# Does density affect sinking speed?

1. Apr 18, 2015

### Pippythehippie

does the density of an object affect how fast it sinks?

2. Apr 18, 2015

### phinds

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. Apr 18, 2015

### Simon Bridge

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. Apr 18, 2015

### Pippythehippie

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. Apr 18, 2015

### Simon Bridge

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 possess the equipment?

Last edited: Apr 18, 2015
6. Apr 19, 2015

### A.T.

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

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.

It will sink faster due to increased weight, while the force of buoyancy is unchanged.

7. Apr 19, 2015

### Simon Bridge

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.

Last edited: Apr 19, 2015
8. Apr 19, 2015

### Tinyboss

Of course it does; if something is denser than water, it sinks, but if it's less dense than water, it floats.

9. Apr 19, 2015

### phinds

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. Apr 19, 2015

### FactChecker

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. Apr 19, 2015

### Tinyboss

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. Apr 19, 2015

### billy_joule

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.

Repeat for an object in a vacuum..

13. Apr 19, 2015

### Tinyboss

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. Apr 19, 2015

### leright

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

Last edited: Apr 19, 2015
15. Apr 19, 2015

### leright

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. Apr 19, 2015

### Simon Bridge

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. Apr 19, 2015

### leright

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. Apr 22, 2015

### Pippythehippie

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. Apr 22, 2015

### AlephNumbers

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

20. Apr 22, 2015

### leright

I apologize if my answer was too technical.

21. Apr 23, 2015

### Simon Bridge

@Pippythehippy: Do you know how the principle of archemedes works?

22. Jan 17, 2016

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.

23. Jan 17, 2016

### leright

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.

Last edited: Jan 17, 2016
24. Jan 17, 2016

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:
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 realise what it meant.

Last edited: Jan 18, 2016
25. Jan 17, 2016

### leright

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.