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me274 e2 fa2008.pdfME 274 – Fall 2008 SOLUTION
me274_e2_fa2008.pdfME 274 – Fall 2008 SOLUTION
me274 e2 fa2008.pdfME 274 – Fall 2...
me274_e2_fa2008.pdfME 274 – Fall 2008 SOLUTION
Page 5
ME 274 – Fall 2008
SOLUTION
Examination No. 2
PROBLEM NO. 3
Part (a) – 6 points
Particle B is attached to
rigid
bar BO with bar BO pinned to
ground at O. Particle A strikes the stationary particle B with
a speed of
v
A1
in the direction shown. The coefficient of
restitution for this impact is e < 1. Consider all surfaces to be
smooth and all motion to be in a HORIZONTAL plane.
Consider the following 12 statements about momentum and
energy during impact and indicate if each statement is TRUE
or FALSE.
HINT
:
Complete the FBD of each of the three systems
shown below prior to responding.
For System A+B
linear momentum in the ndirection
is conserved:
TRUE
or
FALSE
linear momentum in the tdirection
is conserved:
TRUE
or
FALSE
angular momentum about point O is conserved
:
TRUE
or
FALSE
mechanical energy
is conserved:
TRUE
or
FALSE
For System A
linear momentum in the ndirection
is conserved:
TRUE
or
FALSE
linear momentum in the tdirection
is conserved:
TRUE
or
FALSE
angular momentum about point O is conserved
:
TRUE
or
FALSE
mechanical energy
is conserved:
TRUE
or
FALSE
For System B
linear momentum in the ndirection
is conserved:
TRUE
or
FALSE
linear momentum in the tdirection
is conserved:
TRUE
or
FALSE
angular momentum about point O is conserved
:
TRUE
or
FALSE
mechanical energy
is conserved:
TRUE
or
FALSE
A
B
v
A1
36.87°
O
RIGID bar
v
B1
= 0
B
n
t
B
n
t
A
n
t
A
System A+B
System A
System B
Page 6
ME 274 – Fall 2008
SOLUTION
Examination No. 2
PROBLEM NO. 3
Part (b) – 6 points
An arm rotates about the fixed Zaxis with a rate of
Ω
.
A circular disk rotates about its
own axis with a
constant
rate of
p = 4 rad/sec
relative to the arm. Let XYZ represent a
set of fixed coordinate axes, and xyz be a set of coordinate axis attached to the disk.
At the instant shown, the xyz and XYZ axes are aligned. Also at this position,
Ω
= 3
rad/sec
with
Ω
increasing
at a rate of
!
!
=
2
rad
/
sec
2
. For this position, determine the
angular velocity and angular acceleration of the disk
. Express your answer as vectors in
terms of either their xyz or XYZ
components.
!
=
"
K
+
pj
=
3
k
+
4
j
(
)
rad
/
sec
!
=
!
"
K
+
"
!
K
+
!
pj
+
p
dj
dt
=
!
"
K
+
"
0
+
0
()
j
+
p
#
$
j
(
)
=
2
k
+
4
(
)
3
k
+
4
j
(
)
$
j
(
)
=
%
12
i
+
2
k
(
)
rad
/
sec
2
Page 7
ME 274 – Fall 2008
SOLUTION
Examination No. 2
PROBLEM NO. 3
Part (c) – 4 points
Particle P (having a mass of m) is able to slide on a smooth
HORIZONTAL
surface. An
extensible cord (having a stiffness of 50 N/m and unstretched length of 2 meters) is
attached between P and a fixed point O in the plane of motion for P. At position 1, P is
released with a velocity as shown below with R
1
= 2 meters. Assuming that the cord
remains taut for all time, find the
angular speed
ω
of the cord
about point O when P is at
position 2 where R
2
= 4 meters.
HINT
:
consider the angular momentum of P as it moves about the fixed point O.
M
O
!
=
O
"
H
O
2
=
H
O
1
"
mr
P
/
O
!
v
P
2
=
mr
P
/
O
!
v
P
1
R
2
e
R
(
)
!
!
R
2
e
R
+
R
2
"
2
e
#
(
)
=
R
1
e
R
(
)
!
v
P
1
cos
#
e
R
+
v
P
1
sin
#
e
#
(
)
R
2
2
"
2
k
=
R
1
v
P
1
sin
#
k
$
!
2
=
R
1
v
P
1
sin
"
R
2
2
=
2
()
20
(
)
0.6
(
)
4
(
)
2
=
1.5
rad
/
sec
top view of HORIZONTAL PLANE of motion for P
O
P
P
R
1
R
2
position 1
position 2
v
P1
= 20 m/sec
36.87°
ω
O
P
e
θ
e
R
F
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