# Will a heavier body achieve a higher free-fall velocity than a lighter one (of the same size)?

Jaroslav Kores, Ph.D.

I like questions that I can always get right (or always wrong but I’m an optimist).The correct answer to such a question is yes and no. If I wanted to have only one correct answer, I would have to add to the question where the body falls. In a vacuum, all objects fall with the same acceleration, so they will always have the same speed — this is because there is no other force acting on them other than gravity. We can also prove this knowledge experimentally — using Newton's tube or a slightly more financially demanding experiment on the Moon (https://www.youtube.com/watch?v=KDp1tiUsZw8).

In the real environment (typically air) other forces act on bodies. For us, these two forces are important: air resistance and buoyancy. These forces have a different origin and depend on different quantities. The buoyant force causes the body to float and is related to the volume of the body. Air resistance depends mainly on the surface of the body, its shape and on the speed. The value of the buoyant force is still the same. The drag force increases during the fall. The resulting force acting on the body is the difference between weight (pointing downwards) and air resistance with buoyancy (pointing upwards). It is worth noting that none of the forces acting against the body's motion depends on weight. We can show the effect of density in a simple example — we throw a light small ball and a heavy piece of wood into the water — the wood will float on the surface despite its higher weight but the small ball will sink. Air is 1000 times less dense than water, so the effect of buoyancy is hardly noticeable. But if we “throw” a heavy airship, filled with hydrogen/helium and a piece of wood, the heavy airship will go up and the light piece of wood will fall. Drag force is similar, it also doesn’t depend on weight — a person with a parachute has more mass than a person without a parachute but when the parachute opens, the two will move completely differently. So what makes heavier bodies fall down faster? For example, if we take 2 identical bodies, one with a mass of 1 kg and the other with a mass of 10 kg (the first is pulled to the ground by a force of about 10 N and the second by a force of about 100 N), the same forces will act on them in the opposite direction of motion — drag and buoyancy, because these forces depend on shape, area, velocity and volume, which is the same for both bodies. Let’s assume that they will have a magnitude of 2 N at a certain moment. In the case of the lighter body, the effect of the drag force on the result is 20% but for the second one only 2%. This means that the same drag force has 10 times bigger effect on the first body than on the second, heavier body. Therefore, the heavier body will fall with a greater acceleration (being pulled downward by a force equal to 98% of its weight, while the other is accelerated by a force equal to 80% of its weight). In conclusion, I will just add that in the air (and any liquid environment) an increase in the speed of a falling body will result in an increase in the drag force. This will reduce the value of the resulting force (the downward force is still the same but the force against movement increases) and therefore eventually the speed of freely falling bodies will always stabilize at a certain value — after opening the parachute, the parachutist falls downwards at a constant speed after a while. And one last addition — air resistance depends on the square of the speed, which means that a 3x increase in speed produces a 9x drag force.