# DO objects fall at the same speed? NO!

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know that objects with the same surface area but different densities fall at the same speed in a vacuum.

However, there is actually a big argument between me and my girlfriend, at the point of I feel like strangling her to death.

I say heavier objects do fall faster (I provided calculations). She (appears) to think that this is nonsense and am full-of-shit and she knows better because she knows more about the topic and am just a uni student (She was my lecturer, before we started dating. Now shes just my bitch)

I dropped a piece of paper, and a piece of cardboard with similar SA. The cardboard fell much faster.

I could explain this by stating that heavier objects have more force to 'push' air molecules out of the way.

In other words, heavier objects are not as affected by air resistance.

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Objects falling in a vacuume accelerate at the same rate and therefore the same speed if they start at the same height.

Objects with the same air resistance (two identically dimentioned hard spheres for example) fall at the same rate.

This was first postulated by someone who's name I forget with the hammer and feather off of the leaning tower of piza or so the story says, when apollo 11(?) landed on the moon they tested the idea and they indeed fell at the same rate.

The important formula for this is:

$g = \frac{GM}{r^2}$

Where G is the gravitational constant, M is the body enacting the gravity (so earth or moon) and r is the distance between the centre of the two objects.

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Objects falling in a vacuume accelerate at the same rate and therefore the same speed if they start at the same height.

Objects with the same air resistance (two identically dimentioned hard spheres for example) fall at the same rate.

This was first postulated by someone who's name I forget with the hammer and feather off of the leaning tower of piza or so the story says' date=' when apollo 11(?) landed on the moon they tested the idea and they indeed fell at the same rate.

The important formula for this is:

[math'] g = \frac{GM}{r^2}[/math]

Where G is the gravitational constant, M is the body enacting the gravity (so earth or moon) and r is the distance between the centre of the two objects.

You're just as bad as her. They don't try it!

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Of course they don't. Objects of different densities have different bouyancies in the air. Drop a helium balloon and a rock shaped like a balloon. Also, as you say, there is air resistance, which is dependant on shape and is proportional to speed, and works against gravity, which is constant for the object's weight at a given altitude. Thus it can fall only as fast as the equilibrium between these forces, which is obviously greater the more weight (and less surface area) the object has. However, before this maximum speed is reached, the effect is barely noticeable with similar objects, like a wooden sphere and a metal sphere, which is what Galileo was demonstrating, that unhindered acceleration is not proportional to weight but is equal.

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further, even in a vacuum there are differences.

If you have a feather and an iron weight, in no atmosphere, falling toward a planet surface, the two will appear to fall at the same rate. This is because the difference in the mass of the two is insignificant compared to their mass-difference relative to the planet. Nevertheless, the iron weight has more mass and thus more gravity, and therefor the planet and the iron will approach each other more rapidly than the planet and the feather. The thing is, because the iron contributes an amount of gravitational, attractive force that is extremely tiny compared to the attractive force of the much more massive planet, the difference in the rates (feather vs iron weight) will be too small to measure without extremely precise and accurate tools.

So, to conclude, there is a difference in the rate of fall between two objects of similar size but different mass, whether they fall in an atmosphere (where the difference can be very obvious) or in a vacuum (where, in the case of two objects of different mass falling toward a much, much larger body, like a planet, the difference is extremely difficult to detect.

However, the attractive force of the planet (just the planets attractive force) on the two objects is , the same. In a vacuum, there is only a difference because the more massive falling object is also exerting a pull. If you take two objects of different mass and somehow prevent them from exerting a gravitational pull on the planet they are falling toward (in a vacuum), then there is no difference. This is because while there is more mass for the planet to pull on, in the more massive falling object than in the less massive falling object, the more massive falling object also has a greater resistence to a change in velocity, due to it's larger mass/greater inertia.

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oh dear, please ignoring air resistance (yes that includes "lighter than air" things) then they fall at the same rate.

You can argue against it as much as you want but you're wrong.

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If the acceleration is different for "heavier" objects, than the definition of heavy comes into question.

weight = mass x acceleration due to gravity

If acceleration due to gravity were variable you could argue that all objects on Earth had the same mass but only weighed more because their acceleration was different.

That of course wouldn't make sense. Acceleration due to gravity is the constant.

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Its new years eve, I'm home sick with a head cold and chills, I can't go out, so I come here for a look.

Then, I see it appears he's been banned yet again before I got a chance to tell him his girlfriend was correct about....well.......everything she said to him.

But.....I do find him entertaining. Forgive me....I'm sick.

Bettina

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oh dear' date=' please ignoring air resistance (yes that includes "lighter than air" things) then they fall at the same rate.

You can argue against it as much as you want but you're wrong.[/quote']

I'm going to regret delving into phisics, as my brain will no doubt bleed, but... you are talking about in a vacume, yes?

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Say we have two objects, object A and B. Object A is heavier than B.

We tie them together using a length of rope.

Let the tied body fall. What should be its speed?

If we assume that heavier objects fall faster:

From one point of view, the object now weighs A+B, so it should be faster than either the individual A or B when dropped. (A+B>A)

Well, from another point of view, A will fall faster than B because it is heavier, and B will therefore pull A UPWARDS because of its slow falling speed. We achieve an apparent weight of A-B this way, and the speed of the entire object will be SLOWER than either the individual A or B when dropped. (A-B<A)

Two completely opposite answers. Hmm...What's wrong?

Iunno, you tell me.

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I'm going to regret delving into phisics, as my brain will no doubt bleed, but... you are talking about in a vacume, yes?

Yes, else you have to take their aerodynamical properties into account, including density and it can be shown that a lighter object falls faster than a heavier one in air.... i.e. a piece of paper and a hair...

