Fluid Statics (Buoyancy of Metal Cylinder)

Purpose: 

The objective of this experiment was to explore the different methods of measuring the buoyancy of an object in water.  The Buoyant force is described by Archimedes's principle which states when a body is completely or partially emerged in fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.  

Method and Results:

Three separate measurements of the buoyant force were obtained by alternating methods.  

1.  In the underwater weighing method a metal cylinder was held in a cup of water of known volume while force probe was used to determine the tension needed to hold the object up.  The equation needed to determine the buoyant force was:

B= W- T

B= (0.229 +/- 0.006 N) -  (0.165 +/- 0.006 N) = 0.064 +/- 0.012 N

The Tension (T) was determined using the Force probe, the weight of the metal cylinder (W) was recorded with the force probe using statics.  

2.  In the Displaced Fluid Method Water was allowed to flow out of a cup that was filled to its brim.  This water was in turn weighed and multiplied by gravity to determine the weight of the water displaced. This method is a direct use of Archimedes's principle as it states the weight of the fluid displaced is equal to the bouffant force.

B=Ww

B=W=mg= 0.0657 +/- 0.006  N

3.  In the Volume of Object Method the dimensions of the metal cylinder were recorded and used to determine the volume.  This value was multiplied by the density of water and gravity to once again determine the weight of water displaced.

B=Vcrg

V=7.32 E-6 +/-  0.009 m^3

B=W= Vcrg = 0.0724 +/- 0.009 N

Conclusion:

Although the values for the buoyant force are precise the uncertainties for them are not.  This could be due to the fact that each of the three methods for determining buoyancy requires a unique amount of measurements and each measurement needed will typically raise the uncertainty of a result.

	Values
avg	0.0674
range	0.0084
avg uncertanty	0.0072
uncertanty range	0.0114