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11.49.
Model:
We will use the spring, the package, and the ramp as the system. We will model the package
as a particle.
Visualize:
We place the origin of our coordinate system on the end of the spring when it is compressed and is in contact
with the package to be shot.
Model:
(a)
The energy conservation equation is
1g
1s
1
t
h
0g
0s
0e
x
t
22
2
2
11
e
e
t
h
00
e
x
t
()
(
)
KU U
E KU U W
mv
mgy
k x
x
E
mv
mgy
k
x
W
+++
Δ=+++
++
−
+
Δ
=
Δ
+
Using
1
1 m,
y
=
th
0 J
E
Δ=
(note the frictionless ramp),
0
0 m/s,
v
=
0
0 m,
y
=
30 cm,
x
Δ
=
and
ext
0 J,
W
=
we
get
2
2
1
2
1
1
(1 m)
0 J
0 J
0 J
0 J
(0.30 m)
0 J
(2.0 kg)
(2.0 kg)(9.8 m/s )(1 m)
(500 N/m)(0.30 m)
1.70 m/s
mv
mg
k
v
v
+
=
+
+
+
+=
⇒=
(b)
How high can the package go after crossing the sticky spot? If the package can reach
1
1.0 m
y
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This note was uploaded on 12/10/2011 for the course PHYS 1211 taught by Professor Geller during the Fall '09 term at University of Georgia Athens.
 Fall '09
 geller

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