V₁ = V₁-Vcm m₂ V1 m₂ + m₂
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could you explain how we got 7.6.12? I dont understand why we have to substract vcm from v1 in order to get v1bar
Transcribed Image Text:system is zero both before and after the collision. Hence, we can write
P₁+P₂ = 0
Pí + P₂ = 0
The bars are used to indicate that the quantity in question is referred to the center of mass
system. The energy balance equation reads
P₁ P² P₁² P1²
+ +Q
2m₂ 2m, 2m₂
+
2m₁
(7.6.8)
We can eliminate p2 and 2 from Equation 7.6.8 by using the momentum relations in
Equations 7.6.7a and b. The result, which is conveniently expressed in terms of the
reduced mass, is
Hence, we have
=
P₁_P1²
(7.6.9)
2μ
2μ
The momentum relations, Equations 7.6.7a and b expressed in terms of velocities,
read
m₁v₁ + m₂ V₂ = 0
m₁v₁ + m₂v₂ = 0
The velocity of the center of mass is (see Equations 7.1.3 and 7.1.4)
✓ cmn
=
•+Q
(7.6.7a)
(7.6.7b)
miVi
m₂ + m₂
V₁ = V₁-Vcm
m₂ V1
m₁ + m₂
(7.6.10a)
(7.6.10b)
(7.6.11)
(7.6.12)
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