Name ___________________________ Section _____________________ ES204 Examination II January 26, 2009 Problem Score 1 /30 2 /30 3 /40 Total /100 Show all work for credit AND Turn in your signed help sheet AND Stay in your seat until the end of class The exam is closed-hard-drive. Laptop computers running Maple or other math software are permitted. Network connections are not allowed. Mass moment of Inertia of some Common Shapes Solid Sphere Ix Iy Iz z 2 2 mr 5 y r G x z Slender Rod y 1 Iy Iz mL2 12 G L x Solid Circular Cylinder 1 I x mr 2 2 1 Iy Iz m L2 3r 2 12 z y G r x L Thin Disk z 1 mr 2 2 1 I y I z mr 2 4 Ix x Thin Rectangular Plate 1 m b2 h2 12 1 Iy mh 2 12 1 Iz mb 2 12 Ix y r G z y G h x b Brick 1 m b2 h2 12 1 Iy m h2 d2 12 1 Iz m b2 d2 12 Ix b z y h G d x Name ES204 Examination II 30 pts Jan. 26, 2009 Problem 1 The “tee” shaped object is released from an unknown position and pivots on its end. The top of the tee has a mass m1 and length, w, and the vertical part has a mass m2 and a length, L. If the bar is about to slip when = 30 find the angular velocity of the bar at this instant if s= 0.5. Set-up but do not solve the necessary equations to find the angular velocity, , of the object. m1 m2 w L DO NOT SOLVE THE RESULTING EQUATIONS! Your answer should consist of numbered equations and a list of unknowns. Be sure to clearly document your solution Name ES204 Examination II 30 pts Jan. 26, 2009 Problem 2 During an experiment, a bullet of mass mb unexpectedly passes through a uniform bar of mass m clipping off part of the bar. A camera records the initial velocity of the bullet to be v1 at an angle 1 and final velocities of the bullet and chip are found to be ( v 2 , 2 ) and ( v3 , 3 ) respectively. The final velocity of point C (the center of gravity of the original bar) is vC . Set-up but do not solve the necessary equations to find the final angular velocities of the remaining length of the bar and the chip. DO NOT SOLVE THE RESULTING EQUATIONS! Your answer should consist of numbered equations and a list of unknowns. Be sure to clearly document your solution Knowns: v1, 1, vC , v 2 , 2 , v3 , 3 , mb, m, L B B 0.8 L 0.8 L C L mb v C C 1 v1 Instant 1 3 v3 Instant 2 2 v 2 Name ES204 Examination II Problem 3 40 pts Jan. 26, 2009 Gear A has a mass of 0.5 kg and a radius of gyration of 60 mm, and gear B has a mass of 0.8 kg and a radius of gyration of 55 mm. Gear C is fixed. The link is pinned at AB and has a mass of 0.35 kg and can be treated as a slender rod. The assembly is released from rest when = 0° (rod is horizontal) and moves to = 90° (rod is vertical pointing down) under the action of gravity and a constant clockwise torque M = 100 N-m that is applied to link AB. Set-up but do not solve the necessary equations to determine the angular velocity of the link in position 2. DO NOT SOLVE THE RESULTING EQUATIONS! Your answer should consist of numbered equations and a list of unknowns. Be sure to clearly document your solution. M