What Is the Minimum Volume of Ice Needed to Support a Person on a Lake?

• LunarJK
In summary, you have found that the volume of ice that a 73.4 kg person can stand on without getting their feet wet is 0.9175m3.
LunarJK

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.
Vwater displaced = (73.4 kg) / (1000 kgm-3)
Vwater displaced = 0.0734m3

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:
pwaterVwater displaced = piceVice
Vice = pwaterVwater displaced / pice
Vice = (1000kgm-3)(0.0734m3) / (920kgm-3)
Vice = 0.0798 m3

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

Last edited:
You've just worked out what volume 73.4 kilos of ice would be. So you know when the man steps on the ice and the ice sinks into the water due to his weight, it must displace0.0734m3 of water to support his weight without him getting his feet wet. So what you need to do is find what volume of ice has a volume of 0.0734m3 sticking out of the water when its floating there without the man.

Kurdt said:
You've just worked out what volume 73.4 kilos of ice would be. So you know when the man steps on the ice and the ice sinks into the water due to his weight, it must displace0.0734m3 of water to support his weight without him getting his feet wet. So what you need to do is find what volume of ice has a volume of 0.0734m3 sticking out of the water when its floating there without the man.

Alright... well I think I'm correct in saying something floats when its weight is equal to the weight of the displaced fluid (in this case fresh water). So I've figured out that the volume of ice floating above the water is 0.0734m3, than the total volume of the block of ice can equal 0.0734m3+ x, where x is the volume of the ice under water, and therefor also the volume of water displaced with just the ice floating.

So with just the floating ice:

piceVice = pwaterVwater
(920 kgm3)(0.0734m3 + x) = (1000 kgm3)x
(0.0734)(920)+(0.0734)(x) = 1000x
67.528 = 1000x - 920x
67.528 = x (1000-920)
x = 0.8441m3 --> volume of ice under water

Plug this value back into the Volume of ice, which was 0.0734m3 + x, therefore the total Volume of ice for a 73.4 kg man to stand on without getting his feet wet would be 0.9175m3 ?

Very good!

Kurdt said:
Very good!

Killer, thanks.

What is the concept of basic buoyancy?

The concept of basic buoyancy is the upward force that a fluid exerts on an object that is immersed in it. This force is equal to the weight of the fluid that the object displaces.

What factors affect buoyancy?

The factors that affect buoyancy include the density of the fluid, the volume of the object, and the gravitational force acting on the object.

How do you calculate buoyancy?

Buoyancy can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. This can be calculated by multiplying the density of the fluid by the volume of the displaced fluid and the gravitational acceleration.

What is the difference between buoyancy and weight?

The main difference between buoyancy and weight is that buoyancy is a force exerted by a fluid on an object, while weight is the force of gravity acting on an object. Buoyancy can either be a greater or lesser force than weight, depending on the density and volume of the object compared to the fluid.

How does buoyancy affect objects in water?

Buoyancy affects objects in water by providing an upward force that counteracts the downward force of gravity. This allows objects to float or sink depending on their density and volume. Objects with a lower density than water will float, while objects with a higher density will sink.

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