Buoyant Force

[Wolfpack93]

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Can anyone explain why the acceleration of an object that is submerged under water doesn't depend on it's volume? The buoyant force equation is F=pVg, so wouldn't increasing volume increase force and therefore acceleration? According to the practice problems I've been doing in TBR only density matters for acceleration which makes no sense to me.

 

[theonlytycrane]

Is there a specific question you're referring to?

Increasing the volume of the object submerged will increase the volume of fluid displaced which contributes to the buoyant force on the object.

 

[Wolfpack93]

Is there a specific question you're referring to?

Increasing the volume of the object submerged will increase the volume of fluid displaced which contributes to the buoyant force on the object.

Right so wouldn't that increase the acceleration of the object? Yeah let me try to find it.

 

[Wolfpack93]

Three objects with the same density but different sizes are placed in a tank of water. It shows a picture but basically Volume 3>Volume 2>Volume 1. After the objects are released:

A. Object I has the greatest acceleration
B. Object II has the greatest acceleration
C. Object III has the greatest acceleration
D. All 3 objects have the same acceleration.

Their answer is D and that doesn't make sense to me I would think its C since V, therefore buoyant force is greater.

 

[Gurby]

Do a free body diagram and draw all the forces.

Upward force is buoyant force so Fup = pVg as you pointed out.

What downward forces are involved?

 

[Wolfpack93]

Do a free body diagram and draw all the forces.

Upward force is buoyant force so Fup = pVg as you pointed out.

What downward forces are involved?

Wouldn't downward just be mg?

 

[Gurby]

Wouldn't downward just be mg?

Yes. So if we increase volume, Fb increases because pVg increases. What else happens if we increase the volume of our object and it stays the same density?

Might be more obvious if you rearrange mg to something else and factor some things out of the overall equation....

 

[theonlytycrane]

Since all objects have the same density, even though object 3 has a larger volume, it also has more mass such that its density is equal to the density of the other objects. In the acceleration term, the Volume / mass ratio circled is the same for all 3 objects resulting in equal accelerations.

 

[BerkReviewTeach]

The thing to keep in mind here is that BOTH the buoyant force up and the gravitational force down increase with a larger object. As its volume increases, so does its mass and the volume of displaced medium. The two forces increase equally. If the volume doubles, it will be twice as massive (doubling the weight) and displace twice as much fluid (doubling the buoyant force). The net force will also double (FW - FB), but that is equal to ma. FNET = ma, so given that both FNET and m doubled, the value of a remains the same.

 

[Wolfpack93]

Ahh ok thank you all! That makes much more sense. So the acceleration would only depend on the relative densities?

 

[Gurby]

Ahh ok thank you all! That makes much more sense. So the acceleration would only depend on the relative densities?

Those guys gave it away and spoiled all the fun 😛 I think you would not need to ask that question if you wrote everything out for yourself, rearranged and simplified the variables. (ie, if you use density = m/v, you can rearrange the overall equation and replace m with density*volume, and then cancel volume out)