How Much Force to Keep Foam Underwater?

[ChunkymonkeyI]

Homework Statement

A block of foam plastic has a volume of 25.0 cm^3 and a density of 0.800 g/cm^3. How large a force is required to hold it under water?

Homework Equations

F=mg, m=density times volume

The Attempt at a Solution

I first converted 25.0 cm^3 into 2.5 times 10^-5m^3 and .800 g/cm^3 into 800 kg/m^3
Then I used the formula m=density times volume
m=(density)(volume)
m=(800 kg/m^3)(2.5 times 10^-5 m^3)
m=0.02 kg
Then I used the formula F=mg and plugged 0.02 kg for the mass and 9.80 m/s^2 as g and multiply them together to get 0.196N but Ik the answer is suppose to be .0490 and Idk what I'm doing wrong can someone help me. Maybe I didn't think about the density of water or something like that

 

[SteamKing]

Why didn't you just multiply the volume of 25 cc by the density of .8 g/cc to get the mass of the foam? You can always convert g to kg by moving the decimal point.

Yes, if you wish to submerge the foam block, you must account of the buoyancy produced when the block is pushed and held under the water.

 

[ChunkymonkeyI]

Why didn't you just multiply the volume of 25 cc by the density of .8 g/cc to get the mass of the foam? You can always convert g to kg by moving the decimal point.

Yes, if you wish to submerge the foam block, you must account of the buoyancy produced when the block is pushed and held under the water.

Idk what 2 do from there because I tried using Fb=density of fluid times volume of fluid times g and its still not getting me the right answer

 

[LawrenceC]

Compute the weight of object. Compute weight of equal volume of water. Subtract them and you get 0.049 N.

 

[ChunkymonkeyI]

Compute the weight of object. Compute weight of equal volume of water. Subtract them and you get 0.049 N.

How do I compute the weight of equal volume because Idk what formula ur referring 2

 

[LawrenceC]

How do I compute the weight of equal volume because Idk what formula ur referring 2

You multiply the volume of the object by the density of water. Density of water is 1000 kg/m^3. Then convert to weight in Newtons.

 

[ChunkymonkeyI]

Thank u very much but just wondering do u know a way 2 dervive an equation for this type of problem in order to find the force required so that time is saved?

 

[LawrenceC]

Sure but you should be able to do that. To solve for the force to hold the object under water you computed the buoyant force as

Fb = density water * volume * gravity constant

To determine the weight of object

W = density of object * volume * gravity constant

Do the above equations suggest anything to you? Hints: common terms, factoring...

 

[LawrenceC]

Signing off for the day.

 

[ChunkymonkeyI]

Sure but you should be able to do that. To solve for the force to hold the object under water you computed the buoyant force as

Fb = density water * volume * gravity constant

To determine the weight of object

W = density of object * volume * gravity constant

Do the above equations suggest anything to you? Hints: common terms, factoring...

I think I got it but just 2 be on the safe side...
In each equation u factor out Vg so now we have
Equation 1:Fb=Vg(Density of water)
Equation 2:Weight of object or Fw=Vg(density of object)
Combinding them we get Fg/density of water=Fw/Density of object
Weight of object the same as Fw which is Fweight?

 

[hmzone]

Compute the weight of object. Compute weight of equal volume of water. Subtract them and you get 0.049 N.

But if the object isn't moving should'nt it mean ƩF = 0 → buoyancy = mg ?? Why should we subtract them?

 

[LawrenceC]

You must subtract them because the object you are holding under water has some weight itself. If it has too much weight, it sinks due to its own weight. Draw a free body diagram of a motionless body under water and place arrows on it denoting the forces on the object. How many forces are there?

Have you heard of Archimedes principle?