Tension in string of object suspended in liquid

[javashackgirl]

Homework Statement

an aluminum object with volume 100 cm^3 and density 2700 kg/m^3 is suspended in ethyl alcohol (density 790) by a string. what's the tension in the string?

Homework Equations

Fy = Fb + T - mg
T = mg - Fb
Fb = p_f * v_f * g = p_o * v_o * g

The Attempt at a Solution

=(p_o - p_f)p_f*v_o*g

=(2700 - 790)(790)(1*10^-4)(9.81)

Thanks!

 

[mgb_phys]

Not quite, check the units.

It might be simpler if you worked in some numbers.
Tension = weight down - boyancy up
mass = density * volume = 2700 kg/m^3 * 0.0001 m^3 = 0.27 kg
boyancy = weight of fluid = 790 kg/m^3 * 0.0001m^3 = 0.079 kg

So effective mass of block (0.27-0.079) = 0.191kg,
weight = 0.1919kg * 9.81 Newtons

 

[javashackgirl]

i figured out what i did wrong. your way was much easier, thanks :)

 

[mgb_phys]

Useful tip always put the units in your calculation or rearrangment of equations - it makes it much easier to spot any little 'opps'

Eg. to get mass from density.
mass = density * volume
kg = kg m^-3 * m^3 = kg !