Calculating Buoyant Force for Submerged Materials

[astru025]

Homework Statement

A cubic meter of some material has a mass of 8600 kg. The block of material is lowered into a lake by a strong cable until the block is completely submerged. What is the buoyant force on the block?

Homework Equations

Fb=p x V x g. P= density of fluid, density of water = 1000 kg/m^3. V=displacement volume. THIS IS WHERE I NEED HELP. How do I find the displacement volume? I have looked everywhere in my notes and can't come up with it. g= 9.8 m/s^2

The Attempt at a Solution

1000 x V?? x 9.8
Need help finding V! Thanks so much.

 

[NihalSh]

Homework Statement

A cubic meter of some material has a mass of 8600 kg. The block of material is lowered into a lake by a strong cable until the block is completely submerged. What is the buoyant force on the block?

Homework Equations

Fb=p x V x g. P= density of fluid, density of water = 1000 kg/m^3. V=displacement volume. THIS IS WHERE I NEED HELP. How do I find the displacement volume? I have looked everywhere in my notes and can't come up with it. g= 9.8 m/s^2

The Attempt at a Solution

1000 x V?? x 9.8
Need help finding V! Thanks so much.

$$F_{b}=ρ.V.g$$
here $V$ is the volume of part of the object immersed in water, in this case object is fully submerged. You already know what $ρ$ and $g$ is. I hope this helps!

 

[astru025]

So to find V would I use this equation: D=m/v. D= 1g/cm^3. M= 8600 kg. 1= 8600/V. V= 8600. Is this correct! Please answer back!

 

[NihalSh]

So to find V would I use this equation: D=m/v. D= 1g/cm^3. M= 8600 kg. 1= 8600/V. V= 8600. Is this correct! Please answer back!

Numbers without units are meaningless, always indicate the units. Look always try to use standard units for calculation, other wise error creeps unknowingly sometimes. If you check carefully your units in answer of volume, units would be $\frac{cm^3.kg}{g}$. Make adjustments so that units of mass cancel out. This is either ways not what you need to do.

Your question has already mentioned what the volume is:

A cubic meter of some material has a mass of 8600 kg.

 

[astru025]

My final answer for buoyant force needs to be in Newtons. So right now I have 1 g/cm^3 x V x 9.8 m/s^2. My value for V= 8600 kg?? So then my buoyant force would be 84820 g/cm^3 x kg x m/s^2? Is this correct. Or do I change 1 g/cm^3 to 1000 kg/m^3..

 

[NihalSh]

My final answer for buoyant force needs to be in Newtons. So right now I have 1 g/cm^3 x V x 9.8 m/s^2. My value for V= 8600 kg?? So then my buoyant force would be 84820 g/cm^3 x kg x m/s^2? Is this correct. Or do I change 1 g/cm^3 to 1000 kg/m^3..

In what units volume is measured?...Think hard and answer.

I believe you didn't read the question nor my post carefully, or you have some doubt about the equation itself!
$$F_{b}=ρ.V.g$$
What does the variables in the above equation represent?

Edit: For force to be in Newtons, mass should be in $kg$ and volume in $m^3$. Whenever you use a equation try to be consistent with the units, for example in the same equation you used $\frac{g}{cm^3}$ for density and $kg$ for mass, you should use same units of mass so that units of mass cancels out completely. Hence you should have used $\frac{kg}{cm^3}$ or $\frac{kg}{m^3}$ to cancel unit of mass or vice-versa.

 

[astru025]

p= density of fluid V=displaced volume and g= 9.8 m/s^2. Volume is measure in cubic units. Usually cubic centimeters or meters

 

[astru025]

Density of water is 1g/cm^3

 

[NihalSh]

p= density of fluid V=displaced volume and g= 9.8 m/s^2. Volume is measure in cubic units. Usually cubic centimeters or meters

Yes, this is the displaced volume. How much volume is displaced if a block of given volume say, x, is submerged in water??

 

[astru025]

The volume is the same

 

[NihalSh]

Density of water is 1g/cm^3

As I mentioned in my previous posts, use standard units. So,

Density of water is $1.\frac{g}{cm^3}=1000.\frac{kg}{m^3}$

Read about SI units, so that you know which units to use when. And also check out "conversion using conversion factors" to be clear about conversion

 

[NihalSh]

The volume is the same

which volume is the same, be specific?

 

[astru025]

The volume of the object before being submerged in water is the same as the volume of the object after it is submerged in water.

 

[NihalSh]

The volume of the object before being submerged in water is the same as the volume of the object after it is submerged in water.

yes, true. But what is amount/volume of fluid displaced?

 

[astru025]

This is what I don't know. I know the answer is right in front of me , I just can't seem to think straight right now.

 

[NihalSh]

This is what I don't know. I know the answer is right in front of me , I just can't seem to think straight right now.

How much volume of fluid is displaced if a block of given volume say, x, is submerged in water??

 

[NihalSh]

How much volume of fluid is displaced if a block of given volume say, x, is submerged in water??

The answer to this is if an object of volume $x$ is submerged in water then the volume of water displaced is also $x$. Can you figure this out now?

 

[NihalSh]

A cubic meter of some material has a mass of 8600 kg. The block of material is lowered into a lake by a strong cable until the block is completely submerged. What is the buoyant force on the block?

It has been mentioned that volume of solid is $1 m^3$

 

[astru025]

Thank you so much. I came up with 9800 N which proved to be correct.