- #1

LunarJK

- 6

- 0

## Homework Statement

A slab of ice floats on a freshwater lake. What minimum volume must the slab have for a 73.4 kg person to be able to stand on it without getting his or her feet wet?

(use 920kg/m^3 as density of ice and 1000 kg/m^3 for the density of freshwater)

## Homework Equations

Archimedes Principle:

Fg = Fb

mg = pVg

## The Attempt at a Solution

So my problem was I was really sick and I missed my couple first lectures on this topic. I've learned what I can from my textbook... but i think I'm missing a step or something in this problem.

This is what I figured I should do:

Since the buoyant force is equal to amount of liquid displaced, i plugged in the mass of the person and density of freshwater into Archimedes equation to solve for volume of water displaced.

V

_{water displaced}= (73.4 kg) / (1000 kgm

^{-3})

V

_{water displaced}= 0.0734m

^{3}

Than from here, I really haven't worked with this subject for long enough to understand what i can and cannot do. My next attempt would be to solve for the volume of ice by doing:

p

_{water}V

_{water displaced}= p

_{ice}V

_{ice}

V

_{ice}= p

_{water}V

_{water displaced}/ p

_{ice}

V

_{ice}= (1000kgm

^{-3})(0.0734m

^{3}) / (920kgm

^{-3})

V

_{ice}= 0.0798 m

^{3}

Is this the correct answer? if not what should i have done?

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