The experience of the tennis balls

In my last post, I explained how usual terms yielded a confusion in my understanding of a simple experience where tennis balls are dropped. Now, here is more information on this experience and the related explanation.

The experience in which objects of different masses fall towards the ground is considered counter-intuitive as it goes against our logic. One would tend to believe that larger is the mass of an object, more it will fall quickly. In other words, the heaviest objects reaches the ground first.

The results are however not what they seem...

First, we must understand the different forces and laws that come into the game.

Understanding gravity

As already mentioned in the previous article, gravity forces refer to the attraction of two bodies between them. Larger are the masses, stronger is their attraction. It is said that the force of gravity is proportional to the masses.

The example of the Earth is the most familiar one, and easy to understand: the Earth having a mass much larger than a human being, it attracts it very strongly (the little human also attracts Earth, but to an entirely negligible extent :p).

Moreover, the force exerted by Earth on a lighter object is always weaker than the one exerted on a heavier object. It will be said that the most massive object weighs heavier.

If we want to have fun with equations (because @lemouth, he loves equations), this can be seen as the well-known

P = mg

(the weight is equal to the mass times Earth gravitational constant) .

Let us continue with the same logic. An object twice as massive will undergo a force of gravity twice as great. Its weight will be twice larger.

Until then, that's fine. Gravity is understood pretty much... But now, let's talk a little about the speed with which these objects will fall when we let them fall towards the ground.

Newtonian physics

Before talking about speed, you have to consider acceleration.

Newton's law (called the fundamental principle of dynamics) tells us that the acceleration that an object undergoes depends both on the sum of the forces exerted on it and on its mass.

For a given mass: the greater is the force, the greater is the acceleration. And the latter is proportional to the mass.

For a given force: the bigger is the mass, the less important is the acceleration, again in a proportional way.

If I use the same force to move my tennis ball and my dumpster (no… I don’t have a dumpster in my backyard…), their movement will not be the same nor their acceleration: the dumpster being more massive, it will accelerate much less than the ball ...

Another little equation to illustrate all that?

We speak here of

F = m a

(the force is equal to the mass times the acceleration).

In summary, if we increase the force exerted on an object having a specific mass, the acceleration will be more important. If now, by exerting the same force, we take an object twice as massive, its acceleration will be twice less.

Putting everything together

Well, now it is time to get back to our beasts... or rather to our tennis balls. We recall that we undertake an experiments where two tennis balls of different masses are dropped and fall to the ground.

Here the total force exerted on each ball is simply their respective weight.

Let us assume that one ball is twice as massive as the other and let’s take the light ball as our reference. It has some acceleration due to its weight and mass.

The weight of the heavy ball is twice as large. The total force exerted on it is therefore twice as large too. On the other hand, we said above that it takes twice as much force to move it in the same way as the light ball.

Because of the forces involved, the two balls will thus accelerate in the same way. Whatever are the masses of the balls, their acceleration is identical ... and consequently, their speed.

Result: the two balls will reach the ground at the same time.

One tends to believe that since the balls "fall" on the ground, inevitably, the most massive will touch the ground first. Yet, by studying the forces that come into the game, we clearly see that this is not the case.

This can be tested. Galileo had fun doing the same from the top of the Pisa tower!

I had a lot of trouble to understand this principle. Which reassures me is that even scientists continue to experiment it. Even if several principles are now well known, many researchers believe that some deep explanations are still missing: we do not really know why this is so, but it is important that it is so.

References: 1, 2, 3, 4, 5