The determination of the weight of the metal cylinder in air was the first step and the weight of it completely submerged in water was the second. It weighed 200g +-1g in the air and 1.75 +- .2 N in the water. After drawing a free body diagram of the cylinder, the bouyant force and tension added together must equal the weight mg. The tension was measured using the force probe and the weight was already measured giving the bouyant force in terms of the weight of the cylinder and the tension in the string as
B = mg - T
The bouyant force was then calculated to be .212 N. The second method uses Archimede's principle to calculate the bouyant force which is equal to the weight of the displaced water. The bouyant force equals .438 Newtons. The third method uses the volume of the cylinder to determine the volume of the displaced water. Measurements of the height and diameter of the cylinder are taken and the formula for volume of a cylinder must be known as well.
Density(Volume)gravity = Mass(gravity)
The density of water is 1000 kg/ m^3 giving the bouyant force equal to .313 Newtons. For the three values of buoyant force, the results were .212N, .438N, .313N +- .3 N. Uncertainties arise from human error of measurements especially with measuring the mass of the cylinder and water. Other uncertainties arise from the water not 100% overflowing into the overflow cup. The most accurate would probably be the first method, because there is less uncertainties. The overflow method is slightly estimated since some water does still stay on the side. In part A, if the cylinder had been touching the bottom of the water container, the values for the buoyant force would not be accurate since it would not be completely acted on by buoyant force. If it was touching the bottom, the value for buoyant force would be lower.
