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 !

 

[rwisz]

I would first like to clarify the units used in the given information. The volume of the object is given in cubic centimeters (cm^3) while the densities are given in kilograms per cubic meter (kg/m^3). To ensure consistency, the volume should be converted to cubic meters (m^3) by dividing by 1,000,000. This gives a volume of 0.0001 m^3 for the object.

Using the given formula for buoyant force (Fb = p_f * v_f * g), we can calculate the buoyant force of the object in ethyl alcohol:

Fb = (790 kg/m^3) * (0.0001 m^3) * (9.81 m/s^2)
= 0.7749 N

Next, we can calculate the weight of the object using its mass (density * volume) and the acceleration due to gravity:

mg = (2700 kg/m^3) * (0.0001 m^3) * (9.81 m/s^2)
= 2.6517 N

Now, we can plug these values into the equation Fy = Fb + T - mg to find the tension in the string:

T = mg - Fb
= (2.6517 N) - (0.7749 N)
= 1.8768 N

Therefore, the tension in the string is approximately 1.8768 N. It is important to note that this is an ideal calculation and may differ in real-world scenarios due to factors such as air resistance and imperfections in the string.