Fluid Statics: Calculating the Buoyant Force

Fluid Statics

In this experiment we will be taking a metal cylinder and using it to explore three different ways of finding the buoyant force. Not only is will we use known equations but we will support our numerical answers with experimental data. 

Part A

 First we must determine the weight of the metal cylinder both in air and completely submerged in water. Using a balance we estimated the mass to  104.98 + .5 (g) in air. In order to find the mass of the cylinder completely submerged in water , we took a graduated cylinder filled with water and put the cylinder inside in order to find its mass submerged 106 + .3 (g). 

Now, we know that in order to find the buoyant force we need to figure out what it equals to. Using free body diagrams I am able to determine that B = mg - T.  Finding the force of the tension in the string was a bit tricky but we found that if we hang the cylinder from a force probe and submerge it in water we could get that force T(tension) = .67 + .02 N

Finally using our measurements we can calculate the buoyant force. B = mg - T = .37 + .02 N

Part B.

This second method for measuring the buoyant force is called the displaced fluid method. Basically it says, if you were to top a beaker with water and place an object, in my case the cylinder, inside. Whatever the weight water that drips out of the beaker, will be equal to the buoyant force. In order to capture that excess water we ensured to have a cup beneath the beaker in order to catch all that excess. 

This part of the experiment was relatively simple. All we did was take a graduated cylinder, topped it with water, and the lowered the metal cylinder carefully. The excess water that fell out was taken to a balance and weighed. 

Beaker = .004 kg 

Beaker + Water = .039 + .01 kg 

Water = .035 kg + .01 kg

Finally if we multiply the mass of the water by the force of gravity (9.81m/s^2) we can calculate the weight of the water or buoyant force to be .343 + .03 N

Part C.

In order tofind the volume of the cylinder we need to measure the height and diameter using a caliper. 

Height = 7.62 cm

Diameter = 2.53 cm

Therefore, using V = pi * r^2 * h my volume turned out to be 3.83 * 10^-5 m^3.

Now, using the equation W = (rho)*g*V, our W is the weight of displaced water. Which is also equal to the buoyant force. 

B = .36 + .02 N 

Part D. Summary

1. Looking at our 3 values for the buoyant force we can see that all the calculated forces are in close proximity. Due to human error we can see that even though slightly off they are in the range of .34 to .37 N.

2. I would go with part c. even though it may be slightly tedious to measure the cylinder. It gives you the most accurate measurements. Because when you trap the water in part b. you most certainly will not capture all of it. In part a. the force probe isn't the problem, the other problem is that the cylinder touches the sides of the graduated cylinder.

3. If the cylinder was too touch the bottom, the tension would have decreased therefore increasing the buoyant force. I think of it as, the farther down you push a beach ball the harder it is to keep pushing it. Why? because of the buoyant force.