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7aMidterm2Rev_sunday

7aMidterm2Rev_sunday - Midterm 2 Review Sunday 4/1 in 1...

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Midterm 2 Review Sunday 4/1 in 1 Pimentel Ruza Markov Problem 1. A block of mass m is launched across a table using a spring of constant k . In the moment the block is released from rest the spring is compressed a distance x . After the block is launched it runs into a ramp of mass M . Assume that all surfaces are fric- tionless and that the block never reaches the top of the ramp. a) What is the maximal vertical height h a that the block reaches as it moves up the ramp if the ramp is attached to the table? b) What is the maximal height h b that the block reaches if the ramp is free to slide across the table? Problem 2. A thin metal plate of uniform mass density is cut into the shape shown: a) If the curved boundaries are given by y = ± Cx 1 / 3 find the constant C in terms of the maximal x value L and the maximal y value H . b) Find the position of the center of mass. Write your answer in the form ~ r cm = x cm ˆ x + y cm ˆ y . What is the distance r cm of the center of mass to the origin?
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