Experiment 1: Fluid Statics

Experiment 1: Fluid Statics

Three different methods were used to find the buoyant force on an object.

A) Underwater weighing method

The first method, a free body diagram was used (shown below) to determine the buoyant force. 

The expression for the buoyant force is as follows: 

B_F = mg - T

Using a force probe the tension was measured which is the same measurement as the the weight (mg) of the metal cylinder which had a reading of 1.102N

Submerging the cylinder in water the tension was again measured with a reading 0.742N

Using the buoyant force expression above:

B_F = 1.102-.742= 0.360N

B) Displaced Fluid Method

The mass of the dry beaker was measured to 0.14016 kg

Using a graduated cylinder, water was filled to the very top, and the graduated cylinder was placed inside the beaker. The metal cylinder was then placed inside the graduated cylinder and water was displaced into the beaker from the over flow. 

The mass of the beaker and the water measured to 0.17790kg

So the water measured to be 0.17790-0.14016= 0.03774kg

(mass of the water) X (gravity) = Buoyant Force

.03774 kg X 9.8 (m/s^2) = .370N

C) Volume of Object Method

The Volume of the cylinder can be found  by:

V_c = Pi*((d/2)^2)h

where d is the diameter of the cylinder and h is the height.

Using a vernier caliper the following measurements were found.

h = 0.076m; d = 0.0253m  

Therefore the volume is calculated to being 3.82 X 10^-5 m^3

The expression for the weight of the displaced water can be written as

W_F = ρ*V*g

where ρ is the density of water, V is the volume of the cylinder and g is gravity

W_F = 1000 kg/m^3 X 0.0000382 m^3 X 9.8 m/s^2 = 0.374N

After calculating all three different buoyant forces, the following image shows the value of the uncertainties for each of the different buoyant forces.

 Error Propagation and Uncertainty Calculation

1. In BF1 the error was calculated through logger pro and the values would change of a difference of about +/-.005N. For the BF3 the error was chosen based on the caliper and it was found that the error could only come from a difference of about +/- .01. BF2 error propagation originated from the ((max-min)/2) calculation. Comparing the three values of the buoyant force, the second buoyant force seemed to be the most accurate. Based on the error propagation graph, the values are the same for all three buoyant forces in the darkened region. But when looking at BF2 compared to the other buoyant forces, BF2 has same values with either BF1 or BF2,just in different regions from each other. 

2.  Based on the error propagation of BF2 and how it has the same values as BF1 and/or BF3 at different regions, BF2 would be the most accurate. BF3 and BF1 hardly ever have the same values, just only for a small portion of the graph. 

3. if the cylinder had been touching the bottom of the water container in part A, the normal force from the bottom would change the value of the buoyant force. Recall that buoyant Force = Tension - Weight. When the cylinder touches the bottom, the normal force from the bottom will cause the tension to decrease, resulting in a higher buoyant force. Therefore when the cylinder touches the bottom of the water take the buoyant force will too high.