ME104-Midterm2-Solns - ME 104: Engineering Mechanics II...

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ME 104: Engineering Mechanics II Spring Semester 2011 Department of Mechanical Engineering University of California at Berkeley Professor Oliver M. O’Reilly Second Midterm Examination Wednesday April 6 2011 Closed Books and Closed Notes Question 1 Planar Motion of a System of Two Particles (20 Points) As shown in Figure 1, a particle of mass m 1 is at rest and is attached to a ±xed point O by a linear spring of sti²ness K and unstretched length L 0 . At time t = 0, a particle of mass m 2 traveling with a velocity vector v 0 E x impacts the particle of mass m 1 . After the collision both particles adhere to each other, and can be considered as a particle of mass m 1 + m 2 . m 1 + m 2 O O m 2 m 1 (a) (b) v 0 E x E x E x E y E y g g linear spring Figure 1: A system of two particles: (a) Prior to impact at t = 0, and (b) following the impact. (a) (4 Points) Starting from the representation r 1 = r e r , (1) where e r is a unit vector pointing from O along the spring to m 1 , establish representations for
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ME104-Midterm2-Solns - ME 104: Engineering Mechanics II...

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