Tension in the string of a submerged object

[Liketothink]

Homework Statement

An aluminum object suspended from a string with density 2700 kg/m^3 is submerged into ethyl alcohol.

what is the tension in the string? V=142 cm^3

Homework Equations

vsub/vobj=(ro)object/(ro)ethyl alcohol
p=po+rogh

The Attempt at a Solution

I tried to multiply the volume 142 cm^3 (.000142 m^3) by the density 2700 kg/m^3 to get the mass. Then I multiplied the mass by gravity since Archimedes' principle tells us that Ethyl Alcohol pushes with a force equal to the weight. But that is wrong for some reason. Please help me. Thank you.

 

[LowlyPion]

Welcome to PF.

What is the weight of the displaced ethyl alcohol?

Wouldn't you subtract it from the free weight of the object?

 

[Liketothink]

That is correct. But why would you subtract the weight of the liquid from the weight of the object? Is it because the weight I calculated was just the apparent weight?

 

[Doc Al]

I tried to multiply the volume 142 cm^3 (.000142 m^3) by the density 2700 kg/m^3 to get the mass. Then I multiplied the mass by gravity since Archimedes' principle tells us that Ethyl Alcohol pushes with a force equal to the weight.

You calculated the mass of the aluminum object, which you'll need but is not the final answer. Archimedes' principle says that the liquid pushes up with a buoyant force equal to the weight of the displaced liquid, not the weight of the object.

 

[Ophelia_S2]

I have just tried the quesiton..just going to list what i did..
Fnet = Ftension+ Fbuoyancy-Fgravity=0
Ftension = Fgravity-Fbuoyancy
=> m(object)g - P(fluid)*V(fluid)*g
=>P(object)*V(object)*g - P(fluid)*v(fluid)*g
In my case the aluminum has same density,2700kg/m^3..but i has the volum of 100cm^3
and for completely submerged object V(fluid)= V(object)...which is 1 m^3 in my case
The average value of density for ethyl alcohol i found online is 790 kg/m^2
After plug in everythign that is given and know..i got an answer of 1.87 (round of to 1.9 since 2 sig fig)
Hope that help..
P.S this question is from my mastering physics as well..and i am in first year taking introductory physics...i am using physics for scientists and engineers 2nd edition..u can find some helpful informations from chapter 15(pg456) if you didn't get what i wrote..