Steel floating in mercury problem

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Homework Help Overview

The problem involves a steel cylinder floating in mercury, specifically determining the length of the cylinder that remains above the surface of the liquid. The context includes concepts of buoyancy and density comparisons between the steel and mercury.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the buoyancy equation and the relationship between the densities of the steel and mercury. There are attempts to calculate the submerged length and identify potential arithmetic errors. Questions arise about the interpretation of the problem, particularly regarding what is being asked about the length of the steel above the surface.

Discussion Status

Participants are actively engaging with the problem, sharing their calculations and questioning each other's approaches. Some guidance has been offered regarding the conceptual understanding of submerged versus above-surface lengths, but there is no explicit consensus on the correct answer yet.

Contextual Notes

There are mentions of discrepancies in answers provided by the homework platform and potential errors in the problem statement itself. Participants are also considering rounding errors and the specific values used for densities.

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Homework Statement


A 17.85 cm diameter, 32.4 cm tall steel cylinder (ρsteel=7900 kg/m3) floats in mercury. The axis of the cylinder is perpendicular to the surface. What length of steel is above the surface?


Homework Equations


vsub/vobj=(ro)obj/(ro)liquid


The Attempt at a Solution

A
I canceled the two areas so the equation is d/h=(ro)obj/(ro)liquid and then I solved for d. H equals to 32.4 cm I think. I don't know what I'm doing wrong. Please help. Thank you.
 
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What makes you think you're doing anything wrong? What was your answer? Do you know what the answer is supposed to be?
 
I'm using Loncapa for my class. I received .192 m for an answer an it says I'm wrong.
 
I get a different answer. It's close, but you may have a rounding error. Check your math! Edit, also, what value did you use for the density of mercury?
 
13534 kg/m^3
 
I also tried .189 m but that was wrong as well.
 
Pay close attention to what question you're being asked. You are being asked what length of steel is ABOVE the surface. The calculation I posted is NOT for the portion that is above the surface. If you don't know what I mean, then here's a huge hint: what do you think the sub stands for in the formula you posted, vsub/vobj?
 
I tried that as well. The .189 m ,. But that didn't work. It's ok though thank you for your help still. The teacher must have done an error in the homework problem as he frequently does.
 
  • #10
NO! Read my latest post! You have made a conceptual mistake. But what you have to do to get from 0.189 m to the right answer is very easy. ;)
 
  • #11
Oh! Yeah that's right! It's the length submerged so I have to subtract it from the original length. Thank you so much, I appreciate it.
 
  • #12
No problem! I'm glad you got it!
 

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