Do Objects Fall at the same rate according to their Weight? YES!

[bbouch111]

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).

[Mr Skeptic]

What equation did you use to calculate the accelerations, and why does your acceleration have the wrong units?

[swansont]

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

 

No, you can't just "say" that. You can't assume the answer and then show it's true. That's circular reasoning.

[bbouch111]

I am not giving circular reasoning. I don't care about how fast they accelerate, that is why I just made up two accelerations. It's and example. Sure I could get technical, but there is no reason to. I proved that objects fall at the same rate ACCORDING TO THEIR WEIGHT by finding their final velocity before they hit the ground. It's that simple.

[John Cuthber]

"I am not giving circular reasoning."

Oh yes you are.

[insane_alien]

you assume different accelerations so of course it show different accelerations. this is very circular.

[bbouch111]

No, you can't just "say" that. You can't assume the answer and then show it's true. That's circular reasoning.

 

Okay then let me put it another way,

 

Object 2 is 2x the weight of object 1 and is also observed to have the 2x acceleration of Object 1.

[John Cuthber]

Imagine I have two horses.

Say one of them can run a hundred times faster than the other. The slow one runs at 30 KM/H so the fast one runs at 3000 KM/H

 

Do you think I have proved that I have a horse that breaks the sound barrier?

 

Of course not.

The error was this bit "Say one of them can run a hundred times faster than the other."

It simply isn't true.

 

There's a similar problem in your post where you say "Now say Object 2 ... has double the acceleration than Object 1"

Just because you say it doesn't make it true.

[bbouch111]

Imagine I have two horses.

Say one of them can run a hundred times faster than the other. The slow one runs at 30 KM/H so the fast one runs at 3000 KM/H

 

Do you think I have proved that I have a horse that breaks the sound barrier?

 

Of course not.

The error was this bit "Say one of them can run a hundred times faster than the other."

It simply isn't true.

 

There's a similar problem in your post where you say "Now say Object 2 ... has double the acceleration than Object 1"

Just because you say it doesn't make it true.

 

I get exactly where you are coming from but I wasn't being unreasonable with my measurements. If one object falls at 10m/s and the other at 20m/s, that could be entirely true. But your Horse running at 3000 km/h could also be true. I was just trying to be more reasonable. 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? Because I know this is a big argument in the science community. I was using a basic acceleration equation to find the final velocity to find the rate at which the objects fall. I wanted to find the rate, not the speed or acceleration. I want to prove that all objects fall at the same rate according to their weight.

[swansont]

Okay then let me put it another way,

 

Object 2 is 2x the weight of object 1 and is also observed to have the 2x acceleration of Object 1.

 

By "observed" do you mean you have experimental results that show this? I'd like to see the video. If not, then it means nothing. I could similarly "observe" a perpetual motion machine. When you are unencumbered by nature, one can "observe" quite a lot, but we call that fiction.

[Tres Juicy]

I get exactly where you are coming from but I wasn't being unreasonable with my measurements. If one object falls at 10m/s and the other at 20m/s, that could be entirely true. But your Horse running at 3000 km/h could also be true. I was just trying to be more reasonable. 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? Because I know this is a big argument in the science community. I was using a basic acceleration equation to find the final velocity to find the rate at which the objects fall. I wanted to find the rate, not the speed or acceleration. I want to prove that all objects fall at the same rate according to their weight.

 

Acceleration due to gravity is the same regardless of weight, its things like air resistence that cause observable differences.

 

In a vacuum everything falls at the same speed

 

Try this experiment: take a marble and a hammer and drop them out of an upstairs window at the same time

[bbouch111]

Acceleration due to gravity is the same regardless of weight, its things like air resistence that cause observable differences.

 

In a vacuum everything falls at the same speed

 

Try this experiment: take a marble and a hammer and drop them out of an upstairs window at the same time

 

 

 

Yes I know that objects will accelerate at different speeds regardless of weight because of air resistance. By using this fact you can justly prove with very simple math that all objects will fall at the same RATE to their weight. What I am trying to say is that they will fall a certain way at a certain speed because of their weight, density, mass, air resistance, ect, ect. It is this relationship that gives them their individuality. If you take two 16oz hammers that fall at the same speed, those two hammers are individual objects. All objects fall at the same rate because they all have their own individual characteristics. Just like with humans, we are all the same but it is our individual characteristics that set us apart by no degree.

[swansont]

Yes I know that objects will accelerate at different speeds regardless of weight because of air resistance. By using this fact you can justly prove with very simple math that all objects will fall at the same RATE to their weight.

 

Simple, perhaps, but not correct.

[bbouch111]

Simple, perhaps, but not correct.

 

Can I have your reasoning to why I am just "not correct"?

 

 

 

[swansont]

Can I have your reasoning to why I am just "not correct"?

 

Because gravitational acceleration does not depend on the mass of the object.

[Tres Juicy]

Because gravitational acceleration does not depend on the mass of the object.

 

 

On earth at least.

 

If the earth were to encounter another earth-sized object the two would attract at higher speeds because the force of gravity from both would be combined.

 

Eg: The earth accelerates youur dropped hammer at 10m per second per second, the hammer is also to some extent attracting the earth but due to its relatively low mass this effect is negligable. Scale the hammer up to earth-size though and its attraction is increased

[swansont]

On earth at least.

 

If the earth were to encounter another earth-sized object the two would attract at higher speeds because the force of gravity from both would be combined.

 

Eg: The earth accelerates youur dropped hammer at 10m per second per second, the hammer is also to some extent attracting the earth but due to its relatively low mass this effect is negligable. Scale the hammer up to earth-size though and its attraction is increased

 

No, the forces do not combine in this way, assuming you are doing the analysis in an inertial frame of reference, e.g. the center-of-mass frame of the system, which is what we generally do. If you use the earth's surface, then yes, you have to account for its acceleration. One has to be careful about how the question and answer are framed.

[John Cuthber]

I get exactly where you are coming from but I wasn't being unreasonable with my measurements.

The problem is that you didn't make any measurements.

If you had done so you would realise that you were talking nonsense.

[Mellinia]

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).

 

If Object 2 has double the weight, why does it have double the acceleration? If you are suggesting that this is resulted from gravitational acceleration, gravitational acceleration is the same for both objects, assuming that you are doing both experiments at the same location on Earth, probably in a vacuum. Weight takes no part in your equations...

So the '2x' acceleration has to come from somewhere. Why can't I say Object 3 has the same weight as Object 1 and has double the acceleration instead?!

[Samm]

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:

 

Edited December 19, 2011 by Samm

[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]

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:

 

Edited December 24, 2011 by Samm

[yash daddy]

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 !