A question of physics

Mistermystery · Jul 1, 2004

Aeschylus said:
For every action there must be an equal and opposite reaction.

The reaction force is the force that the object exerts on the Earth.

uh... Hold on.. let's take this one step at the time:

what do we have:

- 2 objects simmilar in size, diffrent from mass. (one empty, and one full coke bottle for instance)
- A certain height. (let's say for instance 3 meters. but this can also be 50.)
- Normal air (that means no vaccuum).

right?

Now if you drop both bottles at the exact same time, under the exact same conditions (meaning that there is not external windforce on the bottles) what will happen to those bottles? I think that they hit the ground at the same time because of the wind resistance. I fail to see what action/reaction on the earth has to do with it...

Aeschylus · Jul 1, 2004

Mekkala said:
I'm still confused as to what you mean. How will the objects benefit from each others' "reaction force"? I'm not sure you understand what Newton meant when he said that.

The object's own gravity will cause the Earth to accelarte towards it by a minuscle amount.

If they are dropped at the same time and the same place, the accelartion of the Earth towards both of the objects will no longer affect which object hits the ground first.

Mekkala · Jul 1, 2004

Aeschylus said:
The object's own gravity will cause the Earth to accelarte towards it by a minuscle amount.

If they are dropped at the same time and the same place, the accelartion of the Earth towards both of the objects will no longer affect which object hits the ground first.

How so? Remember, these objects are not rigidly joined.

Aeschylus · Jul 1, 2004

Mistermystery said:
uh... Hold on.. let's take this one step at the time:

what do we have:

- 2 objects simmilar in size, diffrent from mass. (one empty, and one full coke bottle for instance)
- A certain height. (let's say for instance 3 meters. but this can also be 50.)
- Normal air (that means no vaccuum).

right?

Now if you drop both bottles at the exact same time, under the exact same conditions (meaning that there is not external windforce on the bottles) what will happen to those bottles? I think that they hit the ground at the same time because of the wind resistance. I fail to see what action/reaction on the earth has to do with it...

If both objects are dropped at the exact same time in the exact same place then the reaction force no longer affects the outcome (though relaistically it only affected the outcome by a neglible amount in the first place).

Air resistance is much more likely to affect th outcome, as I said before the main consideration is surface area. When the surface ares are eqaul we can naively assume that the force exerted by air resiatnce is equal.

The force due to gravity is larger for the heavier object, but the force due to air resiatnce on both objects are equal. This means that the constant of proportiality between the objects mass and the resultant accelartion for the heavier object will be larger, hence the resultant accelaration will be larger.

Aeschylus · Jul 1, 2004

Mekkala said:
How so? Remember, these objects are not rigidly joined.

Because it's only the resultant acelartion of the Earth that we're interested in.

Mistermystery · Jul 1, 2004

Aeschylus said:
Air resistance is much more likely to affect th outcome, as I said before the main consideration is surface area. When the surface ares are eqaul we can naively assume that the force exerted by air resiatnce is equal.

The force due to gravity is larger for the heavier object, but the force due to air resiatnce on both objects are equal. This means that the constant of proportiality between the objects mass and the resultant accelartion for the heavier object will be larger, hence the resultant accelaration will be larger.

I don't believe that. Infact I think this website says difrently:

http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3e.html

exempt:

In a previous unit, it was stated that all objects (regardless of their mass) free-fall with the same acceleration - 10 m/s/s. This particular acceleration value is so important in physics that it has its own peculiar name - the acceleration of gravity - and its own peculiar symbol - "g." But why do all objects free-fall at the same rate of acceleration regardless of their mass? Is it because they all weigh the same? ... because they all have the same gravity? ... because the air resistance is the same for each? .... <<snip>>

Objects which are said to be undergoing free-fall, are not encountering a significant force of air resistance; they are falling under the sole influence of gravity. Under such conditions, all objects will fall with the same rate of acceleration, regardless of their mass.

I think this website says the same as in my little test:both objects (if they are the same shape, but diffrent in mass) hit the ground at the same time.

Aeschylus · Jul 1, 2004

Mistermystery said:
I don't believe that. Infact I think this website says difrently:

http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/u2l3e.html

exempt:

I think this website says the same as in my little test:both objects (if they are the same shape, but diffrent in mass) hit the ground at the same time.

1) that website talks about objects in freefall, i.e. it is ignoring the affects of air resiatnce

2) It is talking about the instaneous acceleration acting on an object in freefall and not considering the affect of the objects mass on the Earth which woul affect the time taken to cover the distance from some radius r_1 to some radius r_2.

Mekkala · Jul 1, 2004

Aeschylus said:
Because it's only the resultant acelartion of the Earth that we're interested in.

Would you care to explain, in detail, what the hell you're talking about?

Mistermystery · Jul 1, 2004

Aeschylus said:
1) that website talks about objects in freefall, i.e. it is ignoring the affects of air resiatnce

Actually there is a section that discusses the parts with airresistance. And I posted a couple of exempts that say that under the circumstances that if there's air present, and if all other circumstances are equal the mass of the object does not differ.

