How Small Can the Iceberg Get Before the Polar Bear Gets Wet Feet?

[CR9]

Homework Statement

A polar bear of mass 520 kg is floating on an iceberg in the ocean. As the ice melts, how small can the iceberg get before the bear gets wet feet? (The answer should be the volume of the iceberg).

Homework Equations

Buoyant Force, Fb = p(fluid)V g

From a table in my textbook, p(ice)= 920 kg/m^3 and p(sea water)= 1030 kg/m^3

The Attempt at a Solution

I did a sum of the forces in the y-direction to be zero and obtained:

Fb - W(bear) - W(ice)= 0
p(sea water)V = 520 + p(ice)V
V= 4.73 m^3

My answer is wrong... PLease help...

 

[PeterO]

Homework Statement

A polar bear of mass 520 kg is floating on an iceberg in the ocean. As the ice melts, how small can the iceberg get before the bear gets wet feet? (The answer should be the volume of the iceberg).

Homework Equations

Buoyant Force, Fb = p(fluid)V g

From a table in my textbook, p(ice)= 920 kg/m^3 and p(sea water)= 1030 kg/m^3

The Attempt at a Solution

I did a sum of the forces in the y-direction to be zero and obtained:

Fb - W(bear) - W(ice)= 0
p(sea water)V = 520 + p(ice)V
V= 4.73 m^3

My answer is wrong... PLease help...

I like your answer!

 

[RTW69]

I also think your answer is correct.

 

[dynamicsolo]

I also am getting your answer: the iceberg is just completely submerged, so you should be using its full volume in the buoyancy force calculation. Is what is telling you this is wrong an answer in the back of a textbook, or a computer problem system?

 

[rwisz]

I would first like to clarify the question. When it says "how small can the iceberg get before the bear gets wet feet," I assume it means how much of the iceberg can melt before the bear's feet touch the water.

To solve this problem, we can use Archimedes' Principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. In this case, the buoyant force is equal to the weight of the polar bear and the iceberg combined.

Using the given densities, we can calculate the volume of the polar bear as 520 kg / 1030 kg/m^3 = 0.504 m^3. Since the polar bear and the iceberg are floating together, the total weight is equal to the weight of the fluid displaced.

Therefore, the volume of the iceberg can be calculated as follows:

p(ice)V(ice) + p(sea water)V(ice) = p(sea water)(V(ice) + V(bear))
920 kg/m^3 V(ice) + 1030 kg/m^3 V(ice) = 1030 kg/m^3 (V(ice) + 0.504 m^3)

Solving for V(ice), we get V(ice) = 0.504 m^3.

This means that the volume of the iceberg can decrease by 0.504 m^3 before the bear's feet touch the water. However, this does not necessarily mean that the iceberg will completely melt before the bear gets wet feet, as the bear's weight will also contribute to the buoyant force as the iceberg melts.

In conclusion, using Archimedes' Principle, we can determine the volume of the iceberg that can melt before the bear's feet touch the water. However, further calculations would be needed to determine if the iceberg will completely melt before the bear gets wet feet.