Newton's spheres!

Classical Mechanics Level 3

The Newton's spheres are the best way of studying how the Physics of collisions works. The spheres have all the same mass $$m$$. Imagine there are four spheres: $$a,b,c,d$$. The sphere $$a$$ will collide with the others three spheres with an initial speed of $$4 \text{ m/s}$$. After the collision happens, what will be the sum, in $$\text{ m/s}$$, of the speeds of the spheres a, b, c, d?

Details and Assumptions:

• The spheres don't touch each other more than once during this hypothetical experiment. Also, do not consider any loss of mechanical energy in the system. The friction of the spheres' surface is negligible.
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