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1
−
D Collision
(I)
Completely inelastic collision
11
2 2
1
2
COM:
(
)
: common velocity after collision
cc
mm
m
m
υ
υυ
+=
+
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.
Sol
:
Given data:
3 Kg,
5 Kg,
10 m/s,
2 m/s
ABA
B
===
=
10 m/s
2 m/s
3 Kg
5 Kg
A
B
Find the common velocity of the sliders after collision:
()
31
0 52 (
3 5
)
5
m
/
s
AA
BB
A
B c
m
m
+
⇒× +×= +
⇒ =
Find the change in energy:
22
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
fi
iA
AB
B
fA
B
c
EK
KK
Km
m
m
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%
EE
=
=
(II)
General inelastic collision
COM:
′
′
+
Example
Spheres
A
of mass
m
and
B
of mass 2
m
are traveling toward each other with initial speeds of 5
and
, respectively, as
shown. Sphere
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 Fall '08
 TSChang
 Physics, Friction

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