Does the density of a body affect the rate of fall?

If I inflate a balloon in the open air 1. with helium 2. with outside air 3. fill with water, which of the 3 balloons will hit the ground first (all balloons are inflated to the same size)? This one filled with water. The one with helium will rise and the one with air will slowly whirl down.

I repeat this experiment with a (drink) can instead of a balloon. Which can will hit the ground first? Does the full can with water touch the ground first, as with the balloon, and then the empty can? Shouldn’t one take into account a 3rd force when describing falling objects, apart from gravity and air resistance (in connection with the density of the body in relation to that of air)?

If you drop 2 equal sized marbles outdoors, one made of iron and one made of plastic, will the iron one hit the ground first because it has a higher density?

Asker: Martin, 20 years

Answer

Dear Martin,

You are right: we need to consider (in some cases) 3 forces.

– Gravity makes sure that, ideally, every object falls at the same speed. Indeed, a truck falls as fast as a feather… ideally. On the one hand, an object with more mass will experience a stronger gravity. On the other hand, that force will have to act on more mass (it is more difficult to move a truck than a spring). These effects counteract each other and ensure that the mass has no influence on the fall speed. In practice, we know that this is not true. So we need to introduce another effect.

– The air resistance ensures that large and light objects are less likely to fall than others. A bowling ball and a soccer ball of the same shape will encounter the same amount of resistance. With a football, however, this resistance will have a much greater effect because there is less mass on which this force acts. The following applies here: lighter objects fall more slowly. However, this cannot fully explain your experiment with the balloons.

– The Archimedes force is an upward force that is caused here by the air that is under the object. A balloon is attracted to the earth, but so is the air under that balloon! A balloon filled with water will of course win the battle here, as it can overcome the Archimedes force caused by the air. The following applies here: objects with a higher density fall faster. If the density is less than that of air, the balloon does not even fall at all, but rises: that is what happens with a balloon filled with helium.

These three forces are always present in practice. An iron marble will therefore fall faster than one made of plastic, due to both the air resistance and the Archimedes force. A can filled with helium will also fall slower than a can filled with air, but you may not notice it. The gravity here is so strong compared to the other two forces, that the difference between the two cans is negligible. For example, you might wonder what the influence of the Earth’s magnetic field or the position of the moon is on the fall speed. Thousands of forces act on every object on Earth, but a good scientist selects the right forces that are important for each specific case.

Does the density of a body affect the rate of fall?

Answered by

dr. ir. Jan Ronge

Bio-engineer. Electrocatalysis and renewable hydrogen production

Catholic University of Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/

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