[Aubs]

I'm a bit confused as to what exactly you are trying to prove. What do you mean when you say rate (you so clearly state that you do not mean accelerate, but you cannot mean velocity because by your supposed equation the velocities are different)?

In any case, I have to agree with the people above me. You cannot simply double the acceleration of the second object. If the two objects are being dropped in the same place, then acceleration due to gravity is necessarily the same for both of them. Think of the acceleration due to gravity as a constant, not a variable. You can alter the masses all you like, but acceleration must, by necessity, remain the same. This is the flaw in your reasoning.

[Samm]

Samm, on 19 December 2011 - 02:33 AM, said:

There's a formula for the force of gravity upon two objects:

,
Where:
F = the force between the masses.
G = the gravitational constant
m₁ = the first mass
m₂ = the second mass
r = the distance between either mass.

It's called Newton's Law of Universal Gravitation.

If we're talking about an object falling towards earth, we can make the mass of earth m₁ and the mass of the falling object m₂. Now it just so happens that the acceleration of an object is equal to the force on it divided by its mass (a = F/m). So that means we can divide Newton's Universal Law of Gravitation by m₂ (the mass of the falling object).
So we get:



And you'll notice that m₂, the mass of the falling object has nothing to do with its acceleration. This equation will apply on pretty much any planet, moon, object etc. In fact astronauts on the moon have performed an experiment that supports this result:

Apologies for the missing equation. For some reason I can't edit the post, so here it is:

This post has been edited by Samm: 24 December 2011 - 12:27 AM

[yash daddy]

bbouch111, on 22 November 2011 - 12:38 AM, said:

To find out if two objects fall at the same rate, you have to find their final velocity. To do this I used the equation V₂²=(V₁²)+2(a)(d). If I recorded that object 1 fell at 5 m/s and had an initial velocity of 0 and fell a distance of 30 meters then:

V₂²=(0)+2(5m/s)(30m)
V₂²=300m/s

Now say Object 2 is double the weight and has double the acceleration than Object 1 then,

V₂²=(0)+2(10m/s)(30m)
V₂²=600m/s

This clearly shows that if an object with 2x the weight falls 2x faster. This shows that all objects fall at the same RATE (not accelerate) according to their weight (not density).

But, I dont understand how?

[The french tourist]

It's quite easy to show that every objects fall at the same speed in vacuum, it doesn't need mathematics, just a bit of logic. You might know that if you take a statement and, reasoning by equivalences, you find two contradictory conclusions, then the first statement is false (in any logical system).

Well, assuming objects fall in different speeds (depending on their weighs). Let's consider one object heavier than another and with the same shape (two balls for example). It falls faster. Now let's bind the two objects with a rope. The system formed is heavier than each ball, so it must fall faster than each of them. However, during the fall, the lightest ball will fall slower, stretch the rope and slow down the heaviest ball, so the system will be slower.

Hence, we have two contradictory conclusions, me must forget or initial statement : all the objects fall at the same speed in vacuum, weight has nothing to do about it. This was the demonstration proposed by Galileo Galilei, who was probably the first modern scientist.

[engin]

• waw, this is perfect article !

[Tres Juicy]

If you have doubts about this go parachuting in a vacuum and see what happens....

[ewmon]

bbouch111, on 27 November 2011 - 09:25 PM, said:

I will fix my equations and design an experiment. I will post a revised thread when I am done. Any equations anyone suggest I use?

• F = ma
  
• v = Σa

bbouch111, on 7 December 2011 - 10:23 PM, said:

objects ... will fall a certain way at a certain speed because of their weight, density, mass, air resistance, ect, ect. ...

The object's weight is the force of gravity, which is a function of the object's mass and gravity (W = mg), and the resulting acceleration of the object is a = F/m, or here it's W/m, which gives you the original g. Thus, the object's mass gives it its force due to gravitational acceleration, yet this force acting on the same mass results in the original gravitational acceleration. The object's mass, used in both calculations, effectively cancel each other, which is what they've been trying to tell you here.

Quote

If you take two 16oz hammers that fall at the same speed ...

... and when you put these two hammers together, they drop at the same acceleration and reach the same velocity as they did separately.

Why would connecting objects make them fall faster? Why don't we see it happening in simple experiments? Why aren't these people falling five times faster than they do separately?

This post has been edited by ewmon: 2 February 2012 - 02:04 PM