Does density affect sinking speed?

In summary: 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.
  • #1
Pippythehippie
3
0
does the density of an object affect how fast it sinks?
links to pages with more info would be great, thanks.
 
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  • #2
Density affects bouyancy, which affects sinking speed. 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?
 
  • #3
It's a good question.
Why not check for yourself - get some objects with varying density and put them in water and time how long they take to reach the bottom. (See "Cartesian diver")
You can also figure it out from the principle of Archimedes... how does it work?

To continue from phinds - take the same ball, but make it heavier instead of decreasing it's diameter.
 
  • #4
Thanks, do you know of any pages where I can read more about this, i have read that archimedes principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. which means that the density of a object defines whether it sinks or floats, but do things sink at different speeds due to their density, and is there any pages where tis is explined, I have searched everywhere!
 
  • #5
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.

You can google for "cartesian diver" to find out more.
"speed of sinking" and "sink rate" will come up with pages from physics forums discussing this in different circumstances.
But instead of reading about it on some webpage, why not go to the source, so to speak: ask Nature? Why not just do the experiment - you already possesses the equipment?
 
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  • #6
phinds said:
Density affects bouyancy
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 buoyancy

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?
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.

Simon Bridge said:
To continue from phinds - take the same ball, but make it heavier instead of decreasing it's diameter.
It will sink faster due to increased weight, while the force of buoyancy is unchanged.
 
  • #7
Thank you - I am hoping that OP will take the trouble to work that out.
You'll notice that I have made no claims about the force of bouyancy or even how density affects rate of sinking.
However you have just said that increasing the density will increase the sinking rate.

The relationship is a bit more complicated - but easily derived.
 
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  • #8
Of course it does; if something is denser than water, it sinks, but if it's less dense than water, it floats.
 
  • #9
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 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.
 
  • #10
Density is not the entire story. As long as it is denser than water, it will want to sink. The gravitational force on it is greater than the gravitational force on the water that it displaces. But a streamlined object can sink faster than an equally dense object that is not streamlined.
 
  • #11
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.
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.

Since we never see things behaving this way, we can conclude that sinking speed is affected by density.
 
  • #12
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.
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.
Density affects acceleration and terminal velocity ('full speed') only when the object is falling in a fluid.
The Hammer and Feather drop experiment on the moon (a recreation of Galileo famous experiment) shows what happens when objects with different densities are dropped in a (near) Vacuum.

If you follow Simons advice it should become clear:

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.

Repeat for an object in a vacuum..
 
  • #13
Sorry, I was again unclear. I meant it would accelerate to "full sinking speed", whatever that is, independent of density.

I know about buoyancy, I'm just offering a way to see that independence of sinking speed wrt density leads to absurdity.
 
  • #14
I'll explicitly solve it for you. Note that I choose to use units of kg/m^3 for density and Newtons for force. The buoyant force, per Archimedes, is the weight of the water displaced by the object. So, Fb = 9.8*rho_w*V, where rho_w is the density of water and V is the volume of the object. The weight of the object, W, is 9.8*rho*V, where rho is the density of the object. So, the net force is Fnet = W - Fb = 9.8*rho*V - 9.8*rho_w*V. Divide Fnet by the mass of the object, which is rho*V, to find the acceleration (sink rate) of the object.

So, accel = Fnet/(rho*V) = 9.8*V*(rho-rho_w)/(rho*V) = 9.8*(rho-rho_w)/rho = 9.8*(1-(rho_w/rho))

So, accel = 9.8*[1-(rho_w/rho)]. You can see from this equation that as rho increases the acceleration (sink rate) gets larger. Also, when the density of the object is less than that of water the acceleration is negative, and thus the object floats.

I must add that this neglects drag force. In reality there is a third force, Fdrag, which is proportional to the velocity of the object and the coefficient of drag of the object in the liquid. Eventually, the object will reach a terminal velocity, at which the sum of the forces, W, Fb, and Fdrag is zero and the object stops accelerating. This would depend on the coefficient of drag of the object in the liquid. Basically,

accel = Fnet - Fdrag = 9.8*[1-(rho_w/rho)] - Cd*v. Cd is the coefficient of drag and v is the speed of the object.

