Galileo's experiment and a lack of understanding....

[TwoShortPlancks]

Could anyone offer me a little help with understanding why the principles demonstrated in Galileo's (probably fictional, I know) experiment involving two spheres of the same mass from a tower don't apply in the following situation please?

As I understand it, the principle is essentially that two objects of unequal mass will accelerate under gravitational force at the same rate, unless something else (like air resistance) is acting upon them - thus the famous piece of footage of the astronaut with the hammer and the feather on the moon...

So, take two balloons, fill them both to the same diameter - one with water, one with air, then drop them. They have (essentially) the same aerodynamic properties, yet accelerate at dramatically different rates. Forgive my ignorance, but why?

 

[ZapperZ]

Could anyone offer me a little help with understanding why the principles demonstrated in Galileo's (probably fictional, I know) experiment involving two spheres of the same mass from a tower don't apply in the following situation please?

As I understand it, the principle is essentially that two objects of unequal mass will accelerate under gravitational force at the same rate, unless something else (like air resistance) is acting upon them - thus the famous piece of footage of the astronaut with the hammer and the feather on the moon...

So, take two balloons, fill them both to the same diameter - one with water, one with air, then drop them. They have (essentially) the same aerodynamic properties, yet accelerate at dramatically different rates. Forgive my ignorance, but why?

Because one has a greater force acting on it (mg) while the other has less. BOTH will have the same amount of drag force. But because the heavier one has a greater force pulling it down, the "terminal" velocity of the heavier object will be larger than the lighter one. The one filled with air will achieve its terminal velocity quicker and with a smaller magnitude.

Zz.

 

[Dale]

So, take two balloons, fill them both to the same diameter - one with water, one with air, then drop them. They have (essentially) the same aerodynamic properties, yet accelerate at dramatically different rates. Forgive my ignorance, but why?

Umm, you answered your own question:

something else (like air resistance) is acting upon them -

 

[TwoShortPlancks]

Umm, you answered your own question - "something else (like air resistance) is acting upon them" -:

So aerodynamic drag is acting upon them - sure. But to the same degree for both, surely? If aerodynamic drag is the same for both (excepting small deformations in shape I suppose, but that would not be great enough to explain the fact), how would the fact that it is acting upon them explain a different rate of acceleration?

 

[TwoShortPlancks]

Because one has a greater force acting on it (mg) while the other has less. BOTH will have the same amount of drag force. But because the heavier one has a greater force pulling it down, the "terminal" velocity of the heavier object will be larger than the lighter one. The one filled with air will achieve its terminal velocity quicker and with a smaller magnitude.

Zz.

Thanks Zapper, that makes sense.

 

[mjc123]

You are ignoring buoyancy. The force is not mg, but mg - Vρ, where V is the balloon's volume and ρ the density of the external atmosphere. In the case of the air-filled balloon, the net force is very small, and so is the acceleration a = g - Vρ/m. It is true that the heavier balloon would attain a greater terminal velocity, but that does not answer the question about the difference in acceleration.

 

[ZapperZ]

You are ignoring buoyancy. The force is not mg, but mg - Vρ, where V is the balloon's volume and ρ the density of the external atmosphere. In the case of the air-filled balloon, the net force is very small, and so is the acceleration a = g - Vρ/m. It is true that the heavier balloon would attain a greater terminal velocity, but that does not answer the question about the difference in acceleration.

You are right, I did, but the buoyancy is also the same for both, since they have the same volume and thus, the same displacement of air and can be lumped with the constant drag force. It is why for problems like this in intro physics, the free-body diagram often consists of only 2 forces.

Zz.

 

[russ_watters]

If I may add my $.02...

In experiments, scientists try their best to maximize the influence of the effect they are trying to measure and minimize other influences. In this case, it means making the force due to gravity as much larger than other forces (density, air resistance) as possible so you don't accidentally measure the effect of those other forces/effects instead of the one you want to measure.

An additional confounding factor in this experiment is distance, but it interacts with the other two: the higher you drop the objects from, the more time they have to accelerate and more time they have to move apart if their speeds toward the ground differ. When showing that objects of different masses are accelerated by gravity at the same rate, you don't want them falling far enough that they come close to their terminal velocity, and make the effect of air resistance start to matter much.