The discussion centers on whether the density of an object affects its sinking speed in a fluid. Participants explore the relationship between density, buoyancy, and the dynamics of sinking, considering both theoretical principles and experimental approaches.
Participants express a range of views on the relationship between density and sinking speed, with no clear consensus reached. Some agree that density plays a role, while others highlight additional factors that complicate this relationship.
Limitations in the discussion include the neglect of drag forces in some analyses, the dependence on definitions of terms like "sinking speed," and the complexity of interactions between density, buoyancy, and shape.
This discussion may be of interest to individuals exploring fluid dynamics, physics students, and those conducting experiments related to buoyancy and sinking behavior.
The density of the fluid affects the force of buoyancy. But the density of the submerged object, which the OP asks about, does NOT affect the force buoyancyphinds said:Density affects bouyancy
Here you are changing two parameters: density and volume. The reduction in force of buoyancy is due to the decreased volume, not due to the increased density.phinds said:Think about a 1 foot diameter ball of something that is almost buoyancy neutral. Now compress it to 1/10 that diameter. What would you expect to happen?
It will sink faster due to increased weight, while the force of buoyancy is unchanged.Simon Bridge said:To continue from phinds - take the same ball, but make it heavier instead of decreasing it's diameter.
I see that you, like I, sometimes answer without actually paying any attention to what the question really is. He's asking about the SPEED of sinking, which your statement does nothing to address.Tinyboss said:Of course it does; if something is denser than water, it sinks, but if it's less dense than water, it floats.
I didn't make it explicit enough, I guess, but it's supposed to be a thought experiment. If density didn't affect the speed, then something would go from floating to sinking at full speed as soon as a dust grain landed on it. Then it would go back to floating when the water washed the dust grain off.phinds said:I see that you, like I, sometimes answer without actually paying any attention to what the question really is. He's asking about the SPEED of sinking, which your statement does nothing to address.
No object with mass can instantaneously reach 'full speed'. This applies if the object is falling in a fluid (water, air etc) or in a vacuum, or more generally when a force is applied to any mass.Tinyboss said:I didn't make it explicit enough, I guess, but it's supposed to be a thought experiment. If density didn't affect the speed, then something would go from floating to sinking at full speed as soon as a dust grain landed on it. Then it would go back to floating when the water washed the dust grain off.
Simon Bridge said:From the Archemedes principle - draw a free body diagram for an object immersed in a fluid and apply Newton's laws ... solve for the acceleration (the rate of sinking) in terms of the density of the object.
Simon Bridge said:Ignoring drag (which would generally not be a good approximation)...
$$F_{wgt}-F_{buoy} = ma_{down}\\
\implies \rho V g - \rho_f V g = \rho V a\\
\implies a= \frac{\rho-\rho_f}{\rho}g$$ ... here ##\rho_f## is the density of the fluid while ##\rho## is the density of the submerged object.
Increasing ##\rho## increases ##a## ... but the maximum acceleration is g.
In practice there is also a drag force that depends on sinking speed so most objects will also have a terminal velocity that is also affected by density (among other things).
I would have preferred OP to pursue this ... it would then have been possible to ascertain the origin of any confusion leading to the question and so address the real problem. Ho hum. We really need to hear from OP before we can continue.
Simon Bridge said:Ignoring drag (which would generally not be a good approximation)...
$$F_{wgt}-F_{buoy} = ma_{down}\\
\implies \rho V g - \rho_f V g = \rho V a\\
\implies a= \frac{\rho-\rho_f}{\rho}g$$ ... here ##\rho_f## is the density of the fluid while ##\rho## is the density of the submerged object.
Increasing ##\rho## increases ##a## ... but the maximum acceleration is g.
In practice there is also a drag force that depends on sinking speed so most objects will also have a terminal velocity that is also affected by density (among other things).
I would have preferred OP to pursue this ... it would then have been possible to ascertain the origin of any confusion leading to the question and so address the real problem. Ho hum. We really need to hear from OP before we can continue.
Pippythehippie said:all that fancy numbers and stuff made me dizzy
Pippythehippie said:I did do an experiment for myself, and my results proved that density does change the time that it takes to sink.
Adam al-Girraweeni said:The simple answer to the OP's question, which no-one provided here, is this:
The force acting on the sinking object (which will effect the rate at which it sinks) is the difference between its weight (which is proportional to its mass), pulling down, and and its buoyancy, pushing up.
