1D Collision
(I)
Completely inelastic collision
1
1
2
2
1
2
COM:
: common velocity after collis
(
ion
)
c
c
m
m
m
m
υ
υ
υ
υ
+
=
+
Example
Two sliders are moving along a frictionless track with initial
velocities shown. Slider
A
then collides with slider
B
, and the two
sliders are lodged by a coupling mechanism. Calculate the percent
energy loss during collision.
10 m/s
2 m/s
3 Kg
5 Kg
A
B
Sol
:
Given data:
3 Kg,
5 Kg,
10 m/s,
2 m/s
A
B
A
B
m
m
υ
υ
=
=
=
=
Find the common velocity of the sliders after collision:
(
)
3
10
5
2
(3
5)
5 m/s
A
A
B
B
A
B
c
c
c
m
m
m
m
υ
υ
υ
υ
υ
+
=
+
⇒
×
+
×
=
+
⇒
=
Find the change in energy:
2
2
2
2
2
2
(1/ 2)
(1/ 2)
(1/ 2)
3
10
(1/ 2)
5
2
160 J
(1/ 2)(
)
(1/ 2)
8
5
100 J
60 J
f
i
i
A
A
B
B
f
A
B
c
E
K
K
K
K
m
m
K
m
m
E
K
υ
υ
υ
Δ
= Δ
=
−
=
+
=
×
×
+
×
×
=
=
+
=
×
×
=
⇒ Δ
= Δ
= −
The negative sign indicates decrease in energy, confirming that energy is indeed lost after collision. The percentage can be
calculated to be
% loss =
/
60/160
0.375
37.5%
E
E
Δ
=
=
=
(II)
General inelastic collision
1
1
2
2
1
1
2
2
C
OM:
m
m
m
m
υ
υ
υ
υ
′
′
+
=
+
Example
A
B
5
υ
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 Spring '08
 TSChang
 Physics, Friction, Mass, 5 m/s, 2MB, 4.5m

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