Question

Two point masses 2kg and 3 kg are moving along a straight line with speeds 3m/s and 5m/s respectively find the speed of centre of mass the system if both min masses are moving in the same direction and in opposite direction

Answer 1

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 centre mass coordinate X and its velocity as V.

By definition the centre 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