Quiz_4_Solutions

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University of Michigan *

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240

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Mechanical Engineering

Date

Jan 9, 2024

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5

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Page 1 of 5 ME 240, Fall 2023 Koller ME 240: Introduction to Dynamics & Vibrations Fall 2023 Quiz 4 Wednesday, November 8 th , 2023 Name: _________________________________________________ Part 1 /15 Part 2 /20 Part 3 /15 Total /50 Read all questions carefully and answer them to the best of your ability. Circle all final answers. Circle only one final answers per question and show all of your work. Cross out or erase any work you would not like to be considered in grading of this exam. You are allowed a writing utensil/eraser and one page of double-sided notes. Place all mobile phones and smart watches out of sight in your bag. No equipment of any type is allowed that can be used to communicate with others during the exam. Doing so would be a breach of the honor code. If you need additional room to show your work, there is scrap paper at the front of the room. Please label clearly on the exam where you have transitioned to the scrap paper and staple all scrap paper to the back of the exam. ©Jeffrey Koller all rights reserved. This exam may not be used, archived, distributed, or copied in any form without the express permission of the authors. Per the College of Engineering honor code, all students must copy and sign for the following statement upon finishing this exam to comply with the honor code policy: I have neither given nor received aid on this examination, nor have I concealed any violation of the UM College of Engineering honor code. __________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________ Signature: _____________________________________________________________________________________________________
Page 2 of 5 ME 240, Fall 2023 Koller Consider the linkage system shown below in the given orientation. The yellow collar attached to point ? is traveling at a constant speed of 𝑣 ? downward. In answering the following, you can assume that 𝑣 ? and are known values. Part 1 (15 points): Suppose you wanted to determine the angular velocity of the link ?? (i.e. the green link). Outline a roadmap to solving for this. Include all kinematic analysis equations you would need to solve like we do in class with a check mark or ‘X’ over each value to signify if the magnitude or direction is known. You do not need to ultimately solve for the angular velocity, we just want a description of how you would do so with equations to support your approach. Ultimately, we want you to show that you have as many equations as you do unknowns.
Page 3 of 5 ME 240, Fall 2023 Koller Part 2 (20 points): Suppose you solved through for Part 1 and found that at this instant 𝜔 ?? = 𝜔 ?? = 𝑣 𝐴 2ℓ and that both are in the counterclockwise direction. Determine the angular acceleration of the link ?? (i.e. the green link). Express your answer as a vector expression using a coordinate system you clearly define/draw. For reference:
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Page 4 of 5 ME 240, Fall 2023 Koller Part 3 (15 points): Consider point ? (shown in red) that is located at the midpoint of link ?? . Determine what the velocity of point ? is relative to point ? (i.e. if you were situated at point ?, what velocity would you see point ? moving with from your perspective). Express your answer as a vector expression using a coordinate system you clearly define in the above diagram.
Page 5 of 5 ME 240, Fall 2023 Koller When finished, we ask that you please stay in your seat as to not distract others. If you’re looking for something to occupy your time, may we suggest the Sudoku puzzle below. Rules of Sudoku: Sudoku is a puzzle game where you are looking to fill in the blank tiles with any number between 1 and 9. Each row, each column, and each of the nine 3x3 grids can only contain one instance of each of the numbers 1 through 9. Have fun!