Calculating Buoyancy Force & Length of Submerged Cube

[vinamas]

Homework Statement

A layer of oil that has a density of 930kg/m^3 is floating on the surface of water in a container if a wooden cube with a length of 4 cm becomes submerged where it's lower half is in water and it's upper half is in oil
the cube's density is 960kg/m^3 find
A) the buoyancy force affecting the cube
B) the length of the cube that is submerged in water

Homework Equations

density=m/v
buoyancy=density*volume*gravity
cubic volume=L^3

The Attempt at a Solution

so I know the cube's density is less than water so it floats
so I use FB=Fg. 960=m/0.04^3. m=0.06144
FB = 0.06144*9.81=0.6027N is that correct?
B)FB=Fg
1000*Vsubmegred*9.81=0.6027
V=0.000061m^3
0.04*0.04*L=V
L=0.038 now this is my problem the answer sheet says that the submerged part's length is 1.71*10^-2
I can't seem to find the significance of oil and it's density what am I doing wrong?

 

[SteamKing]

Homework Statement

A layer of oil that has a density of 930kg/m^3 is floating on the surface of water in a container if a wooden cube with a length of 4 cm becomes submerged where it's lower half is in water and it's upper half is in oil
the cube's density is 960kg/m^3 find
A) the buoyancy force affecting the cube
B) the length of the cube that is submerged in water

Homework Equations

density=m/v
buoyancy=density*volume*gravity
cubic volume=L^3

The Attempt at a Solution

so I know the cube's density is less than water so it floats
so I use FB=Fg. 960=m/0.04^3. m=0.06144
FB = 0.06144*9.81=0.6027N is that correct?
B)FB=Fg
1000*Vsubmegred*9.81=0.6027
V=0.000061m^3
0.04*0.04*L=V
L=0.038 now this is my problem the answer sheet says that the submerged part's length is 1.71*10^-2
I can't seem to find the significance of oil and it's density what am I doing wrong?

Remember, the submerged part of the cube is said to be half in the water and half in the oil.

Treat the total submergence as a variable T and work out what T must be so that the cube is floating in equilibrium with the oil and water.

 

[vinamas]

Remember, the submerged part of the cube is said to be half in the water and half in the oil.

Treat the total submergence as a variable T and work out what T must be so that the cube is floating in equilibrium with the oil and water.

well I have seen the problem again and am sorry because I translated it wrong it doesn't say half it just says the lower surface is in water and the upper surface is in oil

 

[SteamKing]

well I have seen the problem again and am sorry because I translated it wrong it doesn't say half it just says the lower surface is in water and the upper surface is in oil

OK, so T may not be evenly split between the water and the oil. You still should be able to find a relationship between the two parts given the densities of each fluid and the fact that the cube is floating in equilibrium.

 

[vinamas]

OK, so T may not be evenly split between the water and the oil. You still should be able to find a relationship between the two parts given the densities of each fluid and the fact that the cube is floating in equilibrium.

The closest thing on my mins is
Fnet=FBwater+FBoil-Fgcube=0 but that still doesn't get me the answer

 

[SteamKing]

The closest thing on my mins is
Fnet=FBwater+FBoil-Fgcube=0 but that still doesn't get me the answer

Have you adjusted your calculations from what you posted in the OP?

 

[vinamas]

Have you adjusted your calculations from what you posted in the OP?

nope

 

[SteamKing]

nope

Why not?

 

[vinamas]

Why not?

What am I required to change?I think that FBwater is correct and the mass of the cube is correct too I can also obtain the volume of of the part of the cube in oil but I don't know what to do with it

 

[CrazyNinja]

What am I required to change?

Your original post does not include the buoyant force exerted by the oil. Add that according to your equation in #5.

 

[vinamas]

Your original post does not include the buoyant force exerted by the oil. Add that according to your equation in #5.

well after hours of crying and thinking why did I go into the advanced high school program I think I've found the answer and it goes like this
FBwater+FBoil-Fg=0
1000*0.04*0.04*L*9.81+930*(0.04-h)*0.04*0.04*9.81-0.602=0
L=0.0171 m.
I feel good now btw

 

[CrazyNinja]

Always feels nice to help. We can feel a little bit better @SteamKing #peaceout