Mechanical Engineering Ph.D. Preliminary Qualifying Examination
Dynamics – January 28 , 2009 (Wednesday)
Show all work on the exam sheets provided and write your student personal identification (PID) number
on each sheet. Do not write your name on any sheet.
Your PID number:____________________________
QUESTION 1
A car of mass m is traveling at a slow velocity V0 . If it is subjected to the drag resistance of the
wind, which is proportional to its velocity, i.e., FD  kV , and assuming no other frictional forces
act on the car:
 Draw the free body diagram
 Determine the distance and the time the car will travel before its velocity becomes 0.5V0
Your PID number:____________________________
Question 2.
Each of the three balls has the same mass m . If A is released from rest at  , and the coefficient
of restitution between each ball is e :
Determine the angle  to which C rises after collision (in terms of e and  ).
Your PID number:____________________________
Question 3.
The pendulum consists of a 10-lb solid ball of radius 0.3 ft and welded to a 4-lb rod of length
2 ft . If the pendulum is released from rest when 1  0o , and if the coefficient of restitution
between the pendulum ball and the vertical wall is e  0.6 ,
 Determine the angle  2 which the pendulum attains after the ball strikes the wall and the
pendulum swings up to the point of momentary rest.
 Determine the angular momenta of the system about O just before and just after the
impact.
0.3 ft
O

2 ft
0.3 ft
Your PID number:____________________________
Question 4.
Each of the three plates has a mass of 10 kg. If the coefficients of static and kinetic friction at
each surface of contact are s  0.3 , and k  0.2 , respectively.
 Examine if the three blocks will move together as one mass under the action of the given
loads. Support your work by drawing the Free body diagram.
 Determine the acceleration of each plate when the three forces are applied. Draw the
necessary free body diagrams of each mass.
 Examine your assumption for sticking or slipping for each combination.
18N
D
100N
C
15
B
A
Your PID number:____________________________
Question 5.
The pendulum consists of a uniform 5 kg rectangular plate and a 2 kg slender rod. Determine the
horizontal and vertical components of the reaction that the pin O exerts on the rod at the instant
  30o , at which time its angular velocity is   3 rad /s . Draw the necessary free body
diagram.
Determine the tangential reaction force at O using the concept of center of percussion and verify
your answer using Newton’s second law.
0.5m
O

  0.3 rad /s
0.3m
0.2m
1.
2.
3.
4.
5.