Use Archimedes' law of buoyancy.
- to calculate what fraction of the volume of an iceberg floating in the ocean is above the water level.
-how many 20kg penguins can be supported by a 1000 cubic meter iceberg that is on the verge of being completely submerged?
physics-buoyancy - bobpursley, Monday, May 9, 2011 at 6:12am
you need the density of ice, and the density of sea water. abbreviate these as di, and ds
weight of iceberg: di*VolumeIce*g
weight of displaced seawater: ds*VolumeIce*k*g where k is a fraction
Archemedes says these two forces are the same.
di*volumice=ds*volumeice*k
solve for k.
Now, knowing k, you can solve the penguin question.
volumeice*di*g+ mg =volumeice*ds*k*g
so when k equals 1, it is submerged, so
m=volumeice(ds-di)
numberpenguins*20=m=above
solve for number penguins.
To answer these questions, we will use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. It can be expressed as:
Buoyant force = Weight of the fluid displaced
1. Fraction of iceberg above water level:
To calculate the fraction of an iceberg above the water level, we need to compare the volume of the submerged portion of the iceberg to the total volume of the iceberg.
Let's assume that the iceberg has a total volume of V_total and a submerged volume of V_submerged. The fraction of the iceberg above the water level can be calculated using the formula:
Fraction above water level = V_submerged / V_total
To measure the volume of the submerged portion of the iceberg, you can use various methods such as sonar imaging, or by measuring the visible portion and estimating the submerged part. Once you have the values for V_submerged and V_total, you can calculate the fraction above the water level.
2. Number of penguins supported by an iceberg:
To determine the number of penguins that can be supported by an iceberg, we need to consider the buoyant force provided by the iceberg and the weight of the penguins.
The buoyant force exerted by the iceberg is equal to the weight of the displaced water. The weight of the displaced water can be calculated using the density of water (ρ_water) and the submerged volume of the iceberg (V_submerged). It can be expressed as:
Weight of displaced water = ρ_water * V_submerged * g
Where g is the acceleration due to gravity.
Now, we need to compare the weight of the displaced water with the weight of the penguins. If the iceberg is on the verge of being completely submerged, then the buoyant force is equal to the total weight of the iceberg and the penguins combined.
Number of penguins = (Weight of submerged iceberg + Weight of penguins) / Weight of each penguin
Here, you'll need to know the weight of each penguin, and you can substitute the value obtained for the weight of the submerged iceberg.
So, to answer the question, you'll need to know the submerged volume of the iceberg, the density of water, the weight of each penguin, and the weight of the iceberg.