Everyone in physics knows that an ok aproximation at near earch surface fro the acceleration of gravity is 9.81ms-2 If two things are accelerating at the same rate then if they both start accelerating at the same time they must be going the same speed, ignoreing any outside effect which would alter that acceleration...

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will they reach the same maximum speed due to gravity in a vaccume, reguardless of mass?

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will they reach the same maximum speed due to gravity in a vaccume, reguardless of mass?

There's nothing acting on them to limit the speed, so yes.

cheers

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Why are you arguing about falling in a vacuum? The first post made it clear that that was a given. The question is about falling through air, for which both density and aerodynamic properties most definitely affect the outcome.

Obviously we have to take hindrances into account. Acceleration due to gravity is NOT constant, because I'm an object, and I'm not accelerating due to gravity at all, although it's certainly acting on me. The resistive force of the floor is countering it. What we CAN say is that the FORCE of gravity acting on an object is proportional to its mass, which means that UNHINDERED, acceleration will be constant. That was the original question, and he's right, as any experience at all could confirm.

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know that objects with the same surface area but different densities fall at the same speed in a vacuum.

However' date=' there is actually a big argument between me and my girlfriend, at the point of I feel like strangling her to death.

I say heavier objects do fall faster (I provided calculations). She (appears) to think that this is nonsense and am full-of-shit and she knows better because she knows more about the topic and am just a uni student (She was my lecturer, before we started dating. Now shes just my bitch)

I dropped a piece of paper, and a piece of cardboard with similar SA. The cardboard fell much faster.

I could explain this by stating that heavier objects have more force to 'push' air molecules out of the way.

In other words, heavier objects are not as affected by air resistance.[/quote']

Ummm, nope. You can easily get a heavier object to fall more slowly by using the atmosphere to slow it down. For example, a small pebble would fall more quickly than a brick in a parachute.

So things fall at different speeds in atmosphere not because of their mass, but because of their areodynamics (of which mass can be a factor, but not necessarly the deciding one).

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I say heavier objects do fall faster (I provided calculations). She (appears) to think that this is nonsense and am full-of-shit.

Her conclusion is perfectly correct!

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The op has a point, albeit a trivial one. The statement that all objects fall at the same speed assumes that the object(s) in question have a negligable mass compared to the earth so that the earth can be assumed not to fall toward the object(s). I don't think the op realizes that the discrepency is so small for comman objects (say a hammer and a feather) that no experiment could even theoretically distingish between them. (Pretty sure you'd run afoul of quantum uncertainty.)

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']Ummm' date=' nope. You can easily get a heavier object to fall more slowly by using the atmosphere to slow it down. For example, a small pebble would fall more quickly than a brick in a parachute.

So things fall at different speeds in atmosphere not because of their mass, but because of their areodynamics (of which mass can be a factor, but not necessarly the deciding one).[/quote']

But he was talking about similar aerodynamics and different masses, and he's correct. A brick with a parachute will fall a lot slower than a brick-shaped hunk of neutronium with the same parachute, because the gravitational force is proportional to mass, but air resistance depends only on shape and speed. Terminal velocity occurs when gravitational force and air resistance become equal. With two differently massed objects of identical shape, the heavier one will have a higher terminal velocity.

And, like I said before, there is also bouyancy, which plays a noticable role in objects of very different densities. A 1 foot sphere of lead will fall through a vacuum with exactly the same acceleration as a 1 foot helium balloon, but the result is rather different in the atmosphere!

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In the "perfect physics world" with no air resistance, objects regardless of mass or size will fall at the same rate under gravitional pressure. But as Ali Algebra have paper and cardboard with the same surface area, obviously air resistance have a part in it. Paper is not heavy enough to go go straight down, it would "fly". Therefore, the outcome with air resistance will be different. It is just that heavier objects are less affected than lighter objects.

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Its new years eve' date=' I'm home sick with a head cold and chills, I can't go out, so I come here for a look.

Then, I see it appears he's been banned yet again before I got a chance to tell him his girlfriend was correct about....well.......[i']everything[/i] she said to him.

Being a skeptic I doubt the girlfriend story to begin with

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Of course they don't. Objects of different densities have different bouyancies in the air. Drop a helium balloon and a rock shaped like a balloon. Also, as you say, there is air resistance, which is dependant on shape and is proportional to speed, and works against gravity, which is constant for the object's weight at a given altitude. Thus it can fall only as fast as the equilibrium between these forces, which is obviously greater the more weight (and less surface area) the object has. However, before this maximum speed is reached, the effect is barely noticeable with similar objects, like a wooden sphere and a metal sphere, which is what Galileo was demonstrating, that unhindered[/i'] acceleration is not proportional to weight but is equal.

proportional to speed squared

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So if i dropped the sun from a height of say ... 20m, it was fall to Earth at the same rate a chicken would? (Excluding air resistance)

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You'd have to take into account the acceleration of the earth towards the sun aswell as the sun towards the earth... I think....

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The piece of paper mentioned in Ali Algebra's experiment seemed to fall at a lesser speed than the cardboard because it reached it's state of equilibrium faster. It is was accelerating at the same rate, however, it stopped accelerating sooner because the net force equaled zero, and the air molecules that were causing resistance equaled the amount of mass in the paper sooner than in the cardboard.

acceleration = Fnet/mass = weight-resistance/mass

If his experiment was in a vacuum, they would have fallen at the same rate, but the experiment he used to justify his theory was not in a vacuum.

I hope I explained this well enough, but I just finished physics and did not commit all of it to memory. Thank goodness for notebooks.