Physics - Archimedes principle

In summary, the question is asking for the proportion of a wooden board, with an area of 4.55m^2 and a density of 812 kg/m^-3, that would float above the surface of the dead sea, which has a density of 1240 kg/m^-3. Using Archimedes' principle, we can determine that the proportion of the board above the surface is equal to 1 minus the submerged depth over the physical height. This can be simplified to 35% without needing to know the other dimensions of the board.
  • #1
bigpoppapump
5
0
Im having trouble with the following question regarding Archimedes principle.

A wooden board with an area of 4.55m^2 is dropped into the dead sea (P sea- 1240 kg/m^-3). Calculate the proportion that would float above the surface. (P wood - 812 kg/m^-3).

My understanding is that the volume (V sub) of the submerged object over the total volume (V) of the object is equal to the density (P wood) of the Object over the density (P sea) of the water.

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Because the question has given me an area and not a volume or even dimensions to calculate the volume, i am confused as to how to complete the question.
 
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  • #2
\(\displaystyle \dfrac{4.5 \cdot d}{4.5 \cdot h} = \dfrac{812}{1240}\)
where $d$ is the submerged depth of the wood and $h$ is the physical height of the wood

note the question being asked is the proportion of the wood that floats above the surface …

\(\displaystyle \frac{h-d}{h} = 1-\frac{d}{h}
\)
 
  • #3
Thank you. So by my calculations, this would have 35% floating above the surface.
 
  • #4
The point is that you don't need to know the other dimensions- they cancel out of the fraction:
$\frac{V_{sub}}{V}= \frac{d_{sub}A}{dA}= \frac{d_{sub}}{d}$
where V is the volume of the stick, $V_{sub}$ is the volume of the submerged part, d is the thicknes of the stick, $d_{sub}$ is the thickness of the submerged part, and A is the cross section of the stick which is the same both submerged and not submerged.
 

FAQ: Physics - Archimedes principle

1. What is Archimedes principle?

Archimedes principle is a law of physics that states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. This principle is used to explain why objects float or sink in a fluid.

2. Who discovered Archimedes principle?

Archimedes principle was discovered by the ancient Greek mathematician and scientist, Archimedes, in the 3rd century BC. He is also known for his contributions to mathematics, engineering, and astronomy.

3. How is Archimedes principle applied in real-life situations?

Archimedes principle is applied in various real-life situations, such as shipbuilding, hot air balloons, and submarines. It is also used in determining the density of an object, as well as in the development of water displacement methods for measuring volume.

4. What is the relationship between an object's density and its buoyancy according to Archimedes principle?

According to Archimedes principle, an object will float if its density is less than the density of the fluid it is submerged in. If the object's density is greater than the fluid's density, it will sink. This is because the buoyant force is greater when the object displaces more fluid.

5. Can Archimedes principle be applied to gases?

Yes, Archimedes principle can also be applied to gases. It states that the buoyant force on an object in a gas is equal to the weight of the gas that the object displaces. This principle is used in the design of hot air balloons and other air-based transportation methods.

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