Experiment 1: Fluid Statics

This experiment was designed to measure the buoyant force of a metal cylinder with three different methods, and compare which of the methods was the most accurate.
Method 1: underwater weighing

In the first method we used a free body diagram to determine the expression of the bouyant force was B = mg-T.  The mg was found by the tension in the string in air with a force prob.  "T",the tension when the cylinder is submerged, was obtained by a force probe when the cylinder is in water.  From the measurements the buoyant force was determined.
B = mg-T

mg(N)	T(N)
1.112	0.8064
1.088	0.6268
avg mg	avg T
1.1	0.7166

B = mg_avg – T_avg = 0.3834N ±0.1556
Method 2:  Displacement fluid method

We measured the buoyant force by the weight of water that overflowed out of a full graduated cylinder into a beaker as the metal cylinder. According to Archimede’s principal the weight of the over flow is equal to the buoyant force. So we found the mass of the water over flow and multiplied it by gravity to obtain the buoyant force. Uncertainty of uncollected water is estimated to 1 gram.

Beaker mass(kg)	0.00434
Beaker + water mass(kg)	0.04243±0.001
Water mass(kg)	0.03809
B(N)	0.373663

B= 0.373663±0.01962
Method 3: Volume of object

We found the buoyant force is the product of the density of the liquid and the volume of the object. Since the object was a cylinder we use V = πr²h.  We used digital calipers to make the measurements.  However we could not measure the hook to add uncertainty.. We found the weight of water displaced by the equation  

.

h	0.0766
r	0.0126
volume	3.81856*10^-5±0.000002
water density	1000 kg/m3
B(N)	0.37460064

Summary
Question 1
Method 1: B = 0.3834N ± 0.1556
Method 2: B = 0.374N ± 0.01962
Method 3: B = 0.374 N ± 0.03924
The uncertainty of method 1 was the largest because of the fluctuating values of the force probe.  Method 3 had some uncertainty because of the sum the hook that was not measured.  The most accurate was Method 2, which had the least uncertainty.
Question 2
The most accurate method was the Displaced fluid method, since it produces the least uncertainty.
Question 3
If the cylinder was touching the bottom of the water container in part A, the buoyant force would be too large because the tension of the wire would be decreased by the normal force of the container.