COLLEGE OF ENGINEERINGMECHANICAL ENGINEERING

Ph.D. Preliminary Qualifying Examination

Signature PageDYNAMICS

Wednesday January 26, 20119:30 am – 12:30 noon

Room 2145 Engineering Building

For identification purposes, please fill out the following information in ink. Be sure to print and sign your name. This cover page is for attendance purposes only, and will be separated from the rest of the exam before the exam is graded. Write your student number on all exam pages. Do NOT write your name on any of the other exam pages besides the cover page.

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COLLEGE OF ENGINEERINGMECHANICAL ENGINEERING

Ph.D. Preliminary Qualifying Examination

Cover Page

9:00 am – 12:00 noonRoom 2145 Engineering Building

GENERAL INSTRUCTIONS:

This examination contains five problems. You are required to select and solve four of the five problems. Clearly indicate the problems you wish to be graded. If you attempt solving all of them without indicating which four of your choice, the four problems with the worst grades will be considered.

Do all your work on the provided sheets of paper. If you need extra sheets, please request them from the proctor. When you are finished with the test, return the exam plus any additional sheets to the proctor.

Your PID number:____________________________

QUESTION 1

Two particles A and B start from rest at the origin and move along a straight line such that the acceleration of A is and the acceleration of B is , is in seconds.

Determine the total distance traveled by each particle in 4 seconds Determine the linear displacement of each particle in 4 seconds Determine the distance between the two particle when seconds.

Your PID number:____________________________

Question 2.

The 10-kg box starts from rest under the influence of the horizontal force. The time history of the horizontal force is as shown in the figure. The coefficients of static and kinetic friction between the box and the surface are and , respectively.a) Determine the maximum velocity of the box during the course of motion.b) Determine the time when the box will come to a stop.

Your PID number:____________________________

Question 3.

Motor M draws in the cable with an acceleration of , measured relative to the 200-lb mine car, neglect the mass of the pulleys and friction:

Draw the free-body diagram of the car.Determine the acceleration of the car.Determine the tension in the cable.

Your PID number:____________________________

Question 4.

The pendulum consists of a 10-lb sphere and of radius 0.3 m. Its rod has a weight of 4-lb rod and length of 2 ft hinged at O. If the pendulum is released from rest when , i.e. from the inverted vertical position:

1. Determine the location of the system center of mass 2. Determine the mass moment of inertia of the pendulum about O3. Determine the angle of rebound after the sphere strikes the floor if the coefficient of

restitution between the sphere and floor is

. .c gL

. .c g. .c gL

. .c g

Your PID number:____________________________

Question 5.

A uniform plate has a weight of 50-lb and is hinged at the left corners by rods AB and CD in the vertical plane as shown.. Link AB is subjected to a moment and has a clockwise angular velocity of at the instant . The masses of the two links AB and CD are negligible and can be taken zero:

Draw the free-body diagrams of the plate and each link. Determine the force developed in link CD Determine the tangential component of the acceleration of the plate’s center at this

instant.

1.

2.The applied force as a function of time is:

(1)

a) The basic equations of motion are:(2)

Physics: Initially, the box is at rest and the applied force has to overcome the maximum static friction before motion would begin. After motion begins, the box will continue to accelerate until it reaches the maximum velocity when the acceleration is instantaneously zero (happens during period). Beyond this instant, the box will decelerate until it comes to a stop.

: The maximum static friction is . The is achieved at the time

(3)

Once motion begins, . Net impulse during this period is:

: Net impulse during this period is:

: Maximum velocity occurs when . The is achieved at the time

(4)

Net impulse during this period is:

The maximum velocity is thus

b) First determine the velocity of the box at 12 seconds. The total impulse is

The velocity at 12 seconds is thus equal to 17.62 m/s. Since this value is positive, the box will continue to slide after 12 seconds under only the influence of the friction force. The net impulse (or momentum gained) at 12 seconds is balanced by the friction loss for . Thus,

3.

4.

5.