Two particles of masses of 20g and 40g are moving opposite to each other with speed 2m/s and 5m/s resectively on a straight line. They collide elastically . Find the change in momentum of each particle
Answers
Let the two bodies of masses m1 and m2 be placed at x1 and x2 and are moving with their velocities v1 and v2.
Let the center mass coordinate X and its velocity as V.
By definition the center of mass coordinate will be
X = {m1.x1 + m2.x2 } / (m1 + m2)
therefore substituting the masses
X = {2kg.x1 + 1kg.x2 } / (2 + 1) kg = (2/3).x1 + (1/3) . x2
therefore,
dX/dt = Velocity of center of mass = (2/3).dx1/dt + (1/3) . dx2/dt or
V = (2/3).v1 + (1/3) . v2
as v1= 2m/s and v2 = 5m/s
V= (2/3).2 + (1/3) . 5 = (4/3) + (5/3) = 9/3 m/s
V= 3m/s
What we learn that if the masses are moving with v1 and and v2 linearly in the same direction the center of mass will move with difference of their velocities.
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