So, dv(t)/dt = 9.8*[1-(rho_w/rho)] - Cd*v(t). This is a differential equation that you can solve for velocity. It is pretty easy to solve. You'll find that the velocity asymptotically approaches a terminal value,

-Matt
 
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  • #15
So I cranked out the solution of the DE in MATLAB. Basically, it is [9.8*[1-(rho_w/rho)]]*[1+exp(-Cd*t)]. So, the object starts out with a velocity equal to 2*9.8*(1-rho_w/rho)/Cd and falls and asymptotically approaches a velocity of 9.8*[1-(rho_w/rho)]/Cd. The terminal velocity is only dependent on the density of the liquid, the density of the object, and the Cd. So, not only can the density have an effect, but also the shape and coefficient of drag of the object in that particular medium.

Also, the time it takes to reach terminal speed, as tinyboss pointed out, is very small. so the object effectively sinks at a constant speed. This sinking speed depends on the density of the liquid, the density of the object, and the Cd value in the given situation.
 
  • #16
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.
 
  • #17
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.

Yes, my approach was the same before taking into account drag. However, the object generally reaches terminal speed very rapidly but the terminal speed is also dependent on the density of the object.
 
  • #18
Thank you all for your information, I did do an experiment for myself, and my results proved that density does change the time that it takes to sink. however I don't understand why, I am a simple student in tenth grade, and all that fancy numbers and stuff made me dizzy, would you be able to simplify it into words, that would make sense to a tenth grader? PLEASE! and thankyou!
 
  • #19
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

Does anything in Simon's post make sense to you?

Pippythehippie said:
I did do an experiment for myself, and my results proved that density does change the time that it takes to sink.

What are your thoughts on your findings?
 
  • #20
I apologize if my answer was too technical.
 
  • #21
@Pippythehippy: Do you know how the principle of archemedes works?
 
  • #22
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
 
  • #23
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

This has been pointed out many times in the thread. And the net force will actually eventually become zero as the object accelerates due to an additional drag force, which is significant. The object will eventually reach terminal velocity in the water. However, the terminal velocity in fact does depend on density as I pointed out earlier.
 
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  • #24
leright said:
This has been pointed out many times in the thread.

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 text of an email which I sent to a friend of mine earlier today:
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

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.
 
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  • #25
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.

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.
 
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  • #26
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.

Yes, but (1) it's not relevant to the OP's question, and (2) it's a constant (a constant factor, anyway, if the objects have the same size and shape, even though its value might change with speed of sinking).

Anyway, as a newbie, I'd better emphasise that I mean no disrespect. Thanks to all here for their contributions to learning!

A
 
  • #27
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).
Good to hear - part of the reason for replying to public questions like this is so that others will benefit from the discussion.

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.
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.
Your example explicitly excluded drag, OP did not, and was concerned with the order of arrival at the bottom rather than the speed while sinking... issues of drag and velocity vs acceleration were, therefore, more important to the question being answered than they were to you. Leaving them out in favour of the simplistic explanation you (or OP) would have preferred would have been doing the OP a disservice and risked spreading a bunch of really common misconceptions about buoyancy.

A complete answer to your question would still have involved mention of drag: the test-tubes reach their terminal velocity at different rates. The terminal velocity is the "speed of sinking" ... which is the same for all objects same size and shape as you point out. The test tubes likely spent almost all their time sinking at that speed.

Mind you - in some of these threads, a summary at the end would be useful.

Do you now understand what you would need to set up the experiment to demonstrate the effect you wanted?

To really test your understanding of buoyancy, have a look at:
https://www.lhup.edu/~dsimanek/museum/themes/buoyant.htm
 

1. How does density affect sinking speed?

The density of an object affects its sinking speed because it determines how much water it displaces. Objects with higher density will displace more water and therefore experience a greater buoyant force, causing them to sink faster.

2. What factors contribute to the density of an object?

The density of an object is determined by its mass and volume. The more mass an object has in relation to its volume, the higher its density will be.

3. Does the shape of an object affect its density and sinking speed?

Yes, the shape of an object can affect its density and sinking speed. Objects with a more streamlined shape will have a lower density and experience less resistance as they sink through water, resulting in a faster sinking speed.

4. Can an object with a lower density sink faster than an object with a higher density?

Yes, an object with a lower density can sink faster than an object with a higher density if it has a more streamlined shape and experiences less resistance as it sinks through water.

5. How does the density of water affect the sinking speed of objects?

The density of water affects the sinking speed of objects because it determines the buoyant force that acts on the object. Objects with higher density than water will sink, while objects with lower density will float. However, the shape and density of the object also play a role in determining the sinking speed.

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