Experiment 1: Fluid Statics

Purpose:
In this lab our objective was to measure the buoyant force of a metal cylinder in three different ways.

Equipment:

• force probe
• string
• beaker
• metal cylinder (mass)
• graduated cylinder
• caliper

Set Up/Data:
The first technique was to weigh the metal cylinder using a force probe first in the air and then in the water.

The buoyant force equals the difference between the weight of the air and the weight in the water

                                         

For this method B = 0.3740 ± 0.2 N.

The second technique used was the overflow technique. We filled a graduated cylinder with water to the top. A beaker's mass was recorded and then the beaker was set underneath the cylinder to catch the water. The metal was placed in the cylinder and the water overflowed over the top of the tube. This extra water would add to the mass of the beaker. The weight of the extra water is the buoyant force on the cylinder.

mass of beaker = 0.14207 ± 0.01 kg

mass of beaker + water = 0.18013 ± 0.01 kg

mass of water = 0.03986 ± 0.02 kg

For this method B = the weight of the displaced water = 0.03986 * 9.8 = 0.3906 ± 0.2 N

The third method was simple. A caliper was used to measure the dimensions of the metal cylinder.

h = 0.0761 ± 0.005 m

r = 0.0126 ± 0.005 m

V = 3.796 E-05 ± 3E-05 cu. m

The buoyant force once again equals the weight of the displacement water. The weight of the water is:

W = ρgV = 1000 * 9.8 * 3.796 * 10^(-5) = 0.3720 ± 0.2 N (density of water is 1000 kg/cu. m)

Summary:

1.   Compare your three values for the buoyant force.  I am interested in seeing how you treat error analysis and answer the question in terms of your uncertainties. 

B = 0.3740 ± 0.2 N,  0.3906 ± 0.2 N, 0.3720 ± 0.2 N

the average B value = 0.3789 ± 0.2

All the values are roughly around the same number. The overflow method accounts for the highest buoyant force, and the caliper method and underwater weighing are almost the same value. Therefore the overflow method is the least accurate of the three.

2. Which method do you think was the most accurate and why?

The most accurate method would be the method that gave us the experimental value closest to the true value. I think the method of underwater weighing was most accurate since the lab pro force probe can give us a better reading than measuring the dimensions of the cylinder manually by hand using the caliper or the mass of the displaced water with the scale. Although every method has a chance of error, I think the underwater weighing method is the most accurate.

3.  In part A, if the cylinder had been touching the bottom of the water container, how would that have changed your value for the buoyant force?  Would your value have been to low or too high? Explain.

If the cylinder was touching the bottom the weight recorded on the force probe would have been less than it actually is. If it was touching the bottom the tension of the string from the weight from the cylinder would not be directed upward as demonstrated in the free body diagram.

The tension would be less which means the recorded weight of the water would be less which would make the buoyant force have a higher magnitude.

Conclusion:

After conducting this experiment we successfully conducted 3 trials that gave us a buoyant force. Although they are all different techniques, the methods all came up with roughly the same magnitude for the force.