1) A uniform cylindrical pop (soda) can of mass 0.140 kg is 12.0 cm tall and fil
ID: 1696611 • Letter: 1
Question
1) A uniform cylindrical pop (soda) can of mass 0.140 kg is 12.0 cm tall and filled with 1.31kg of pop (soda). Small holes are drilled in the top and bottom to drain the pop (soda).
a) What is the height h of the center of mass of the system (system = the can and its contents) as a function of the x, where x is the height of the pop (soda) level remaining within the can?
b) What are the maximum and minimum values for h (i.e. what is h when the can is full and empty)?
c) What is the smallest value of h that occurs while the can is draining?
Explanation / Answer
please give points. Since the can is of uniform construction, its COM is at the point in the center of the can (i.e., half its height and at the center of its area, assuming a cylindrical can). The COM of the liquid is going to be 1/2 the remaining height of liquid in the can, again at the center of the area. a, b) The height of the COM in both cases is 6cm. The height of the COM of the can itself is 6cm, no matter what the liquid level. When all the liquid is present, the height of its COM is 6cm. When there is no liquid, you only have the can. c) As the liquid drains, the height of the COM decreases. The soda is about 0.11 kg/cm of height. If M is the mass of remaining soda and h is its height at any given time, the height of the COM (x) will be: x = [6*.140 + (h/2)*(0.11*h)] / (.140 + .11*h) = (.84+.055*h^2) / (.140+.11h) d) To find the minimum value of x, you could either determine the derivative of the the function above or plot a graph. As my calc is very rusty, I did a quick graph in Excel. The minimum occurs at about 2.84cm.
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