Fluid Statics Lab

During this "Fluid Statics" lab the objective was to find the Buoyant Force experimentally using various methods and compare the results.

Equipment needed:

• Force Probe 
• Logger Pro 
• String 
• Graduated Cylinder 
• Bucket (to catch overflow) 
• Metal cylinders with hooks 
• Vernier caliper or micrometer caliper 

A. Underwater Weighing Method

This method measures the buoyant force by taking the difference of the weight of the cylinder in the air and in the water.
The force probe was connected to Logger Pro and mounted on a ring stand. The Force probe was then attached to some known weights (via string) in order to calibrate the sensor. Finally the metal cylinder was attached to the force probe.



The force of the tension was taken and recorded to be 1.09 ± 0.01 N. This is also the measure of the weight of the metal cylinder since the system was in equilibrium. Then the graduated cylinder was nearly filled with water and the metal calendar was placed inside while still attached to the system.

The new reading of the tension was 0.69 ± 0.02 N.




The Buoyant Force was 0.40 N ± 0.03.


B. Displaced Fluid Method

The Displaced Fluid Method measures the buoyant force by finding the weight of the water displaced

The mass of the bucket was measured to be 0.252 kg ± 0.001.

The graduated cylinder was then filled with water and placed in the bucket. The metal cylinder was placed in the graduated cylinder and a volume of water overflowed from the graduated cylinder equal to the volume of the metal cylinder.




The cylinders were removed from the bucket and the mass of the bucket with the overflow water was taken. It was 0.289 kg ± 0.001.




By Archimedes principle the weight of the displaced water and the buoyant force is 0.363 N ± 0.020.


C. Volume of Object Method

With the Volume of Object Method you fine the volume of the object and with the density of the liquid you are able to find the weight of the water displaced (similar to the previous one).



The metal cylinders dimensions were taken with a micrometer caliper and were as follows:

height: 0.0762± 0.00005m Diameter: 0.0253± 0.00005m



Using the dimensions to find the volume and using the known density of water and acceleration due to gravity the buoyant force was found to be 0.375 N ± 0.018.

Conclusions:

All the values were consistent within the uncertainty. For the first method the uncertainty could have come from measuring the tension in water. The graduated cylinder was a tight fit and if the metal cylinder was touching the sides of the graduated cylinder then it could have given a higher reading for the buoyant force. The second method would have had a lot of uncertainty from the mass of the water. The outside of the graduated cylinder retained some of the water and that wasn't accounted for. The cylinder may also not have been filled to the exact top with water. This would result in a lower buoyant force. In the third part error arose from the fact that the hook on the metal cylinder was no accounted for in the displaced volume. All of these methods were, however, consistent within reasonable error.

I believe that the first method was most accurate because there was less room for error where as the other two had obvious error associated with the procedure (the excess water and the unaccounted for hook).

If, in part A the cylinder had been touching the bottom of the container this would have made our experimental buoyant force much greater because there would be a normal force on the metal cylinder. It would have added to what would have been thought of as the buoyant force and made it too high.