Bouyancy Question: Two weights on strings, with one weight submerged

[norcal36]

Homework Statement

You have two scales with a weight suspended from them on a string. Scale one has a tension of T1 and scale two has its mass submerged in water with tension T2. If you have T2<T1, find the density of the weight in terms of only density of the water, T1 and T2.

Relevant Equations

Density = mass/volume
Volume = mass/density
mass = density*volume
Buoyancy = Density of liquid*Volume Displaced*gravity

Hi new to the physics world and the symbiology is hard to understand completely. Attached is the work I've done to a final solution but I can't seem to get the answer in terms of only density of water and T1 and T2. Thank you for any assistance.

[ Mentor Note -- Word file replaced with a screenshot. Please use PDF or JPEG format for posting files. ]

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[BvU]

Hello norcal, $\qquad$ $\qquad$ !

If you can use MS equation, you can use $LaTeX$ too -- makes ist much easier to assist

I love your word 'symbiology'
-- in this context I propose you create a variable $V$ for the volume of the weight. Definition of density $\rho$ (using a $\delta$ is confusing to others) is $m = \rho V$ . Rings a bell in the algebraic treatment ? [edit] greyed out after a cup of coffee and a decent read of your word doc

[edit] never mind, you are nearly there already: your last line reads $$\rho_b = {mg\; \rho_w\over T_1-T_2}$$ and to get it in the required form, you need something else for $mg$. Guess ...

 

[norcal36]

Thank you for that insight. With that I do get the correct answer with replacing the mg with T1. However, is there a way to manipulate the equation without just replacing that mg with T1? Again thank you for the insight!

 

[norcal36]

Also I apologize for my inexperience with formatting . I don't know what LaTeX is and only way I could show my work was to use Word Possessor.

 

[haruspex]

Also I apologize for my inexperience with formatting . I don't know what LaTeX is and only way I could show my work was to use Word Possessor.

Click the link @BvU provided in post #2 for LaTeX.
Or use the pull-downs above the text entry panel:
$\sqrt x$ for Greek letters, math symbols..
... for subscripts and superscripts.

 

[norcal36]

Thanks!