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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
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
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.
(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]
(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)
(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
(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