10.42. Model:
Model the two packages as particles. Momentum is conserved in both inelastic and elastic
collisions. Kinetic energy is conserved only in a perfectly elastic collision.
Visualize:
Solve:
For a package with mass
m
the conservation of energy equation is
22
1g
1 0g
0
1
1
0
0
11
()
mm
K
UK
U
m
v
m
g
y
m
v
m
g
y
+=
+⇒
+
=
+
01
Using ( )
0 m/s and
0 m,
m
vy
==
10
1
0
1
( )
( )
2
2(9.8 m/s )(3.0 m)
7.668 m/s
2
mv
mgy
v
gy
=⇒=
=
=
(a)
For the perfectly inelastic collision the conservation of momentum equation is
fi
2
3
1
1
2
(2
)
(
)
(
)
(
2
)
(
)
x
xm
m
m
p
p
m mv
=⇒+
=
+
12
Using ( )
0 m/s, we get
m
v
=
23
1
( )
( ) /3
2.56 m/s
vv
The packages move off together at a speed of 2.6 m/s.
(b)
For the elastic collision, the mass

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