Calculating Minimum Volume for Floating Ice Slab - AP Physics B Problem

[llama0lover]

AP physics B problem- Buoyant Forces?


A slab of ice floats on a freshwater lake. What is the minimum volume of the slab such that a 70 kg man can stand on it without getting his feet wet? The density of ice is 0.922 kg/m^3 and the density of freshwater is 1,000 kg/m^3

I have gotten to mass(ice) + mass(person) = Density of water x volume submerged

From there I have two unknown variables I am at a loss

 

[diazona]

Your unknown variables are the mass of the ice and the volume of the ice, right? What other equation relates them to each other?

 

[Doc Al]

Hint: How does the volume submerged relate to the volume of ice?

 

[llama0lover]

density = mass/volume , but I only know the density. Also the volume submerged would equal the total volume, but I don't know where to go with that...

 

[Doc Al]

density = mass/volume , but I only know the density. Also the volume submerged would equal the total volume, but I don't know where to go with that...

Good. Express the mass of the ice in terms of its volume.

 

[llama0lover]

so density= m/v so m=density x volunme submerged, but how would that help you if you don't know the volume submerged.

 

[Doc Al]

The volume is what you are trying to find.

 

[llama0lover]

so volume submerged = m/density (sorry if I'm a little slow at this I'm not really great at physics) how would you solve that if you only know the density... You still have two unknown variables

 

[Doc Al]

so volume submerged = m/density (sorry if I'm a little slow at this I'm not really great at physics) how would you solve that if you only know the density... You still have two unknown variables

Use the definition of density to rewrite the equation you gave in post #1 completely in terms of volume, not mass. You'll only have one variable.

 

[llama0lover]

so you would end up with mass of ice + mass of person = density of water x (mass of ice/ density of ice)

so you would just simplify it from there, but how would you do that

[ m(i) + m(p) ] / density of water= m/ density of ice

how would you get both onto one side?

 

[llama0lover]

thank you by the way :-) You're a huge help

 

[Doc Al]

so you would end up with mass of ice + mass of person = density of water x (mass of ice/ density of ice)

so you would just simplyfy it from there, but how would you do that

Start with your original equation:

I have gotten to mass(ice) + mass(person) = Density of water x volume submerged

Replace each mass with its equivalent in terms of density and volume.

 

[llama0lover]

densityof ice(volume ice) + 70 = Density of water x volume submerged

I can't separate the mass into volume and density of the person because I don't know either of those

 

[Doc Al]

densityof ice(volume ice) + 70 = Density of water x volume submerged

Perfect. Now you can solve for the volume. (Remember your answer to my question in post #3.)

I can't separate the mass into volume and density of the person because I don't know either of those

Skip that one--my mistake. You already know the person's mass.

 

[llama0lover]

so [ density of ice(volume ice) + 70 ] / density of water= volume of ice
how would you divide it with the seventy still there

 

[Doc Al]

so [ density of ice(volume ice) + 70 ] / density of water= volume of ice

No. Go back to the previous equation and collect all terms with volume to one side. Then you can isolate the volume and solve for it.

 

[llama0lover]

70 = Density of water (volume ice) + density of ice(volume ice)

70= volume of ice(density of water +density of ice)

would that be right?

 

[Doc Al]

70 = Density of water (volume ice) + density of ice(volume ice)

70= volume of ice(density of water +density of ice)

would that be right?

Almost. But you messed up a sign when you moved a term from left to right.

 

[llama0lover]

70= volume of ice(density of water - density of ice)

so from there you would just simplify

ohhhhh I get it.

Thanks you so much you were a huge help