Lab1. Fluid Statics

Introduction

The buoyant force acting on an object was measured experimentally using three different methods. Also, the results from each method was compared by error analysis to get uncertainties of results. 

Procedure

Method 1. Underwater Weighing Method

   Find out the weight of a metal cylinder in air and in water.

  Measure weight of a metal cylinder in air and in water

Method 2. Displaced Fluid Method

1.     Measure the weight of Dry beaker.

2.     Put the metal cylinder in the can which filled with water (overflow).

3.     Lower the metal cylinder so that create overflow of water -> collect the overflowed water in dried beaker from procedure 1.

4.     Weigh the collection of overflowed water in a beaker.

Method 3. Volume of Object Method

1.     Measure height (h) and diameter (D) of the cylinder.

2.     From method 2; using the weight of displaced (overflowed) water, find out the buoyant force. 

Method 2, 3

Data

Method 1. Weight (in N)

in Air	in Water
1.089 N	0.70 N

All forces acting on a cylinder

From above free diagram, B(=F_B) = mg-Ts = 0.389 N. 

Method 2. Mass (in kg)

Beaker	0.141 kg
Beaker + Water		0.180 kg
Water			0.039 kg

According to Archimede's principle, the weight of displaced water, Wf , is equal to buoyant force. 

This gave the Wf = B = 0.383 N

Method 3. Heights (h) and Diameter (D) (in m)

Heights (h)	0.077
Diameter (D)	0.025

The volume of cylinder was calculated using V =πr² = 3.78 x 10^-5 m³.

The weight of displaced water can be expressed in terms of volume of the metal cylinder and density of the water.  Wf = ρvg = B = 0.371 N

Discussion

1. Compare Buoyant force of three different methods with uncertainties (error analysis)

2. I think the third method would be the most accurate. Simply looking at uncertainties of final value (buoyant force), the third method showed the least value (+/- 0.001 N while other methods were +/- 0.1 N). Also, there are least possible errors on method 3. From method 1, the tension measurements were keep changing on instrument (could be due to minor vibration of table, etc). From method 2, it was hard to get exact weight of overflowed water because they tend to wet the outer surface of graduate cylinder).

3. From method 1, if the cylinder had been touching the bottom of the water container, there would be one more force (normal force) acting on the cylinder other than buoyant force, tension, and weight. In other words, the buoyant force would be low because normal force will acting upward. 

mg = Ts + B + N where B = buoyant force, N = normal force

If we solve for B; B = mg - Ts - N

Therefore, the buoyant force will get smaller. 

Summary

The buoyant force of the metal cylinder could be measure in three different method within the  percent deviation of ~2.41% (average three values and get standard deviation -> calculate percent deviation). Due to uncertainties of measurement, the method 3 would be the most accurate way to measure the buoyant force of cylinder.