of Earth’s gravity. How they fall through air also depends on air resistance. Without that resistance, small objects released together at the same height, with no initial push, would fall with the same acceleration regardless of mass. To understand the difference between our sheets, we need to separate these two effects. NASA: free fall.
Gravity acts before we open our fingers
When an object rests on your palm, Earth already attracts it. It does not fall because your hand supports it: the force from the palm balances the gravitational force. Once you release it, that support disappears while Earth’s attraction remains. The object’s motion therefore starts to change. NASA: forces and changes in motion.
Gravity is the interaction through which bodies attract one another. For ordinary falls near Earth, Newton’s model describes it well. Attraction needs neither a rope nor a stream of air between the object and the planet. A vacuum removes air resistance but does not remove Earth’s gravity. NASA: gravitational force.
Our “down” means approximately towards Earth’s centre. It is a local direction related to the planet, rather than one universal bottom for the entire Universe. Someone on the other side of Earth also drops an object towards their feet, because the planet’s centre lies in a different direction for them.
The attraction is mutual: the object also attracts Earth. The forces on the two bodies have equal magnitudes, but the planet’s mass is enormously larger, so the change in its motion in this experiment is extremely small. We can conveniently treat Earth as the stationary reference for our description. NASA: what gravity does.
Falling means a changing speed
An object just released does not yet have a high downward speed. Gravity gradually increases it. Acceleration describes how velocity changes with time; it is not another name for speed itself.
For a short fall without resistance near Earth’s surface, we use an acceleration of approximately 9.8 m/s². This means the downward speed would increase by about 9.8 m/s each second, while the model remains applicable. It does not mean “9.8 metres of distance every second.” During successive equal time intervals, the object travels increasingly long distances. NASA: free-fall acceleration.
In the diagram below, the gap between the first two positions is small, and later gaps are larger. The time steps are equal. This is why increasing the height does not increase the fall time in the same proportion: the object travels the additional part of the distance at a greater speed.
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How height and time are related
Measure the distance travelled, s, downwards from the release point. With zero initial speed and constant acceleration g:
s = (g(t)^(2))/(2), v = gt.
Here t is time in seconds, s is in metres, v is the downward speed in m/s, and g = 9.8 m/s². After 0.2 s, for example, s = 0.196 m and v = 1.96 m/s. These numbers describe different things: the distance travelled and the speed at the end of the interval.
From a height h, the time to the surface in this model is t = √(2h/g). A 0.5 m drop takes about 0.32 s, and a 2 m drop about 0.64 s: four times the height gives twice the time. This is an Earth calculation without air resistance, rather than a measurement of falling paper. A constant g is a local approximation here; large heights, significant drag or an initial push require a different description. NASA: ballistic flight equations.
Why a more massive object does not win in a vacuum
You might object that Earth attracts a more massive object more strongly. Yes: the force on it is larger. But a greater mass is also harder to accelerate. In this model, gravitational force and mass increase in the same proportion: double the mass and Earth’s pull doubles too, leaving the acceleration unchanged.
Matching conditions therefore matter. The feather and ball must be near one another, released at the same time and height, with the same initial velocity. Throw one ball downwards and simply release the other, and they need not land together, even though gravity accelerates them equally. NASA: mass and free fall.
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Where did mass go in the calculation?
In Newton’s description for constant mass, the net force F and acceleration a are related by F = ma. Near the surface, the gravitational force is F_(grav) = mg. If it is the only force acting, then:
a = (F_(grav))/(m) = (mg)/(m) = g.
The mass m cancels. This shows how the model reproduces equal acceleration; it does not mean mass has no effect on forces. Once another force, such as air resistance, is added, we can no longer substitute mg alone for the entire net force. NASA: the second law of motion, gravitational force.
Gravity remains; the conditions change
Without air resistance
A ball and a feather are released together from rest. After the same time they have descended the same distance. The snapshots show both objects every 0.1 s.
| Time, s | Distance down, m | Speed, m/s |
|---|---|---|
| 0 | 0 | 0 |
| 0.1 | 0.049 | 0.98 |
| 0.2 | 0.196 | 1.96 |
| 0.3 | 0.441 | 2.94 |
In air
Two identical sheets: one flat, one crumpled. Their masses are equal, but their shapes and interaction with air differ. Their motion can therefore differ.
Gravity acts downwards
Drag opposes motion relative to air
For vertical descent through still air, drag points upwards. Arrow lengths are illustrative; no paper fall time is calculated here.
Air brings shape back into the problem
Return to the paper. As it falls, it moves relative to the air and makes the air flow around its surface. Air resistance, or drag, opposes that relative motion. For vertical descent through still air, it points upwards, opposing the downward motion.
Drag depends on speed, air density, and the object’s shape, size and orientation. A flat sheet and crumpled paper interact differently with the flow. The sheet can also sway and turn over. Mass alone is therefore insufficient to predict their exact fall times. NASA: what drag depends on.
Crumpling does not “switch on” extra gravity. It changes the shape and thus the effect of air. That makes this example more useful than a rule saying “heavy objects fall faster”: the sheets can have equal masses but different motion.
Test the reasoning in your mind: what happens to the crumpled paper’s advantage if we remove the air and keep the release conditions identical? In our vacuum model, it disappears. Without different air resistance, shape does not give one sheet a different acceleration.
On the Moon, a hammer and feather tested the idea
During Apollo 15 in 1971, David Scott simultaneously released a hammer and a feather above the lunar surface. With virtually no air resistance there, both fell together, within the accuracy of their release and observation. NASA preserves the demonstration’s description and video. NASA: Apollo 15’s hammer and feather.
The lunar experiment illustrates a useful distinction: remove the effect of air and falling remains. Gravity does not need an atmosphere. The video nevertheless does not promise that any two real objects will move identically under any circumstances: the comparison’s conditions matter.
Opening your fingers removes the support of your hand, while Earth’s gravity changes the object’s motion. Air can substantially alter that fall and make shape matter. To explain which object reaches the floor first, ask both “what is its mass?” and “what are the initial conditions, and which forces act?”
The same attraction connects bodies in the Solar System. Next in the course, we will explore why Earth’s gravity does not make the Moon crash into the planet’s surface.