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quiz1 (2) - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Ocean Engineering Department of Civil and Environmental Engineering 13.013J/1.053J Dynamics and Vibration Fall 2002 Quiz I “Closed book and notes”, one sheet of formulas allowed. Individual effort. Read all problems first. This quiz contains 6 printed pages.
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Figure for Problem 1: M L m v g O d 2
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Problem 1: (50 Points) A pendulum of mass M with a massless rigid rod of length L hanging from a fixed frictionless pin O is initially at rest in a field with acceleration due to gravity g. The mass M can be considered as a point mass (particle with negligible dimensions). A particle of mass m and horizontal velocity v flying at a vertical distance d from the pin collides with the pendulum rod and sticks to it. a) a i. Explain why kinetic energy and linear momentum are not in general conserved during the collision. a ii. Determine the angular velocity and kinetic energy of the system immediately after the collision, and the kinetic energy loss during the collision, as a fraction of the initial kinetic energy of the mass m . a iii. Determine the impulse from the pin O on the rod during the time of the collision.
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