Calc Density Unknown Liquid: Buoyancy & Tension | Fluid Physics

[racassidy]

A styrofoam block with a volume of 5.00cm cubed and a density of 45 kg/m cubed is submerged in an unknown liquid tethered from floating to the surface by a rope fixed to the bottom of the container. the tension in the rope measures 3.63x10^-2 N. Determine density of unknown liquid.

I set buoyant force equal to mass x gravity since the styrofoam would be at the surface if not for the rope and substituted in density x gravity x volume of water for buoyant force but i think i am doing something wrong. Can anyone help?

 

[edgepflow]

Include the tension of the rope in the force balance.

 

[racassidy]

ok. so buoyant force=mg-tension, and then density x volume x gravity= m x g -T?

it dosent give the mass of the block though

 

[Dadface]

buoyant force=mg+T