Simple physics question

You may join the ranks of the people who laughed at Galileo.

He postulated, to much derision from his peers, that two objects with the same mass should take the same amount of time to fall from an equal height to the ground.

As it turns out, he was right.

The gravity of the earth acts to accelerate almost (a non-measurable difference) equally any two objects of small enough mass as compared to that of the earth.

This is most dramatically demonstrated in that, on the moon, a hammer and a feather fall to the ground in the exact same amount of time. Spooky, huh?

Cheers,
Twilight Dragon

a ball of 5kg, and a ball of 500kg fall to the ground in the same time ?
is a non-measurable difference in earth ?

Silly: Try it out right now. Take two soda bottles, fill one with water and leave the other one empty, and cap both. Drop them off something high (try it a few times). Then come back and report your results. Most of us did the same experiment (probably with different objects) in elementary school, but if you haven't, it's surprisingly fun. I"m not joking about that. [grin]

Gravity accelerates all objects at a rate of 32 feet/second every second or 9.8 meters/second/second.

The reason many people think lighter objects drop more slowly comes from exprerience with dry leaves, feathers, and pieces of paper. Unfortunately, all of these are highly affected by aerodynamics. In a vacuum, each of those objects would drop at the same rate as a bowling ball.

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Original post by Sneftel Silly: Try it out right now. Take two plastic soda bottles, ... [grin]

Anyway, for the mathematical explanation: the force of gravity between two objects is given by the following equation (thanks to Newton, no thanks to "intelligent falling"):

    F = Gm<sub>0</sub>m<sub>1</sub> / r<sup>2</sup> 

G is the "gravitational constant", m₀ and m₁ are the objects that are attracting each other. So, lets say we are dropping an object. The force due to gravity is determined by the mass of the Earth (let's make that m₀) and the mass of the object (let's make that m₁). Now, the acceleration of an object is given by this equation (also thanks to Newton):

    F = ma, or a = F / m 

So, what is the acceleration of our falling object?

    a = (Gm<sub>0</sub>m<sub>1</sub> / r<sup>2</sup>) / m<sub>1</sub>    a = Gm<sub>0</sub> / r<sup>2</sup> 

As you can see mass of the falling object cancels out, so it has no effect on its acceleration. On the surface of the Earth, the acceleration due to gravity is 9.8 m/s², regardless of the mass of the falling object.

[Edited by - JohnBolton on October 11, 2005 1:43:09 PM]

Quote:

Original post by JohnBolton Take two plastic soda bottles

Sissy. Don't you care about SCIENCE?

Quote:

Original post by Sneftel Quote: Original post by JohnBolton Take two plastic soda bottles Sissy. Don't you care about SCIENCE?

Empirical tests have shown, that a thick recyclable 1.5 liter plastic bottle, containing vodka and coke, dropped at height of about 180cm, may break; and should it do so, the event is usually followed by a lot of harsh language.

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Original post by Silly_con a ball of 5kg, and a ball of 500kg fall to the ground in the same time ? is a non-measurable difference in earth ?

Earth weight is 5.974 × 10^24 kg different just 450 kg is about 1 in 10^22

If your time for object to reach the ground is 10 second

So, you need be super man to tell different in 10^-21 of second that is about 10^-12 nanosecond =.="

Thanks, I've understood now, but if the volume of one object is bigger than the other, and his mass bigger too, why the two objects fall to the ground in the same time (in havok-reactor case) ? this seems very unrealistic.

Other engines do the same ? like havok realtime, novodex, meqon, newton ...

Yes, it will fall same if there is no other forces such as air drag.
It is not unrealistic, it's just how it happens in absense of air. I think that in good physics engine you can specify air drag coefficients for objects, if you are interested in simulating the drag. This is why in real world things that have big drag (for same mass) fall slower.

also I can probably answer other possible question...
I remember some thing in the school: almost everyone in the class(except me [grin]) believed that in this setup A will hit ground much sooner than B

     (A)      (B)----->with horisontal velocity around few tens meters per second.      .            .       .               .       .                 .________________________________________floor

(height is few meters, experiment is done in the room)
A is just dropped and B is thrown horisontally. no air drag.
Indeed if B has velocity of few kilometers per second, and floor is not flat, it could be correct (B would orbit the Earth a bit), but for meters per second difference will be practically inmeasurable.

Also keep in mind that, for the majority of solids, air drag is negligible and you can discount it. A physics engine might calculate for it in specialized cases, but it's much more efficient not to.

Yes. Try dropping 1kg and 10kg from height of few meters, in the real world. Heck, you wouldn't even notice difference between 1kg and many tons.

Dmytry, your example of the the object with horizontal velocity falling at the same speed as the object without horizontal velocity reminds me of a cool physics demonstration in High School. The teacher hung a stuffed monkey on a pole and put a steel ball on a metal track at the same height about 4 or 5 feet away. When she set the ball rolling down the track it tripped an electronic switch as it flew off the end of the track that caused the stuffed monkey to be dropped, and the steel ball hit the monkey in mid-air.