Verifying information on Archimedes

In summary, the conversation discusses a homework problem involving determining the height of an object immersed in water, given its dimensions and densities. The solution involves using equations for volume, specific weight, weight of object, and upward thrust of Archimedes. The conversation also includes a question about the calculation process and a suggestion for a different approach to solving the problem.
  • #1
fessia175
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Homework Statement


This is the information and calculations I have been given, but am not sure it is correct. Please verify.
An object in the form of a cube with sides of 50 cm is immersed in water. Determine the height of immersed object, knowing that the density of water is 1000 kg/m^3 and the density of the object is 800 kg/m^3.


Homework Equations


V = lxbxh
Specific weight = density x gravity
Weight of Object = Specific weight x Volume


The Attempt at a Solution


/ = devided
Volume object = 0.5^3 = 0.125 m^3
γ Object = 800 x 9.81 = 7848 N/m^3
γ Liquid = 1000 x 9.81 = 9810 N/m^3
Weight of Object = 7848 N/m^3 x 0.125 m^3 = 981 N
Ab = Area of base

If the object floats Weight of Object = Upward thrust of Archimedes

981/ 9810 (0.5) = 1/5 = 0.2 m
Why is the 9810 multiplied by 0.5 and where does the 0.5 come from?
The calculation given for height immersed is : upward thrust / γ liquid x Ab (which in this case should be .25 m^2.

I can only continue figuring the rest of this out once the above query has been answered.

Thanking in advance
MOM ( trying to) helping with homework
 
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  • #2
"981/ 9810 (0.5) = 1/5 = 0.2 m"

The above makes no sense to me. Newtons are being divided by N/m^3 implying the unit of 0.5 is m^2 in order for the result to have the unit of m.

A straightforward way to look at this problem (because it has straight vertical sides and bottom is planar and horizontal) is to determine what pressure multiplied by the area of the bottom gives a force that equals the weight of the object. The pressure is fluid density multiplied by depth.
 

FAQ: Verifying information on Archimedes

1. How do we know that the information we have about Archimedes is accurate?

The accuracy of information on Archimedes can be verified through various primary and secondary sources. Primary sources include written accounts from ancient Greek and Roman historians, such as Plutarch and Livy, who lived during or shortly after Archimedes' lifetime. Secondary sources, such as modern biographies and scholarly articles, analyze and interpret these primary sources to provide a more comprehensive understanding of Archimedes' life and work.

2. Did Archimedes really invent the lever and the concept of buoyancy?

While Archimedes is often credited with inventing the lever and discovering the principles of buoyancy, he was not the first person to discover or use these concepts. However, he did make significant contributions to their development and popularization through his famous works "On the Equilibrium of Planes" and "On Floating Bodies".

3. How do we know that the stories and anecdotes about Archimedes are true?

The stories and anecdotes about Archimedes, such as his famous "Eureka!" moment and his use of mirrors to set fire to enemy ships, are often difficult to verify as they were written long after his death. While some of these stories may have a basis in truth, they should be approached with caution and considered as more of a representation of Archimedes' character and brilliance rather than factual accounts.

4. What is the most reliable source of information about Archimedes?

The most reliable source of information about Archimedes would be his own writings, such as his treatises "On the Sphere and Cylinder" and "Measurement of a Circle". These works provide insight into his mathematical and scientific discoveries and are considered more reliable than secondary sources written centuries later.

5. Are there any controversies surrounding the information on Archimedes?

One controversial aspect of Archimedes' life is his death, which according to some sources, was at the hands of a Roman soldier during the capture of Syracuse. However, this account is not mentioned in any primary sources and is believed to be a later addition to his biography. Additionally, some scholars debate the accuracy of certain mathematical proofs attributed to Archimedes, as they may have been discovered by other mathematicians before him.

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