Answer:
Yes, if the two carts are moving into opposite directions
Explanation:
The total momentum of the system of two carts is given by:
where
m1, m2 are the masses of the two carts
v1, v2 are the velocities of the two carts
Let's remind that v (the velocity) is a vector, so its sign depends on the direction in which the cart is moving.
We want to know if it is possible that the total momentum of the system can be zero, so it must be:
From this equation, we see that this condition can only occur if v1 and v2 have opposite signs. Opposite signs mean opposite directions: therefore, the total momentum can be zero if the two carts are moving into opposite directions.