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A marble with a mass of 2 grams moves to the left with a velocity of 2 m/s when it collides with a 3 gram marble moving in the opposite direction with a velocity of 2 m/s; if the first marble has a velocity of 1.5 m/s to the right after the collision, determine the velocity of the second marble after the collision.

I thought it could be solved using the conservation of momentum:

momentum before = momentum after

p.moving right + p.moving left = p.moving left + p.moving right

3(2) + 2(-2) = 3(v1') + 2(+1.5)

solving for v1' gives -0.3333... I think and ignoring sig.figs.

But then I checked using the conservation of energy. It didn't check.

So I guess one of the velocities is wrong. Let's say the velocity of the first marble after the collision is unknown. Then what would v1' and v2' be?

Someone else on that website said v2' would be 2.333...., but then that doesn't seem right. Why would the larger mass have more energy aft.than before?

I don't have my books and I forgot the formulas. I tried deriving, but I am not sure how to deal with the signs after equating the momentum factors in the difference of two squares. In fact I don't think I have seen this derivation for probably ten years - I couldn't even find it on the web.

Finally, could it be that the collision is not totally elastic? How would that work? I guess then the velocity of the 3 gram after could be 1.5, but not sure. Idk, brain fried. I stayed awake trying to figure it out last night. I guess what I really want to know is what do you get for velocities when it is a totally elastic collision?