# Tension in the string of a submerged object

1. Jun 12, 2009

### Liketothink

1. The problem statement, all variables and given/known data
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

2. Relevant equations
vsub/vobj=(ro)object/(ro)ethyl alcohol
p=po+rogh

3. 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.

2. Jun 12, 2009

### 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?

3. Jun 12, 2009

### 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?

4. Jun 12, 2009

### Staff: Mentor

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.

5. Nov 26, 2010

### Ophelia_S2

I have just tried the quesiton..just gonna 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 quesiton 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..