Question

CLASS ID#: (1) CONCEPT QUESTIONS & SHORT ANSWERS (30 PTS) (A) (10 pts) A latch spring is constructed from slender steel rod material assembled as shown. The ring has radius r and mass 3m. Each of the three straight links are length 2r and have mass m. Develop an expression (DO NOT SIMPLIFY) for the mass moment of inertial of this assembly about an axis perpendicular to the page through point O. ما B (B) (10 pts) Each of the double pulleys shown has a mass moment of inertia of 15 lb-ft-s about the pivot and is initially at rest. Their outer and inner radii are 18 inches and 9 inches respectively. For the instant when point A on each cord has descended 10 ft, answer the following questions. Using the index numbers (1)-(4) provided, list the configurations in order of SMALLEST to LARGEST: (1) Kinetic energy (KE) of the system of masses SMALLEST KE: LARGEST KE (ii) Angular velocity of the pulley. SMALLESTO: _LARGEST (1) (3) PPRO 160 lb 160 lb 400 lb 300 lb 80 lb (C) (10 pts) The motion of the 2.5 kg, a circle rod AB is guided in the horizontal plane by two small wheels which roll freely in horizontal slots. If a force P of magnitude 8 N is applied at B, determine (a) the acceleration of the rod, (b) the reactions at A and B. Note the location of the rod CG. 2r/ B 2014 P=0.3 m ME 3133: Dynamics Spring 2018 - Final Exam

Answer 1

Solution:

Principle Used: Parallel Axis theorem of MOI

Analysis: MOI of the given assembly will be the sum of MOI of each component about O

MOI = MOI of ring about centre + MOI of CD about O + MOI of BO about O + MOI of AB about O

• MOI of ring about centre = 3mr²
• MOI of CD about O = MOI of CD about about its centre + mr² = m(2r)²/12 + mr² = 4mr²/3
• MOI of BO about O = m(2r)² /12 = mr² /3
• MOI of AB about O = MOI of AB about B + m(2r)^{2 =} mr² /3 + 4mr² = 13mr² /3

MOI of the given assembly = 9mr²

Result: The MOI of the whole assembly about O is 9mr²

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