# Finding buoyant force

1. Oct 16, 2013

### astru025

1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. The attempt at a solution
1000 x V?? x 9.8
Need help finding V! Thanks so much.

2. Oct 16, 2013

### NihalSh

$$F_{b}=ρ.V.g$$
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!

3. Oct 19, 2013

### 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!

4. Oct 19, 2013

### NihalSh

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.

5. Oct 19, 2013

### 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..

6. Oct 19, 2013

### NihalSh

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.

Last edited: Oct 19, 2013
7. Oct 19, 2013

### 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

8. Oct 19, 2013

### astru025

Density of water is 1g/cm^3

9. Oct 19, 2013

### NihalSh

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

Last edited: Oct 20, 2013
10. Oct 20, 2013

### astru025

The volume is the same

11. Oct 20, 2013

### NihalSh

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

12. Oct 20, 2013

### NihalSh

which volume is the same, be specific?

13. Oct 20, 2013

### 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.

14. Oct 20, 2013

### NihalSh

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

15. Oct 20, 2013

### 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.

16. Oct 20, 2013

### NihalSh

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

17. Oct 20, 2013

### NihalSh

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?

18. Oct 20, 2013

### NihalSh

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

19. Oct 20, 2013

### astru025

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