Question

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?

Answer 1

Answer:

Yes, if the two carts are moving into opposite directions

Explanation:

The total momentum of the system of two carts is given by:

$p=m_1 v_1 + m_2 v_2$

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:

$p=0\\m_1 v_1 + m_2 v_2 = 0\\m_1 v_1 = -m_2 v_2$

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.