MECH 220 MECHANICS 2 FINAL EXAMINATION Thursday, December 15, 2005 Examiner:
Prof. I. Sharf
Associate Examiner:
Prof. A. Misra
14:00 to 17:00
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY: • THIS EXAM IS CLOSED BOOK. ONE 8.5” x 11” CRIBSHEET, HANDWRITTEN OR TYPED ON BOTH SIDES, IS PERMITTED. • PLEASE ANSWER ALL SIX (6) QUESTIONS. • QUESTIONS MUST BE ANSWERED DIRECTLY ON THE EXAMINATION PAPER, IN THE SPACE PROVIDED BELOW OR BESIDE THE QUESTIONS. • FACULTY STANDARD CALCULATOR PERMITTED.
STUDENT NAME: STUDENT NUMBER:
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FOR EXAMINERS ONLY 1.
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PROBLEM 1
[10]
A dual axis accelerometer at the end of an extensional robotic arm gives an acceleration reading of a = (4e r + 5eθ ) m/s2. At this instant, r = 1.5 m, &r& = 10 m/s 2 , θ = 45 o , and θ&& = −0.5 rad/s 2 . Determine the velocity of the end of the arm and sketch it in the figure.
Mech 220/04
1
FINAL/04
PROBLEM 2
[15]
Car B weighing 3200 lb and traveling west at 30 mi/hr collides with car A weighing 3400 lb and traveling north at 20 mi/hr as shown. If the two cars become entangled and move together as a unit after the crash, compute: a) the magnitude v of their common velocity immediately after the impact and the angle made by the velocity vector with the north direction; b) the energy loss during impact.
Mech 220/04
2
FINAL/04
PROBLEM 3
[25]
A 0.2 kg bar BC rotates with a constant counterclockwise angular velocity of 2 rad/s in the horizontal plane. A pin at B slides without friction in a circular slot in the rectangular plate. At the instant shown, calculate the following: a. The angular velocity of the plate; b. The velocity at which the pin slides relative to the circular slot; c. The reactions at pin C.
Mech 220/04
3
FINAL/04
Mech 220/04
4
FINAL/04
PROBLEM 4
[20]
Model the arm ABC as a single rigid body. Its mass is 300 kg, and the mass moment of inertia about its center of mass is I = 360 kg-m2. Starting from rest with its center of mass 2 m above the ground (position 1, NOT shown in the figure), the hydraulic cylinders push arm ABC upward. When it is in the position shown in the figure (position 2), its counterclockwise angular velocity is 1.4 rad/sec. How much work do the hydraulic cylinders do on the arm in moving it from position 1 to position 2?
Mech 220/04
5
FINAL/04
Mech 220/04
6
FINAL/04
PROBLEM 5
[25]
The slender bar weighs 10 lb and the disk weighs 20 lb. The coefficient of kinetic friction between the disk and the horizontal surface is μ k = 0.1. a) Draw the free-body diagram of the bar and write down the moment equation about B. b) Draw the free-body diagram of the disk and write down the three equations of motion for the disk. c) If the disk has an initial counterclockwise angular velocity of 10 rad/s, how long does it take for it to stop spinning?
Mech 220/04
7
FINAL/04
PROBLEM 6
[25]
The unsupported, homogeneous rigid body, depicted in the figure, has a total weight of 40 lb and is acted on by a force FQ = ( 20i − 8 j + 10k ) lb at point Q. The body is also under the influence of gravity. If the angular velocity of the body is ω = ( −5i + 4 j − k ) rad/s at the instant the force FQ is applied, determine a) the acceleration of the mass center, aG; b) the inertia matrix of the body with respect to the x-y-z frame located at the center of mass G; c) the angular acceleration αG. The length h is 8 inches.