Question

# Mass A (8.5 kg) slides across a frictionless surface with a velocity of 6 m/s in...

Mass A (8.5 kg) slides across a frictionless surface with a velocity of 6 m/s in the positive direction. Mass B (8.5 kg) slides across the same surface in the opposite direction with a velocity of
?12 m/s.
The two objects collide and stick together after the collision. Calculate the center-of-mass velocity (in m/s) of the system both before and after the collision. (Indicate the direction with the sign of your answer.)

It is given that the collision is inelastic

let positive x direction be to the right

then, from Conservation of Momentum:

8.5(6) + 8.5(- 12) = (8.5 + 8.5)V

=> V = - 3 m/s

this is the velocity of the center of mass after the collision.

Now, center of mass is the point where all the mass is assumed to be present. This implies that before and after the collision, the velocity of the center of mass will not change as long as there is no external driving force.

Therefore, the velocity of the center of mass before the collision is also - 3 m/s.

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