MHB Physics - Archimedes principle

bigpoppapump
Messages
5
Reaction score
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.

1620039254897.png


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.
 
Mathematics news on Phys.org
$$\dfrac{4.5 \cdot d}{4.5 \cdot h} = \dfrac{812}{1240}$$
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 …

$$\frac{h-d}{h} = 1-\frac{d}{h}
$$
 
Thank you. So by my calculations, this would have 35% floating above the surface.
 
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.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Back
Top