Floating on Ice: Calculating Volume Needed to Stay Afloat

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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 :)
 

Discussion

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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?
 
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TSny said:
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 said:
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 said:
OK. What type of fluid is being displaced?
Water ?
 
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?
 
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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?
 
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F= mass x a
60.0 kg x 9.81 m/s2=588.6 N
 
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.
 
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TSny said:
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
 
Good. To be clear. let's write this as ρice Vice 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?