 #1
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Homework Statement:

1. if two bodies of masses m are moving toward each other with a constant speed v and 2v find the speed of the CoM.
2. If two bodies of masses m are accelerating towards each other due to the force of gravity on each of them what is the speed of the CoM.
Relevant Equations:
 $$V_{cm} = \frac {m_{1}v_{1} + m_{2}v_{2}}{m_{1}+m_{2}}$$
In question 1. since there is no external force on the system of particles(and since it was initially at rest) shouldn't the ##V_{cm}## be zero?
But the correct answer applies the above stated formula for ##V_{cm}## and gets ##V_{cm} = v/2##
and in question 2 again as there is no external force on the system the ##V_{cm} = 0## (as they will also collide at the CoM) but here how exactly can you apply the above formula(maybe in a differential eqn form as they are accelerating) to get ##V_{cm} = 0##
in short I am confused as to when to apply $$V_{cm} = \frac {m_{1}v_{1} + m_{2}v_{2}}{m_{1}+m_{2}}$$
But the correct answer applies the above stated formula for ##V_{cm}## and gets ##V_{cm} = v/2##
and in question 2 again as there is no external force on the system the ##V_{cm} = 0## (as they will also collide at the CoM) but here how exactly can you apply the above formula(maybe in a differential eqn form as they are accelerating) to get ##V_{cm} = 0##
in short I am confused as to when to apply $$V_{cm} = \frac {m_{1}v_{1} + m_{2}v_{2}}{m_{1}+m_{2}}$$
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