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No, it depends on the actual mass, aswell as density.
Drop a hammer and a feather at the same time and ask yourself;
i) Which item reached its terminal velocity first.
and
ii) What the magnitude of the terminal velocity is.
Now repeat with two feathers of equal density; one small one, and one very large one. You will find again that the Terminal V's are different.
I have not ignored the nature of the medium through which they are falling, though assumed it is not a vacuum.
I don't think it's quite that simple.
If an object is falling it is doing so because of gravitational pull - the net result of the different effect of the relative masses - exerted on the object by the larger one to which the smaller one is falling. On this much I think we are all agreed.
In a vacuum, therefore, the rate of acceleration increases inexorably. There is no terminal velocity, except that at which the smaller object eventually hits the larger mass (or should I say, at which the two objects collide?).
In a gaseous medium, such as a planetary atmosphere, the resistance to the motion of a falling object increases with both increasing atmospheric density and increasing speed. Measured over a short distance, after having reached its terminal velocity, one might record a constant speed for the object. But measured over a great distance one would surely find a small but continuous change in the so-called terminal velocity of a falling object as it continues to experience increasing gravitational pull against increasing resistance due to the increasing density of the atmosphere. I imagine that in one set of circumstances the falling object's terminal speed might gradually increase (eg above the surface of a large planet with a thin atmosphere), and in another that it might gradually decrease (eg above the surface of a small planet with a thick or more dense atmosphere).
This being so - and I've convinced at least myself that it is - I wonder what happens in our Earth's case? Has any advanced mathematician done the necessary calculattions?
If an object is falling it is doing so because of gravitational pull - the net result of the different effect of the relative masses - exerted on the object by the larger one to which the smaller one is falling. On this much I think we are all agreed.
In a vacuum, therefore, the rate of acceleration increases inexorably. There is no terminal velocity, except that at which the smaller object eventually hits the larger mass (or should I say, at which the two objects collide?).
In a gaseous medium, such as a planetary atmosphere, the resistance to the motion of a falling object increases with both increasing atmospheric density and increasing speed. Measured over a short distance, after having reached its terminal velocity, one might record a constant speed for the object. But measured over a great distance one would surely find a small but continuous change in the so-called terminal velocity of a falling object as it continues to experience increasing gravitational pull against increasing resistance due to the increasing density of the atmosphere. I imagine that in one set of circumstances the falling object's terminal speed might gradually increase (eg above the surface of a large planet with a thin atmosphere), and in another that it might gradually decrease (eg above the surface of a small planet with a thick or more dense atmosphere).
This being so - and I've convinced at least myself that it is - I wonder what happens in our Earth's case? Has any advanced mathematician done the necessary calculattions?
i don't know if this is related and is probably too simple. BUT
if 2 objects fall from the same height no matter what the weight the terminal velocity, well at least the velocity they hit the groung at should be equal.
this is because at say height 100 metres, the potential energy of the objects wil be mgh.
m=mass g= gravity h= height.
when the ojects hit the ground the maximun]m kinetic energy will be 0.5mv^2 v being velocitZ
so the as mgh = 0.5mv^2 the m's cancel out, so mass is irreleverent to the final speed its the height which is important.
well i hope
if 2 objects fall from the same height no matter what the weight the terminal velocity, well at least the velocity they hit the groung at should be equal.
this is because at say height 100 metres, the potential energy of the objects wil be mgh.
m=mass g= gravity h= height.
when the ojects hit the ground the maximun]m kinetic energy will be 0.5mv^2 v being velocitZ
so the as mgh = 0.5mv^2 the m's cancel out, so mass is irreleverent to the final speed its the height which is important.
well i hope
-- answer removed --
S'funny how I happened to mention a hammer and a feather in my first post.......
Now let's ignore variations in gravity, air density, relativity etc.and apply the question to various bodies of variable masses and densities in a fluid medium of homogeneous density and pressure, that are subject to a constant force such that it produces an equal rate of positive acceleration in each body....
...errr, where were we?
Ha, ha! Well, Brachiopod, unless you like staying up all night, I'd say you're probably somewhere in the Americas or Canada, while I'm in the UK. (Why doesn't this site include indications od the geographical location of its members?).
As for this problem, with regard to my previous answer I feel I may be guilty of diverting some of the attention away from the original question, although Coins made no mention of medium or vacuum. Perhaps by introducing thoughts of variations in gravitational pull, etc, I took the problem one step beyond where it should sensibly be considered by us? So, let's have constant gravitational pull and homogenaiety of the medium for this purpose.
So to take the original question and your last answer, I think we might all agree to conclude that, provided the bodies are in a vacuum, they will all reach the same terminal velocity in the same elapsed time. But if they are in a medium (actually whether homogenous or not!) they will not all reach the same terminal velocity, nor will they do so in the same elapsed time. Further, some objects will achieve a positive terminal velocity (in the direction of the force acting upon them) while others will achieve a negative one.*
* I have this bizarre image of King Kong standing atop the Empire State Building and releasing two objects simultaneously: Ann Darrow and a helium-filled balloon.
As for this problem, with regard to my previous answer I feel I may be guilty of diverting some of the attention away from the original question, although Coins made no mention of medium or vacuum. Perhaps by introducing thoughts of variations in gravitational pull, etc, I took the problem one step beyond where it should sensibly be considered by us? So, let's have constant gravitational pull and homogenaiety of the medium for this purpose.
So to take the original question and your last answer, I think we might all agree to conclude that, provided the bodies are in a vacuum, they will all reach the same terminal velocity in the same elapsed time. But if they are in a medium (actually whether homogenous or not!) they will not all reach the same terminal velocity, nor will they do so in the same elapsed time. Further, some objects will achieve a positive terminal velocity (in the direction of the force acting upon them) while others will achieve a negative one.*
* I have this bizarre image of King Kong standing atop the Empire State Building and releasing two objects simultaneously: Ann Darrow and a helium-filled balloon.
Quite so, Roguepink. In a very short time indeed the helium-filled baloon would accelerate upwards to reach its terminal velocity away from Earth, what I referred to as negative terminal velocity. But that terminal velocity would then proceed to decrease extremely gradually until the balloon rose no further, and then it would start to fall very slowly as the gravitational pull on the low mass of the balloon material began to outweigh the factors relating to pressure and density.
But do we really want to go into that? :-)
Qapmoc, I believe the parachutist's downward velocity, once he's reached terminal velocity, would gradually decrease from that point because the density of the atmosphere, and hence the air reistance, would gradually increase as he fell. This disregards the gradual increase in the gravitational force, naturally!
Should we call a halt to this now? What say you, Coins? You started it all!
But do we really want to go into that? :-)
Qapmoc, I believe the parachutist's downward velocity, once he's reached terminal velocity, would gradually decrease from that point because the density of the atmosphere, and hence the air reistance, would gradually increase as he fell. This disregards the gradual increase in the gravitational force, naturally!
Should we call a halt to this now? What say you, Coins? You started it all!
no.
but if i released 2 same shaped objects from the same height no matter what the mass of the object they would hit the ground at the same time,
I think. once the terminal velocity has been reached and the conditions don't change the object cant get faster,
i dont really know where im going with that....
but if i released 2 same shaped objects from the same height no matter what the mass of the object they would hit the ground at the same time,
I think. once the terminal velocity has been reached and the conditions don't change the object cant get faster,
i dont really know where im going with that....
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