# Archimedes Law

1. Jan 17, 2016

### Nanu Nana

1. The problem statement, all variables and given/known data
A person (with mass 60.0 kg) is located on a volume of ice, floating on the water. Calculate the smallest volume of the ice so that the person would remain above the water ( ice density = 917kg / m3)

2. Relevant equations
F= m xg
Archimedes F = density x V xg

3. The attempt at a solution
If the object is floating then we know that F(g) = F(a)
therefore
m xg = d x V x g
g cancels out
m = d x v
60kg= d (ice) x V
V= 60kg / 917 kg/m3
V = 0.065 m 3
But the answer should be 0.72 m3

Thank you :)

2. Jan 17, 2016

### TSny

Should the force of gravity include the weight of the ice as well as the person?

Also, are you sure you want to use the density of ice when finding the buoyant force?

Last edited: Jan 18, 2016
3. Jan 17, 2016

### Nanu Nana

You have to use density of water ???

4. Jan 17, 2016

### TSny

Can you state Archimedes' principle in words?

5. Jan 17, 2016

### Nanu Nana

Its a principle that states that a body immersed in a fluid is buoyed up by the force which is equal to the weight of displaced fluid

6. Jan 17, 2016

### TSny

OK. What type of fluid is being displaced?

7. Jan 17, 2016

### Nanu Nana

Water ?

8. Jan 17, 2016

### TSny

Yes. But instead of typing "water ?", you should type "water!"

9. Jan 17, 2016

### Nanu Nana

Ok water!

10. Jan 17, 2016

### TSny

Good. So, how would you calculate the weight of the fluid displaced?

11. Jan 17, 2016

### Nanu Nana

W= rho x V x g

12. Jan 17, 2016

### TSny

OK. What density would you use here?

13. Jan 17, 2016

### Nanu Nana

1000 kg/ m3

14. Jan 17, 2016

### TSny

Yes (water). And what volume V should be used to find the weight of the fluid displaced?

15. Jan 17, 2016

### Nanu Nana

0.0654 m3

16. Jan 17, 2016

### TSny

I wasn't clear. When calculating the weight of fluid displaced, should you use the volume of the ice, the volume of the person, or the total volume of both?

Last edited: Jan 18, 2016
17. Jan 17, 2016

### Nanu Nana

Total volume of both

18. Jan 17, 2016

### TSny

We don't want the person to get wet.

19. Jan 17, 2016

### Nanu Nana

The volume of ice then

20. Jan 17, 2016

### TSny

Right. So you have that the buoyant force acting upward on the system is ρwater Vice g.

How does this force relate to the weights of the person and the ice?

Last edited: Jan 18, 2016