n exam 03: chapters 16–17 - uca

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Exam 03: Chapters 16–17Instructions

• Solve each of the following problems to the best of your ability. You have two hours in which to complete this exam.

• You may use your calculator and your textbook.

• Read and follow the directions carefully. Pay attention to the hints!! They are there for a reason!!

• Solve using the method required by the problem statement. If you are not explicitly required to use a specific technique, please be sure to show sufficient work so that your method is obvious.

• Show all your work. Work as neatly as you can. If you need scratch paper, blank sheets will be provided for you.

• It is permissible to use your calculator to solve a system of equations directly. If you do, state this explicitly. If you need to use a solver to evaluate a trig equation, you will be allowed to either use your mobile device briefly, or you may borrow mine. You may only use the device to solve the specific equation; you may not look up formulae or solutions to any other problems.

• Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units.

ScoringProblem 01: Chapter 16 /15

Problem 02: Chapter 16 /15





ENGR 3311: ENGINEERING DYNAMICS! SPRING 2017

EXAM 03! PAGE 01

Problem 01 Chapter 16: Problem 16.17 A motor gives Gear A an angular acceleration αA = (2 + 0.006θ2)rad/s2, where θ is in radians. If this gear is initially turning with ωA = 15 rad/s, determine the angular velocity ωB of Gear B after Gear A undergoes an angular displacement of 10 revolutions.

Hint: You’re going to have to integrate ωdω =αdθ to get ω as a function of θ for Gear A. Also, remember to change rev to rad!


EXAM 03! PAGE 02

Problem 02 Chapter 16: Problem 16.40

At the instant when θ = 60°, the slotted guide is moving to the left with an acceleration a = 2m/s2, and a velocity v = 5 m/s. Determine the angular acceleration α and angular velocity ω of the link AB at this instant.

Hint: Define x as the position of the vertical guide with respect to fixed origin at A. Write x as a function of θ, then start taking time derivatives. Be very careful with signs!


EXAM 03! PAGE 03


Block D of the mechanism is confined to move within the slot of member CB. If link AD is rotating at a constant rate of ωAD = 4 rad/s, determine the angular velocity and angular acceleration of member CB at the instant shown.

Hint: No shortcuts on this one, just brute force vector cross-producting! Align your fixed coordinate system X-Y with origin at C, aligned with CB. Do the same thing with your rotating reference frame x-y. Also, this is pretty much exactly the same as 16.140 (which we solved in class); same technique!

X, x

Y, y


EXAM 03! PAGE 04


A force P = 300N is applied as shown to the cart, which has mass m = 60kg. Determine the reaction forces NA and NB at wheels A and B, and the acceleration a of the cart.

Hint: Straight up Newton #2, sum the forces, sum the moments.

NA NBmg


EXAM 03! PAGE 05


The roll of paper has mass m = 20kg, and a radius of gyration kA = 90mm. Pins at A and B support the roll and attach the bracket to the wall. The coefficient of friction µk = 0.2 at point C, and a vertical force F = 30N is applied as shown. Determine the normal force N at point C, the reaction force R at A, and the angular acceleration α of the roll of paper.

Hint: IA = m(kA)2. Then Newton #2.

Sign convention! I assumed ccw = (+), which was counter-intuitive, since spin is clockwise! Negative α still indicates speeding up in this context!

mg

R

N

µkN


EXAM 03! PAGE 06


The coefficient of static friction at point C is µs = 0.3. Determine the largest force F that can be applied to the ring (mass m = 10kg) without causing it to slip. Also solve for the linear acceleration of the ring aG, and its angular acceleration α.

Hint: Iring = mr2. And Newton #2.

mg

NµsN

30°

15°

Fsin15°


EXAM 03! PAGE 07

n exam 03: chapters 16–17 - uca

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