ME 375 EXAM #1
Wednesday, February 23, 2011
Division
Shaver / Krousgrill/Deng (circle one)
SOLUTION
Instructions
(1)
This is a closed book examination, but you are allowed one 8.5
×
11 crib sheet.
(2)
You have one hour to work all three problems on the exam.
(3)
Use the solution procedure we have discussed: what are you given, what are you asked to
find, what are your assumptions, what is your solution, does your solution make sense.
You must show all of your work to receive any
credit.
(4)
You must write neatly and should use a logical format to solve the problems. You are
encouraged to really “think” about the problems before you start to solve them.
Please
write your name in the top righthand corner of each page.
(5)
A table of Laplace transform pairs and properties of Laplace transforms is provided at the
end of this exam.
Problem No. 1 (30%)
________________________
Problem No. 2 (40%)
________________________
Problem No. 3 (30%)
________________________
TOTAL (***/100%)
________________________
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View Full DocumentFebruary 23, 2011
SOLUTION
2
PROBLEM 1
(30%)
A system is made up of a homogeneous wheel A and blocks B and C (each having a mass of m).
Consider the small wheels supporting blocks B and C to be massless. A motor at O connecting
block B and the wheel provides a torque T to the wheel. A spring and dashpot connects blocks B
and C. A second spring connects block C to ground, as shown in the figure. The wheel is able to
roll without slipping on a horizontal surface. Blocks B and C are able to slide without friction on
the horizontal surface. Let
θ
represent the rotation of wheel A and
x
represent the translation of
block C. Assume that the springs are unstretched when
x
=
=
0
. The centroidal mass moment
of inertia of a homogeneous wheel of mass m and radius R is given by:
I
O
=
1
2
mR
2
.
For this problem:
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 Fall '10
 Meckle
 Laplace, 3s

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