Fluid Statics

There are three methods which we used to calculate the bouyant force of a fluid.

In the first method we measure the weight of the cylinder, and then place the cylinder in the fluid and measure the tension with LoggerPro. The difference between the two forces gives us the bouyant force of the liquid.

Bouyant force = Weight - Tension

data:

 mass = .11237 g

Tension = .73 N

Weight = 1.1 N

Bouyant Force = 0.37 N

In the second method, we measured the displacement of the fluid when the cylinder is dropped. Archimedes principle states that the displacement of a fluid equals the bouyant force of the fluid. 

data:

beaker = .14718 kg

beaker + water = .17872 kg

water = .0316 kg

Water displacement = Bouyant force = .31N

The third method, in my opinion is more elegant uses the fact that the volume of the cylinder will determine the displacement of the water. Since the density of the water is uniform we can simple find the displacement of the water.

water displacement = (density of water)(volume of cylinder)(9.81)

data:

height = .0771m

diameter = .0253m

Volume = 3.876 * 10^-5 m^3

Water displacement = Bouyant force = (1000 kg/m^3)(3.876*10^5m^3)(9.8m/s)

Bouyant force = .38N

error analysis:

we could have an upper bound and a lower bound for possible values since no experiment is 100 percent certain. 

In the first case:

U. mass = .11237+.00005

L. mass = .11237-.00005

U. Tension = .73 +.05

L. Tension = .73-.05

U. Weight =  1.1N

L. Weight 1.1N

U. Bouyant force = U.Weight - L. Tension = .42N

L. Bouyant force = L. Weight - U.Weight = .32N

In the second case:

U. beaker = .14718+.00005

L. beaker = .14718-.00005

U. beaker+water =.17872+.00005

L. beaker+water =.17872-.00005

U.water=U. beaker+water-L. beaker = .03164

L.water=L. beaker+water-U. beaker = .03144

U. Bouyant force = .310N

L. Bouyant force =  .308N

In the third case:

U.height = .0771 +.001

L.height = .0771-.001

U.diameter = .0253+.001

L.diameter = .0253-.001

U.Volume = .00004243

L.Volume = .00003529

U.Bouyant force = .42N

L.Bouyant force = .35N

I think that the method that was the most accurate was the third method because the value that we attained is well within the error, but also the range of error was not too great. My second choice would be the first method because the value we attained was also well within error. The second method was barely within error which concerned me, but the range of error was significantly lower than the other experiments.

If in the first method, the cylinder had fallen to the bottom of the water container, then the value we attained would be greater than the true value because then there would also be a normal force pushing upwards as well as the bouyant force of the liquid.