Experiment 1: Fluid Statics

Purpose:

The purpose of this experiment is using three different types of measurement to measure the Bouyant force acting on the object. Moreover, students will compare the three methods to see which one is most accurate.

Method 1:

Method #1 is using computer to measure the weight of the metal cylinder.

1. Obtain the metal cylinder, string, cup of water and force probe.

2. Set up the computer.

3. Measure the weight of the metal cylinder in air by attaching the cylinder to the force probe using the string. The computer reading is 1.126 ± 0.003N.

4. Submerge completely the cylinder in the water, and the cylinder does not touch the bottom of the cup.

5. Record the computer reading value is 0.738 ± 0.003N.

6. Draw a FBD for the cylinder in the water.

The weight in air is mg,  and the weight in the water is actually T (tension) in the string.

As shown, the B-buoyant force = mg - T.

B = 1.126 - 0.738= 0.388 ± 0.006 N

Method #2: 

Method #2 is using a container to get the overflow water when we place the metal cylinder into the full beaker.

1. Obtain an overflow beaker and weight it: m1 = 0.10322 ± 0.00001 kg

2. Get another beaker and fill it with water.

3. Place the beaker with water inside a foam cup.

4. Lower the cylinder into the beaker with water until the water stops dripping.

5. Pour the water into the first beaker and weight it : m2 = 0.14280 ± 0.00001 kg

6. The mass of the water in the first beaker is m = m2 - m1= 0.03958 ± 0.00002 kg

7. According to Archimede's priciple, the weight of the water is equal to the buoyant force,                        B= m×g =(0.03958 ± 0.00002)× 9.81 = 0.388 ± 0.000196 N.

 Method #3:

Method #3 is using a caliper to measure the volume of the metal cylinder.

1. Measure the height h = 0.077 ± 0.0001 m

 and the diameter D= 0.0255 ± 0.0001 m

2. Calculate the volume of the cylinder

 V = π*h* D²/4 = π(0.077)(0.0255²)/4 = 3.9324E-5 m3

3. The weight of the displaced water in terms of the volume of the cylinder and the density of water. 

               W = vp.g = (3.9324E-5)(1000)(9.81) = 0.3858 N

4. The buoyant force is equal to the weight of water, B = 0.3858 N.

Summary:

 

	Method #1	Method #2	Method #3
Buoyant  force, B	0.388 ± 0.006 N	0.388 ± 0.000196 N	0.386 ± 8.22×10-8 N

        As shown in the table of the results, the three values for the buoyant force are within reasonable. All the results are within their uncertainties. In the method #1, the uncertainties were created by the mass of the string attached the cylinder and the inaccuracy of the force probe. In the method #2, the uncertainties were from the hook of the cylinder. We might not fill the water to the top of the beaker. Moreover, we might not get all the overflow water in the beaker. In the method #3,  the uncertainties were from when we measured the height and diameter by the caliper, we did not the accurate measurement. 

        I think the method #3 was the most accurate because there was not extra equipment needed to attach the cylinder. The volume which we measured was actual volume of the cylinder (no extra mass of the string in the method #1, and the hook in the method #2). Moreover,  we were using only the caliper to measure the cylinder which I can know how accurate I am doing.

       If the cylinder touches the bottom of the water container, the result will be affected. The buoyant force will be lower, because the bottom of the container will exert a normal force into the cylinder (as show in the picture below.)
 B = mg -T -N.