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ExamECOR21011996April.pdf
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DURATION: 3
HOURS
No. of Students: 125
Department
Name& Course
Number: Mechanical
& Aerospace
Engineering
91.211D
Instructor(s)
ProfessorJ. Kirkhope
U
RlZED MEMORANDA
Calculators, Drawing Instruments
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Students
MUST count
the number
of pages
in this examination
question
paper
before beginning
to write. and reportany
discrepancy
immediately
to a proctor. This question
paper
has7 pages.
This examination
question
paperMAYbe
takenfrom the examination
room,
This
exam has five (5) questions.
You may attempt
all questions.
Full
marks
in this
examination
may be obtained
by correct
answers in four (4) questions.
1.
The ends of the bar AB are confined to move along the paths shown.
At a given instant,
A has a veln(';tv of 8 ftls and an acceleration of 3 ftls2. Determine the angular velocity
and angular acceleration of AB at this instant.
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2.a.
Arm BC has a mass of 12 kg and the mass moment of inenia about its centre of mass is
'i!~
3 kgm2. Point B is stationary. Arm BC is initially aligned with the (horizontal) x axis
~
with zero angular velocity and a constant torque M applied at B causes it to rotate
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upward.
When it is in the position shown, its counterclockwise angular velocity is 2
rad/s. Determine the value of the torque M which has been applied.
b.
Assume that the torque M applied is 44 Nm counterclockwise, and that arm BC has the
!:~
angular velocity 2 rad/s counterclockw~se at the instant shown,oin ~e figure.
For ~s
ijijlt
instant determine the angular acceleratIon of arm BC and the horizontal and vertIcal
ti
components of the force applied at B.
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Exam
I
.1 1996
,
3.
A 3kg uniform slender rod AB 800 mm long hangs in a vertical plane from a frictionless
II
pivot when a 0.03 kg bullet strikes the rod and becomes embedded in it (Figure (a)).
If
the initial velocity of the bullet is Vo= 350 mis, determine:
#
a)
The angular velocity of the rod and the velocity of end B immediately after the
impact.
b)
The average force of contact between the rod and the bullet fOF
an impact duration
& = 0.001 s.
c)
The average magnitude of the force exerted on the rod by the pin at A for an
f
impact duration & = 0.001 s.
I
If instead of being hinged at A, the rod is balanced with end B on a smooth table, Figure
I
(b), and the bullet embeds at the same location and with the same velocity Vo= 350 mis,
determine:
I
d)
The angular velocity of the rod and ~e velocity of end B.
I
I
For a uniform rod 10 = ML 2/12
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0.5m
0.5 m
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B
B

Figure
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