Fluid Statics

The objective was to measure the buyont force of a metal cylinder in three distinct fashions. One may refer to the first technique used as the Water Weighing Method, since the metal cylinder was submerged in water to find buyont force. The second was the Displaced Fluid Method where Archimede's principle was used to calculate the buyont force, and the third is the Volume of Object Method where the volume of the cylinder was used to find the volume of the displaced water and multplied by gravity and the density of water to obtain the buyont force, rho*g*V.

Equipment:

1. Force Probe
2. String
3. Overflow Can
4. Beaker to Catch Overflow
5. Metal cylinder
6. Meter Stick
7. Verinier Caliper or Micormeter Caliper

1) The Under water Method:

To measure the buyont force, one initial used a force sensor and measure net to find the weight of the cylinder in air. This value was 1.101 N. Once that was accomplished, the metal cylinder was drowned in water to find the new tension in the spring, which was 0.730 N. After drawing the free-body diagram of the cylinder, one can find the buyont force.

Here one sees F_b = mg-T.  This value is 0.371 N. 

2) Displaced Fluid Method:

In this case, the metal cylinder was dunked into a graduated cylinder filled with water--to the very, very top.  From there the water was allowed to overflow into a large beaker.  The mass of the beaker before the cylinder was dunked was measured to be 0.1282 +/- 0.00005 kg.  Once all the water from the graduated cylinder was done spilling into the beaker, the mass of the beaker plus water was obtained.  This value was 0.1672 +/- 0.00005 kg; hence, the mass of the water was 0.039 +/- 0.0001.

From here one can use Archemides Principle which suggest that the weight of the ater displaced is equal to the buyont force; therefore, the buyont force for the second method was 0.3812 +/- 0.0001 N.

3) Volume of Object Method:

The volume of a cylinder today is defined as pie*r^2*h, where r is the radius of the cylinder and h is the height of the cylinder. These values are 0.076 +/- 0.0005 and 0.025 +/- 0.0005 meters respectively.  Nonethelss these values are used to find the volume of the amount of water that would be displaced if suppose the cylinder was sitting in an arbitrary position in the pacific ocean. The volume is then 3.73 *10^-5 +/- 3.2*10^-6 meters cubed.  Here once can see that the buyont force for this third part is 0.38024 +/- 3.2*10^-6 Newtons by multyplying the volume by the gravity g and density of water rho(note that the density of water is 1000kg/m^3). 

Boiled down to its purest form, the technique that produced the most accurate buyont force was the first method--The Under water Weighing Method--because the error in the force sensors has to be much smaller than the error rooted in humans introduced in the last two methods ideally. So if one had to gamble on either of the three, the first basket should get all of the eggs--or at least the majority of them.