- #1

gionole

- 281

- 24

## V = \frac{\sum\limits_{i = 1}^{n} m_iv_i}{\sum\limits_{i = 1}^{n} m_i} ##

I understand how it's derived, so no need to explain this further. It's a velocity of the frame in which total momentum of our objects is zero. Forget about the center of mass as well and let's focus on this ##V## only.

Imagine, we got 2 objects moving both to the right with masses 2 and 3 kg with the speeds: 10 and 25. If there is a train moving to the right by ##19m/s##, in this frame, total momentum would be 0, but what's so special about this that is different if train had moved by ##20m/s## ? I know that total momentum wouldn't be 0, but so what ?

Let's analyze this example.

Case 1: train moving by ##19## and see the distances travelled by objects and our tain.

After 1sec, 10 -> 19 -> 25 ( 9 - train - 6)

After 2sec, 20 -> 38 -> 50 ( 18- train - 12)

After 3sec, 30 -> 57 -> 75 (27- train - 18)

Case 2: train moving by ##20## and see the distances travelled by objects and our tain.

After 1sec, 10 -> 20 -> 25 ( 10 - train - 5)

After 2sec, 20 -> 40 -> 50 ( 20- train - 10)

After 3sec, 30 -> 60 -> 75 (30- train - 15)

What's so special in this example ##19m/s## moving, that for ##20m/s## train, it's not special anymore ?