# Floating Ice Block: Height & Penguin Capacity

• mattmannmf
In summary, a rectangular block of ice with dimensions of 5m x 5m x 0.5m and a density of 917 kg/m3 floats in seawater with a density of 1025 kg/m3. To determine the height of the ice block above the water level, we can use the fraction of the total volume of the ice that is submerged (917/1025) to find the fraction of the total height of the ice that is above water. For question B, we can use the principle that a floating object displaces its weight in water to determine how many penguins of mass 19 kg each can stand on the ice block before their feet get wet. By comparing the weight of the ice
mattmannmf
A rectangular block of ice 5 m on each side and 0.5 m thick floats in seawater. The density of the seawater is 1025 kg/m3. The density of ice is 917 kg/m3.

a) How high does the top of the ice block float above the water level?

b) How many penguins of mass 19 kg each can stand on the ice block before they get their feet wet?

So what i did first was 917/1025= fraction of total volume of ice submerged..than subtracted it by 1 to find fraction of ice above water... I am just not sure where to go from there..i can take the fraction of the volume...but they are still just looking for height...

For part A you know the fraction below the water - so what fraction of the total height is above water.

For B - a floating object displaces water equal to it's weight.
So if the block was totally submerged how much water would it displace. How much more mass is this than the mass of the ice - the difference is the penguins

I tried that for A and got it wrong...

917/1025= .8946*5= 4.47 (under water)-5= .52 above water right? i checked it and it was wrong

Erm if it's only .5 high it's difficult to see how you can have .52m above water.
What about (917/1025) * 0.5m below water or 0.5 - (917/1025) * 0.5m above.

Quick check 917 is roughly 90% of 1025 so you expect to have roughly 10% above water so the answer must be about 0.05m

ahh yep...thats correct..idk why i was getting a decimal place off...

Im not really understanding B.. for what you wrote

The volume of the berg is 5m * 5m * 0.5m
It weighs 917kg/m^3 so you can work out how many kg this is.
When it is underwater it is displacing the same volume (5m * 5m * 0.5m) of water that weighs 1025kg/m^3
So work out how much the ice weighs and how much the water weighs. The extra weight of the water is the weight needed to force the ice down = the penguins

## 1. How does the height of a floating ice block affect its penguin capacity?

The height of a floating ice block does not directly affect its penguin capacity. However, a taller ice block may provide more surface area for penguins to rest on, therefore potentially allowing for a higher penguin capacity.

## 2. What factors determine the maximum height of a floating ice block?

The maximum height of a floating ice block is determined by the density of the ice, the temperature of the surrounding water, and the weight of any objects placed on top of the ice.

## 3. Can the height of a floating ice block change over time?

Yes, the height of a floating ice block can change over time due to factors such as melting or added weight. This can also affect the penguin capacity of the ice block.

## 4. How do penguins affect the stability of a floating ice block?

Penguins can affect the stability of a floating ice block by shifting their weight and movements on the ice. This can potentially cause the ice block to tip or become unstable.

## 5. Can a floating ice block support a large number of penguins?

The capacity of a floating ice block to support penguins depends on its size, shape, and stability. It is important to consider these factors when determining the maximum number of penguins that can safely rest on the ice block.

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