Experiment 1: Fluid Statics

Introduction

The purpose of this experiment is to make a comparison of various methods which are used to calculate the buoyant force to the metal cylinder. The experiment also intends students to understand and apply the Archimedes' principle which states that the buoyant force is the weight of the fluid displaced by an object.

The experiment was conducted in three methods by using a force probe, a string, a beaker, a metal cylinder with hook, a meter stick, and a graduated cylinder. In part A of the experiment, the weight of the metal cylinder in air and in water were measured using the force probe, and the buoyant force was computed by subtracting the weight of the metal in the water to that of the metal in the air. In part B, the mass of a dry beaker was measured using the balance. The cylinder was filled with full amount of water until it stops dripping. Next, the metal cylinder was put into the cylinder, and let the water in the cylinder overflows into the beaker. The mass of the water overflow was calculated by subtracting the mass of the combination of the beaker and the water to the mass of the beaker. The buoyant force was obtained by multiplying the mass of the beaker and the acceleration due to gravity. In part C, the height and the diameter of the metal cylinder were measured, and the volume of the cylinder was calculated. The computed volume was used to calculate the buoyant force, B.

Figure-1: Measuring the weight of the metal cylinder using force probe. This measurement was used in method A.

Figure-2: Overflow of water from the graduated cylinder upon adding the metal into the cylinder. The water overflow was captured by the beaker. This method was used to compute buoyant force in part B.

Data and Analysis

Table-1: Recorded data for each method

Method A	Method B	Method C
Wair = 1.13 ± 0.05 N Wwater = 0.67 ± 0.05 N	Wbeaker= 0.15086 ± 0.00005 kg Wbeaker+water= 0.19177 ± 0.00005 kg	h=0.076 ± 0.005 m d=0.025 ± 0.005 m

Table-2: Comparison of buoyant force, B

Method	Equation used to compute B	B(N)	Largest possible B(N)	Smallest possible B(N)
A	Wair - Wwater	0.46 ± 0.10	0.56	0.36
B	(mbeaker+water - mbeaker)g	0.40092 ± 0.00098	0.40190	0.39994
C	ρgV	0.37 ± 0.29	0.66	0.08

Figure-3: Calculations of uncertainties

Discussion

According to table-2, the values of the buoyant force calculated from different methods were within the uncertainties of each other even though B value in each method was greater or smaller than the others. Yet the results fell within their uncertainties. For instance, the largest possible B in method A was 0.56N and the smallest possible was 0.36N. Both of these numbers were within the values of the other two methods. In same manner, the largest and smallest possible buoyant force in method B and method C were within uncertainties of method A.

Among these three methods, according to table-2, the method B was the most accurate since it had the smallest uncertainty. In addition, as shown in table-1, the devices used in method B measured to more decimal places comparing to the devices used in other methods. Thus, less deviation from the actual values, hence, greater accuracy. In contrast, method C had very great inaccuracy since the only device used in method C was a meter stick. Since everyone reads the measurements differently and the way each person measured were not the same; it led to possible large deviations from actual values. The meter stick also did not read to smaller decimal points which led to greater inaccuracy in the measurement.

If the cylinder had been touching the bottom of the water container in part A, the buoyant force will be larger since there will be less tension detected by the force probe. Since there will also be a normal force adding to an upward force, smaller buoyant force will be required to equal to the same weight of the metal.

Conclusion

               By applying the Archimedes’ principle in this experiment, it was found that values of buoyant force in three different methods were within the uncertainties of each other. Among these methods, method B was the most accurate method.