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me274 e2 fa2008.pdf
me274_e2_fa2008.pdf
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me274 e2 fa2008.pdf-ME 274 – Fall 2008 SOLUTION
me274_e2_fa2008.pdf-ME 274 – Fall 2008 SOLUTION
me274 e2 fa2008.pdf-ME 274 – Fall 2...
me274_e2_fa2008.pdf-ME 274 – Fall 2008 SOLUTION
Page 8
ME 274 – Fall 2008
SOLUTION
Examination No. 2
PROBLEM NO. 3
Part (d) – 4 points
Cart A and block B (having masses of M = 4 kg and m = 2 kg, respectively) are
connected by a spring of stiffness k = 300 N/m.
The system is released from rest with the
spring being compressed by 0.2 meters (position 1). Find the
speed of cart A
at position 2
when the spring is unstretched/uncompressed. Consider all surfaces to be smooth.
HINT
:
Consider both the energy and the linear momentum of system A + B as it moves.
F
!
x
=
0
"
lin
.
momentum in x
#
dir
.
conserved
"
Mv
A
1
+
mv
B
1
=
0
=
Mv
A
2
+
mv
B
2
!
v
B
2
=
"
2
v
A
2
No external forces do work. Therefore,
T
1
+
V
1
=
T
2
+
V
2
!
0
+
1
2
k
"
1
2
=
1
2
Mv
A
2
2
+
1
2
mv
B
2
2
=
1
2
M
+
4
m
(
)
v
A
2
2
!
v
A
2
=
k
M
+
4
m
"
1
=
300
4
+
8
0.2
(
)
=
1
m
/
sec
Position 1
(at rest)
B
k
m
M
A
A
B
Position 2
(both A and B moving)
A
B
x
y
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