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The University of Western Ontario Faculty of Engineering Department of Mechanical & Materials Engineering MME 2213 Engineering Dynamics Mid-term Examination, Thursday 12 February 2009 Limited Open Book 2 hours Total for working Intramural AIDS: 8 1/2" x 11" Equation Aid Sheet allowed Calculator (all calculators allowed) Answer ALL questions Questions are NOT of EQUAL value Questions carry the number of marks indicated Question 1 part marks are indicated Total Marks 100 Cheating: University policy states that cheating is a scholastic offense. The commission of a scholastic offence is attended by academic penalties which might include expulsion from the program. If you are caught cheating, there will be no second warning. QUESTION 1 (Total marks 20) Provide Brief Answers to the following: (a) How would you find distance from a typical velocity-time (v-t) plot? Draw a v-t plot illustrating a steadily increasing acceleration [2 marks] (b) State fundamental forms of Newton’s Law relating to translational and rotational motion (Hint: I am not looking for F=ma) [3 marks] (c) Describe four possible orbits associated with central force motion and the corresponding eccentricity ( ) values [3 marks] (d) Explain why the conservation of angular momentum holds in the case of central force motion? Illustrate via a simple sketch [3 marks] Page 1 of 3 (e) State work energy principle and explain its relationship to the principle of conservation of energy. State the fundamental assumption associated with application of this principle. [3 marks] (f) Define “coefficient of restitution” and explain its relevance to perfectly plastic impact. [3 marks] (g) A particle of mass m is considered to travel along a curvilinear path in two dimensions. Using polar ( r ) co-ordinate system, mark the relevant acceleration components and their directions together with their names. [3 marks] QUESTION 2 (Total marks 25) The polar coordinates of tip A of the crane shown in Figure 1 are given as functions of time by r 12 0.4t 2 m and 0.02t 3 rad. Determine the velocity and acceleration of tip A in terms of polar co-ordinates at t 2 seconds. Figure 1 (For Question 2) QUESTION 3 (Total marks 25) Two blocks A and B connected via two frictionless pulleys and a cable as shown in Figure 3 are pulled with an external force of 250 N. (a) Determine the relationship between the accelerations of A and B assuming that the cable is inextensible (b) Determine the accelerations of blocks A and B and the tension in the cable due to application of the external force neglecting all friction and masses of the pulleys. Figure 2 (for Question 3) Page 2 of 3 QUESTION 4 (Total marks 30) A satellite describes a circular orbit at an altitude of 19,019.4 km above the surface of the earth. Determine (a) the decrease in speed required at point A for the satellite to enter an elliptic orbit of minimum altitude 6345 km (b) the eccentricity of the resulting elliptic orbit. Figure 4 (for Question 3) Page 3 of 3