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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
ℓ
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:
Your preview ends here
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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!
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