PHYSICS 170 MECHANICS 1: October Exam MARKS This exam counts for a total of 20 marks towards your Final Grade for the course. The exam consists of 2 questions. Each question is worth 20 marks. You are allowed to consult your notes and textbook, but not to communicate with others. NUMERICAL ANSWERS You must write numerical answers correctly to three significant figures and with correct units. CALCULATOR You may use a graphing calculator. Gradescope Upload Please upload your answers to each question separately to gradescope, you are given 20 minutes t There will also be space to upload a copy of your ID as answer to question 3.
Question 1 (20 points The 100lb door has its center of gravity at the point G. The hinge at B resists only forces in the x,y directions whereas the hinge at A resists forces in the x,y,z, directions. There are no couple moments. · Draw a clear free body diagram, indicate all the unknowns (5 points). · Write the force equilibrium equations for translational motion (5 points). · Write the moment equilibrium equations for rotations around the x,y axes (5 point). 1 30° · Find the forces by which the hinges at A,B resist to keep the door at equilibrium (5 points). Z 18 in. B 24 in. 24 in. A 18 in. x y
@ 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *5-68. The 100-lb door has its center of gravity at G. Determine the components of reaction at hinges A and B if hinge B resists only forces in the x and y directions and A resists forces in the x, y, z directions. z 18 in. B 24 in. SOLUTION Equations of Equilibrium: From the free-body diagram of the door, Fig. a, By, B x' and A2 can be obtained by writing the moment equation of equilibrium about the x¿ and y ¿ axes and the force equation of equilibrium along the z axis. 24 in. G A 18 in. OM?¿ = 0; @My¿ = 0; OF z = 0; -By(48) - 100(18) = 0 By = - 37.5 lb Bx = 0 -100 + Az = 0; Ans. Ans. Ans. 300 x y Az = 100 lb Using the above result and writing the force equations of equilibrium along the x and y axes, we have @Fx= 0; Ax = 0 Fy = 0; Ay + (-37.5) = 0 Ay = 37.5 lb By Ans. 48 in Br Ans. Any Z 1Bin 1001b The negative sign indicates that By acts in the opposite sense to that shown on the free-body diagram. If we write the moment equation of equilibrium @M2 = 0, it shows that equilibrium is satisfied. A+ x (a) y 456 Ans: By = - 37.5 lb Bx