Floating on Ice: Calculating Volume Needed to Stay Afloat

[Nanu Nana]

Homework Statement

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)[/B]

Homework Equations

F= m xg
Archimedes F = density x V xg [/B]

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 [/B]

Thank you :)

 

[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?

 

[Nanu Nana]

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

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

You have to use density of water ?

 

[TSny]

You have to use density of water ?

Can you state Archimedes' principle in words?

 

[Nanu Nana]

Can you state Archimedes' principle in words?

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

 

[TSny]

OK. What type of fluid is being displaced?

 

[Nanu Nana]

OK. What type of fluid is being displaced?

Water ?

 

[TSny]

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

 

[Nanu Nana]

Ok water!

 

[TSny]

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

 

[Nanu Nana]

W= rho x V x g

 

[TSny]

OK. What density would you use here?

 

[Nanu Nana]

1000 kg/ m3

 

[TSny]

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

 

[Nanu Nana]

0.0654 m3

 

[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?

 

[Nanu Nana]

Total volume of both

 

[TSny]

Total volume of both

We don't want the person to get wet.

 

[Nanu Nana]

The volume of ice then

 

[TSny]

Right. So you have that the buoyant force acting upward on the system is ρ_water V_ice g.

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

 

[Nanu Nana]

Aren't they equal?

 

[TSny]

Could you state precisely what should be equal?

 

[Nanu Nana]

Fz = F( A)

 

[TSny]

What is the total downward force acting on the system ?

 

[Nanu Nana]

F= mass x a
60.0 kg x 9.81 m/s2=588.6 N

 

[TSny]

OK. That's the downward force of gravity on the person. Is there any other downward force acting on the system of person and ice?

 

[Nanu Nana]

On ice aswell

 

[TSny]

Exactly. How would you express the force of gravity on the ice in terms of the volume of ice and the density of ice? Just in symbols.

 

[Nanu Nana]

Exactly. How would express the force of gravity on the ice in terms of the volume of ice and the density of ice? Just in symbols.

F=m xg = density xVx g

 

[TSny]

Good. To be clear. let's write this as ρ_ice V_ice g.

You know that the total downward force on the system must equal the total upward force (since the system is floating). How would this look as an equation?

 

[Nanu Nana]

m x g= pice x Vice x g

 

[TSny]

Going back to your basic equation F(g) = F(a), the left side is the total force of gravity (acting down) and the right side is the buoyant force (acting upward). Now write out each side. You should find that your unknown V_ice occurs on both sides of the equation.

If you want to create subscripts you can use the tool bar. Greek letters and other symbols can be found by clicking on the Σ symbol on the tool bar.

 

[Nanu Nana]

I've been doing the way you told me But i still don't get the right answerAnd thank you for informing about subscripts :)

 

[TSny]

In the equation F(g) = F(a), what did you write for F(g)? That is, how did you express the total force of gravity on the system?

 

[Nanu Nana]

F= 60.0 kg x 9.81 m/s2 =588.6

 

[TSny]

That's the force of gravity on the person alone. How would you express the total force of gravity on the system? The system consists of the man and the ice.

 

[Nanu Nana]

917 kg +60.0 kg x 9.81 perhaps

 

[TSny]

The total force of gravity is equal to the weight of the person plus the weight of the ice. Post #35 has the weight of the person. Post #31 has the weight of ice. Adding these together gives you the left side of F(g) = F(a). The right side of the equation is the buoyant force given in post #20.