Fluid Statics

Objective: Experience and calculate the buoyant force.

Part A
Underwater Weighting Method

Measure the weight of the cylinder---1.1023N
Attach the metal cylinder to a string and put it in the water.
Measure the reading on the string---0.73N
The difference is the buoyant force.
B=W-T
   =0.3723497 N
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Part B
Displaced Fluid Method

Fill up the beaker with water and measure the total mass---0.17872g
Put the metal cylinder into the beaker and measure the exceeded water---0.0316g
Buoyant force equals to the weight of displaced water.
B=W=0.0316g * 9.8 m/s^2
   =0.30968 N
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Part C
Volume of Object Method

Use the caliper to measure the diameter and height of the cylinder
d=0.253m, h=0.0771m
V=pi*r^2*h
   =3.876*10^-5
B=d*V*g
   =1000*3.876^-5*9.8
   =0.379894 N
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Question:
1. The error of Part A mainly come from the balance and the reading on the string. It's basically a very accurate way to measure the buoyant force. For, Part B, we use the concept of Archimede's principle. Since the volume of the cylinder is small and the exceeded water was just about 30-40 ml, the error of this method could be very large. Any lost of 1 ml costs about 2.5 percent error. Therefore, Part B is not a good way to determine the buoyant force. For Part C, the errors come from (1) the volume of the cylinder. (2) the density of the water. It is not easy to measure the true values of the diameter and height by using a caliper. And the density of water at the room temperature might not be exactly 1000kg/m^3. However, Part C is still a good way to find the buoyant force even it is not as accurate as Part A.

2. Part A (Underwater weighting method ) is the most accurate.

3. If ,in Part A, the cylinder had been touching the bottom of the water container, the container would exert a force N to the cylinder. Then W=T+B+N or B=W-T-N. The value would be to low comparing to B=W-T.