Is it possible for the momentum of a system consisting of two carts on a low-friction track to be zero even if both carts are moving?

Yes, if the carts are travelling into opposite directions

Explanation:

The total momentum of a two carts system is the sum of the momenta of the individual carts:

where

m1, m2 are the masses of the two carts

v1, v2 are the velocities of the two carts

In order to have a total momentum of zero, we must have

(1)

Let's remind that velocity (and so, momentum as well) is a vector quantity: this means that it has a direction, so when summing together the momenta, we must also consider the sign of the velocity, depending on its direction.

Therefore, if the two carts are moving in opposite directions, the signs of the two velocities will be opposite. For example, we can have

This means that the condition in eq.(1) can be satisfied, provided that the two carts are travelling into opposite directions.

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