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

In summary, the new physics student is trying to understand the symbology and is having difficulty because of the complexity of the equation and the different symbols used. The student has found help with the equation using a word processor and LaTeX, but is still having difficulty understanding everything.
  • #1
norcal36
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0
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. ]

1575213822688.png

​
 
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  • #2
Hello norcal, ##\qquad## :welcome: ##\qquad## !

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

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 :smile:

[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 ...
 
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  • #3
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!
 
  • #4
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.
 
  • #5
norcal36 said:
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.
 
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  • #6
Thanks!
 

1. How does the weight of an object affect its buoyancy?

The weight of an object does not directly affect its buoyancy. Instead, the buoyancy of an object is determined by its volume and the density of the fluid it is submerged in. However, the weight of an object can indirectly affect its buoyancy if it changes the volume of the object (e.g. compressing a balloon will decrease its volume, making it less buoyant).

2. Why does one weight sink while the other floats in this experiment?

The weight that floats has a lower density than the weight that sinks. Density is the mass of an object per unit of volume. If an object is less dense than the fluid it is submerged in, it will float. If it is more dense, it will sink.

3. What is the relationship between buoyancy and the weight of the fluid displaced?

According to Archimedes' principle, the buoyant force on an object is equal to the weight of the fluid it displaces. This means that the more fluid an object displaces, the greater the buoyant force acting on it, and the more likely it is to float.

4. Can an object with a higher density than water float?

Yes, an object with a higher density than water can float if it has a shape that allows it to displace enough water to create a buoyant force greater than its own weight. This is why some ships made of steel are able to float, even though steel is denser than water.

5. How does the depth of immersion affect the buoyancy of an object?

The deeper an object is immersed in a fluid, the greater the pressure acting on it. This increased pressure results in a greater buoyant force, making the object more likely to float. However, if the object is submerged too deeply, the pressure may become too great and cause it to sink. This is why objects that are neutrally buoyant (with a density equal to the fluid) can float at different depths depending on their shape and mass.

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