Can you show me diffrently perhaps? If you don't believe me, do the test yourself... It shouldn't be to hard to gather the neccesairy materials...

Aeschylus · Jul 1, 2004

Mekkala said:
Would you care to explain, in detail, what the hell you're talking about?

The resultant accelartion is the vector sum of the forces acting on the Earth divided by the mass.

i.e. for the two objects falling at exactly the same time the resultant accelartion of the Earth caused by the graviational attraction of the objects is the same.

Aeschylus · Jul 1, 2004

Mistermystery said:
Actually there is a section that discusses the parts with airresistance. And I posted a couple of exempts that say that under the circumstances that if there's air present, and if all other circumstances are equal the mass of the object does not differ.

But do you agree with what has been said about the accelartion of the Earth due to the mass of the objects, this hould be an obvious result of Newton's universal law of gravitation. As the Earth accelartes faster towards the heavier object the hevaier object will hit the ground first in our simplifed model (unless of course as I've said before they are dropped at the same time and the smae place)

[/quote]Can you show me diffrently perhaps? If you don't believe me, do the test yourself... It shouldn't be to hard to gather the neccesairy materials...[/QUOTE]
Read this section right at the bottom of the page you posted, it basically illustrates what I have been saying re air resistance:

Thus, more massive object fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals the gravity force.

Ron21647 · Jul 1, 2004

The mass of the object cancels out in the equation for acceleration.

as stated above, F = G * m1 * m2 / r^2

if m1 is our object and m2 is the earth

F = m1 * a, a = F / m1

substituting,

a = G * m1 * m2 / m1 * r^2, or a = G * m2 / r^2

so the acceleration depends on the mass of the earth, but not the mass of the object.

and as someone mentioned above, the earth will also accelerate toward the object. By using the same formula, the acceleration will be very small. If you drop both objects at the same time, the earth will accelerate toward both of them, at one acceleration, and so they will hit very slightly faster, but still at the same time.

Ron

Mistermystery · Jul 1, 2004

Aeschylus said:
Read this section right at the bottom of the page you posted, it basically illustrates what I have been saying re air resistance:

Okay, but does that could for objects that have the same shape?

Aeschylus · Jul 1, 2004

Mistermystery said:
Okay, but does that could for objects that have the same shape?

Yes the example illustarted tacitly assumes thta the two objects are the same shape, you can see that it explains why heavier objects fall faster in terms of mass only.

JGMEERT · Jul 1, 2004

Mistermystery said:
Okay, but does that could for objects that have the same shape?

JM: Yes, the acceleration is equal and they will hit the ground at the same time no matter how different/same their sizes and shapes are.

Aeschylus · Jul 1, 2004

JGMEERT said:
JM: Yes, the acceleration is equal and they will hit the ground at the same time no matter how different/same their sizes and shapes are.

No, we're talking air resistance now, so that is not the case, though I imagine for short drops there would be no discerbable diffrence in the time, but there almost certainly will be if the objects have the chnace to reach their terminal velcoity.

Mistermystery · Jul 1, 2004

JGMEERT said:
JM: Yes, the acceleration is equal and they will hit the ground at the same time no matter how different/same their sizes and shapes are.

See that's what I'm kinda thinking...

Has anyone acces to a very high building and to two bottles? if we just expierement with this in an honest way we could figure out this problem by expierence...

Aeschylus · Jul 1, 2004

Mistermystery said:
See that's what I'm kinda thinking...

Has anyone acces to a very high building and to two bottles? if we just expierement with this in an honest way we could figure out this problem by expierence...

This is basic physics tho', it's not something we need to test:

1) we're not gping to detect the accelartion of the Earth as the total movemnt of the Earth in the experiment will be alot smaller than the atomic radius.

2) Our naive model of air resiatnce (as actual forces due to air resitsance are much, much more difficult to predict) is good enough to give us a qualitive answer about which one will hit the ground first

Mistermystery · Jul 1, 2004

Aeschylus said:
This is basic physics tho', it's not something we need to test:

1) we're not gping to detect the accelartion of the Earth as the total movemnt of the Earth in the experiment will be alot smaller than the atomic radius.

2) Our naive model of air resiatnce (as actual forces due to air resitsance are much, much more difficult to predict) is good enough to give us a qualitive answer about which one will hit the ground first

You must understand though that I'm not really convinced. I can clearly remember my physics things from school, and if I recall it correctly the outcome was that if the objects have the same shape, but a diffrent weight, the objects will fall to the ground in exactly the same speed, and will hit the ground in exactly the same time. Do you have any other source that might confirm your side of it?

Mekkala · Jul 1, 2004

Aeschylus said:
The resultant accelartion is the vector sum of the forces acting on the Earth divided by the mass.

i.e. for the two objects falling at exactly the same time the resultant accelartion of the Earth caused by the graviational attraction of the objects is the same.

Ok, ok. I understand now. I've been a bit confused in this thread because I forgot that the formula for gravity multiplies mass, instead of adding it

Read my freshly-edited post on page 2 for a more detailed treatment.

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