Determine the density of an unknown by submerging the object in water?

Determine the density of an unknown by submerging the object in water?


My teacher gave us an unknown. We tied it to a string and measured the tension in the string while the object was hanging in the air. We then submerged the object in water and measured the tension in the string again. How do we now determine the density of the unknown object?





tension of string (air) - .855N


tension of string (water) - .817N


mass of unk - 25.6g


density of water - 1000kg/m3Determine the density of an unknown by submerging the object in water?
From the original Tension:





Tension (air) = Weight of unknown = mass x g


Therefore, mass = Tension(air)/g = 0.855/9.81 = 0.0872 kg





The difference in the tension(water) and tension (air) is due to the upthrust of the water. From the Archimedes principle, this can give you the volume.





Upthrust = tension(air) - tension(water) = 0.855 - 0.817= 0.038N





but from archimedes principle:





Upthrust = density of water x volume displaced x g


[the volume displaced is equal to the volume of your object]





Therefore volume = upthrust / (density of water x g) = 0.038 / (1000x 9.81) = 3.87 e-6 m3





Therefore density of unknown = mass / volume = 0.0872 / 3.87e-6 = 22520 kg/m3