Why Do Hydrostatic Forces Cause Differing Mass Estimates in a Cone Experiment?

[tommywan410]

I am working on a lab report on hydrostatic forces. I have encountered a problem.
I did the experiment by putting a cone in a container with a opening at the bottom. Here're the procedures.

a. Weight the cone Wc, measure its dimensions, and measure the diameter of the opening at the bottom of the container (See Appendix I).
b. Place the cone (with vertex pointing downwards) on the opening, when the container is empty. After that, keep adding water slowly until the cone pops up. Record the water depth h1 at which the cone pops up.
c. Place the cone (with vertex pointing downwards) on the opening, when the container is near full. After that, keep draining water slowly until the cone pops up. Record the water depth h2 at which the cone pops up.
d. Repeat step b and c for 3 more times and record down all 4 sets of data (See Appendix II).
e. Place the cone (with vertex pointing upwards) on the opening, when the container is empty. After that, keep adding water slowly and see whether the cone will float or not. Record the water depth h3 at which the cone floats.

For the first part of the experiment, we have to estimate Wc from h1, when object is floating, mg = F_b

Since hydrostatic forces = pressure*area. So, I integrate the pressure with the area of the ring at each level. Please see the attachment of calculation. I transform the edge of the cone as a linear function of x and y while x is the radius and y is the height. However, I have got a greater m than the actual m (by weighing).

For estimation by h2, I also use similar method to integrate the force. However, this time I got a smaller m than the above m. Shouldn't it be greater than the m estimated by h1 since some parts of the cone in first step is not in the fluid?

I would like to ask did my calculation go wrong or other things?

 

[gtoguy97]

How can I better estimate the mass of the cone? Your calculations seem to be correct and you have identified the appropriate equation for estimating the mass of the cone (mg = Fb). It is possible that the difference in the two masses could be due to the lack of precision in the measurements. Try repeating the experiment with more precise measurements and see if the results are more consistent. You could also try to use a different type of container or vary the size of the opening at the bottom to see if the results change.