Experiment 1: Fluid Statics

Introduction:

The purpose of this experiment is to calculate the buoyant force to the metal cylinder by three different methods. By using three different methods to determine for the buoyant force, in order to  compare which of the three methods is the most accurate.

Part A: Underwater Weighting Method

 When the cylindrical mass is completely submerged in the water, there are three forces acting upon it. The force of gravity, the tensional force by the string and the buoyant force by the water.

T+B-W=0, or B=W-T.

             The weight of the metal by hanging it in the air and using the force probe to read the data: 1.053±0.05N. Then we completely submerged the solid in water and used the force probe to read the data: 0.670±0.05N. Finally, using the above calculation, the buoyant force is 1.053N-0.670N= 0.383±0.05N.

Part B. The Displaced Fluid Method

For this method, we uses the weight of a displaced fluid to calculate the buoyant force. The weight of a displaced fluid is equal to the buoyant force of that fluid, or W=B.

The mass of the dry beaker is : 0.1090kg and the mass of the beaker + water: 0.230kg. Then, we slowly lowered the cylindrical mass into a beaker full of water.  When the water has completely stopped dripping. Then we calculated the mass of the runoff water by subtraction: 0.230kg-0.1090kg = 0.0391kg. Plugging this mass into the equation:  B=0.0391kg*9.81m/s^2 = 0.383±0.05N.

Part C. Volume of Object Method

The third method we use the volume of the metal cylinder to find the volume of displace water. The formula is W=B, or W=p*V*g.

The volume of a cylinder is V=pi*r^2*h. We used calipers to measure the diameter, d=0.025m and the height, h=0.076m. We then used the formula to calculate the volume, V=(pi)(0.0125)^2(0.076)= 3.729*10^-5 m^3. Using the density of water as 1000kg/m^3, we calculated the buoyant force: B=(1000kg/m^3)(3.729x10^-5 m^3)(9.81m/s^2)= 0.366±0.05N..

Conclusion:

Among all three of the methods, two of the results are the same. We have got the buoyant force to be 0.383N±0.05N for both part A and part B. For part C, the buoyant force is 0.366±0.05N.

The first method is flawed in its inherit method of collecting data values for weight. The force probe readings are not quite stablize, therefore, the results given do have lot of uncertainty.

           The second method which uses the mass of the displaced fluid also is quite inaccurate. We weren't able to completely catch all of the runoff water, and thus some of the mass could have been discarded. This would yield less weight calculated and ultimately less buoyancy.

The third method is the most accurate but it also have some uncertainty. The critical measurement in this method is the measurements for the volume, the diameter and the height. The humans reading the calipers would each be subject to uncertainty. Since the density of water of 1000kg/m^3 which is at STP. However, the classroom temperature was much higher than 0°C, and this could have influenced the calculation. By compare to other two methods, the third method is the most accurate.

In Part A, if the metal cylinder touching the bottom of water container, the buoyant force will be higher then currect value. because if the cylinder touch the bottom, there is another force support the cylinder up which have the same direction as the buoyant force, so the value of the buoyant force will be smaller than the value that we have got in the experiment.