Name: ___________________________ Section: O Genin WASHINGTON UNIVERSITY O Sellers

Department of Mechanical Engineering and Materials Science

MEMS 255 — Dynamics

FINAL EXAMINATION

May 4, 2014

Please show and explain your work. Partial credit will be given if you set up a problem correctly. No credit will be given for correct answers lacking supporting work.

All four problems are of equal weight. 1. After the success of its “bond-with-and-then-euthanize-a-

bear-cub” event, CS40 rents a herd of unicorns and a sausage-maker. The spinning unicorn hammer, a 3m cube of mass 1000 kg, is welded to bar AB. The system rotates about the vertical axis CD at constant angular speed Ω = 2 rad/s as the bar descends. When θ = 90°, the rate of descent is dθ/dt = 1 rad/s. The masses of the rods AB and CD are negligible, and there is no friction in the pin at point B. Neglect wind resistance. When θ = 90°,

(a) What is the angular momentum of the system about

point B? (b) What moment must be applied at the hinge? (c) What is d2θ/dt2?

2. Sensing a disturbance in the Force (May the 4th be with you!), a Jedi abandons his battle on Mustafar to rush to the rescue of oppressed petting zoo animals on campus. Initially at rest on a raft levitating over a quiescent lava pool, he attains a speed of 5 m/s relative to the raft over 2 seconds. Neglect any fluid resistance, tipping of the raft, and Jedi mind tricks. Determine: (a) The velocity of the raft, relative to a stationary observer, after 2 seconds, and (b) The average traction force exerted by the Jedi on the raft over the 2 second interval.

3. A garbage compactor consists of two rods, each with a mass of 1000 kg and length of 5 m; a linear, massless spring; and a massless piston. The linear spring has a spring constant of k = 10 N/m and an unstretched length of 5 m. The garbage provides a constant resistive force F as it is compacted. What value of F is required so that the two rods come to rest at θ = 0° after being released from rest at θ = 60°? Ignore friction and wind resistance and assume that gravitational attraction is a comfy 9.81 m/s2 in the bowels of the Death Star.

4. The bear cub escapes into deep space to live peaceably with the Ewoks on the forest moon of Endor,

leaving the conical nose cone of its rocket rolling without slipping on the ground as shown at constant rate ω2 = 3 rad/s. Neglect rumors that CS40 paid off the cub’s owner to pretend that the bear cub was not euthanized. Find: (a) The rate ω1 at which the cone spins about its centerline, and (b) The angular velocity and angular acceleration of the cone.