Fluid Statics

Purpose:

      The purpose of this lab is to determine the buoyant force that is being applied to a metal cylinder using 3 methods: underwater weighing method, displaced fluid method, and volume of object method. This lab will also observe the accuracy of each method using uncertainty and error analysis.

Equipment:

• Force probe
• String
• Overflow can
• Beaker to catch overflow
• Metal cylinders with hooks or tie with string
• Meter stick
• Vernier caliper or micrometer caliper

Part A: Underwater Weighing Method

      In this part, the metal cylinder was weight was determined in air to be 1.154 N. Once it was determined, the setup below is conducted.

The experiment conduct

In the picture above, you can see that the metal cylinder is hooked on a string to the force sensor and the data is taken on the laptop which shows the value of 0.07766N. The free body diagram of the metal cylinder is shown below

Free body diagram of metal cylinder in water

According to the free body diagram: 

where mg = 1.154 ± 0.0005N, and T = 0.7766 ± 0.00005N

Thus, conclude B = 0.3774 ± 0.0001878N

Part B: Displaced Fluid Method
         In this part, the mass of dry, empty beaker is measured to be 0.14368 ± 0.000005kg. And then the following procedure is done.

1. Graduated cylinder fully filled with water

2. Metal cylinder is inserted into the graduated cylinder

3. The overflow contained in the beaker

4. Measure the mass of the beaker+water, which is 0.18133 ± 0.000005kg

Using these information we can calculate the mass of the water which comes to be 0.03765 kg.
According to Archimedes' principle, the buoyant force is the weight of the water which appears to be:
B = 0.369347 ± 0.00002304N


Part C : Volume of Object Method
        In this part, the volume of the metal cylinder is measured using caliper. The data obtained is as follow:
     h = 0.0691 ± 0.00005 m
     d = 0.0260 ± 0.00005 m
     density of water = 1000kg/m^3
     g = 9.81 m/s²

from the data obtained, the buoyancy can be determined
 B = 0.35990 ± 0.001645 N


Questions

1. The Buoyant force of the three method appear to be closely similar. Some discrepancy in the values may be caused by error created in the method such as in method 2, some water might not totally flow into the beaker instead stick on the surface of the graduated cylinder. They all also pretty accurate since the uncertainty is only around 1% of the value calculated.
2. I think the most accurate method is the underwater weighing method because there are not much room of error since it is all measured by computer. Although it have greater uncertainty than method 2, as said in number 1, method 2 could create error such as the water sticking to the surface of the graduated cylinder. I think method 3 is the least accurate one since there will be errors on the measurement and the third method has the most measurements required which means uncertainty also increases.
3. If the metal had been touching the bottom of the water container, the buoyant force will have been too low because the force acting on the object will increase in numbers. The normal force created will adds up to the upward force which will make the buoyant force decrease to be in equilibrium.