Answer:
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:
[tex]p=p_1 +p_2 = m_1 v_1 + m_2 v_2[/tex]
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
[tex]m_1 v_1 + m_2 v_2 = 0\\m_1 v_1 = - m_2 v_2[/tex] (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
[tex]v_1 > 0 \\v_2 < 0[/tex]
This means that the condition in eq.(1) can be satisfied, provided that the two carts are travelling into opposite directions.