The buoyancy is the weight of water that it displaces.
So, for objects that are identical in size and shape, the buoyancy (upward force) will always be the same, but if their weight is different, then the downward force will be different. The net force will then be different, and the acceleration (sinking) will be more or less.
Adam
leright said:This has been pointed out many times in the thread.
Dear Sir
Daughter was doing some physics homework, and we come across the bit that says that, if it weren't for differential air resistance, all objects would fall at the same rate of gravitational acceleration, and so, if dropped at the same time from the same height, would hit the ground at the same time, irrespective of their mass.
Basic law of physics, which has been branded into our brains since our earliest youth, no?
Well, I had been thinking how to make a demonstration of this, that was practical to set up (ie, that didn't involve both or even either of a spacecraft and the Leaning Tower of Pisa). So, I thought that things sinking in water should obey the same physical law, with water resistance taking the place of air resistance.
Inference: two objects of the same external shape and size (thus having equal hydrodynamics) should sink equally fast, even if one of them is much denser than water, and the other one is only slightly denser than water.
But, I thought "that doesn't sound right" (just as I sometimes find it difficult to imagine a feather falling at the same rate as a rock, if dropped on the moon, despite "knowing" it as an almost Biblical truth ).
So, I came up with this experimental plan:
Two glass test-tubes, same size and weight.
If one were sealed, full of air, it would float.
If the other were filled with water, it would sink (doesn't matter about sealing it, but do so, for the sake of experimental uniformity).
Now, if a tube had just a little bit of water in it, it would still float. There would be an amount of water that, if put in the tube and sealed up, the average density of this part-full tube would be the same as that of water.
If there were more water than this critical amount, it would sink; if less, it would not sink.
Now, if we have one tube completely filled with water, and the other filled with just over the critical amount of water, and both sealed identically, and arrange to let them go just below the surface of a column of water at the same time (and of course in the same orientation), then, as I understand Galileo, they should fall at the same rate, and hit the bottom of the water container at the same time.
Today, I (with daughter) transformed the gedankenexperiment into a wirklichexperiment, and the result is quite clear - the tube filled right up with water hits the bottom of the bucket before the less-filled tube.
Why is it so? You are the only person that I am in contact with who could be smart enough to give me an explanation. Please help! My whole world view, my faith in the fundaments of science, and the respect of my intellect in the eyes of my daughter are at stake!
Your simple friend,
Adam
Adam al-Girraweeni said:Thanks for replying to my post.
Perhaps I should explain why I wrote this response on this (nearly year old) thread, how I came to this forum, and why I signed up to it.
The following is the test of an email which I sent to a friend of mine earlier today:Obvious, now, where I went wrong - but it has taken a lot of digging around to find the answer - which I finally found on this forum (your post, and one of Simon's, in this thread). However, there was not a nice, simple, easily understandable explanation, such as the OP (and indeed anyone starting out in science) needed. There was too much detail, both in the maths, and in all the extraneous suggestions, like quibbles about "acceleration", rather than "speed", and worrying about terminal velocity.
The suggestion "Why not just do the experiment?" is usually a good one, but wasn't particularly helpful here, and the Cartesian Diver doesn't solve the problem either, just shows again that it exists.
FactChecker came closest to a good simple explanation, but perhaps went too far in the simple direction, as I did not initially realize what it meant.
leright said:The problem is drag becomes a dominant effect very quickly in practice (and in theory) and the object reaches terminal velocity extremely rapidly. By only considering the two forces, buoyancy and weight, you get a result that implies the object accelerates indefinitely, but in practice the object reaches terminal velocity in about a second in many cases.
Good to hear - part of the reason for replying to public questions like this is so that others will benefit from the discussion.Adam al-Girraweeni said:Obvious, now, where I went wrong - but it has taken a lot of digging around to find the answer - which I finally found on this forum (your post, and one of Simon's, in this thread).
Your example problem is much simpler than the question being answered above, which is why you did not quite find the simple answer you were looking for.However, there was not a nice, simple, easily understandable explanation, such as the OP (and indeed anyone starting out in science) needed. There was too much detail, both in the maths, and in all the extraneous suggestions, like quibbles about "acceleration", rather than "speed", and worrying about terminal velocity.
The suggestion "Why not just do the experiment?" is usually a good one, but wasn't particularly helpful here, and the Cartesian Diver doesn't solve the problem either, just shows again that it exists.