# mt1 - ME 152A 1 Midterm Exam 1 (9:00-10:15 am on October...

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ME 152A 1 Midterm Exam 1 (9:00-10:15 am on October 24, 2011) Problem 1 (60 pts). A solid cone of uniform density ρ c and height H acts to plug a hole at the base of a container as depicted in ﬁgure 1. The cone protrudes a distance h from the bottom of the container and the container is ﬁlled with a liquid of density ρ l to a level L. This level will change if liquid is added or removed from the container. All exposed surfaces are subject to atmospheric pressure P o . The area of the base of the cone is A, and the area of the hole in the bottom of the container is A o . Figure 1: A solid cone of uniform density acts to plug a hole in a liquid ﬁlled container. (a:10) For what liquid level L is the buoyant force acting on the cone the largest? (b:10) Draw a Free Body Diagram (FBD) for the cone. (c:20) Derive an expression for the buoyant force, F B , as a function of liquid level L, and cone dimensions h and A o . (d:20)

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## This note was uploaded on 12/29/2011 for the course ME 152 taught by Professor Krechet during the Fall '10 term at UCSB.

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mt1 - ME 152A 1 Midterm Exam 1 (9:00-10:15 am on October...

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