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

Objects can have momentum within a system while the system's total momentum is zero if their momenta are equal and opposite. In a low-friction environment, two carts moving in opposite directions at the same speed provide an example where their total system momentum is zero.

Step-by-step explanation:

Yes, objects in a system can have momentum while the total momentum of the system is zero. This occurs when the individual momenta of the objects are equal in magnitude but opposite in direction, thereby canceling each other out. For instance, in a low-friction environment, two carts moving at the same speed but in opposite directions will have individual momenta that are opposite in direction. The total momentum of the two-cart system could thus be zero even if both carts are moving.

Here's a practical example involving two colliding carts on a frictionless surface. If one cart has a mass of 675 grams and is rolling at 0.75 m/s to the right, and the other has a mass of 500 grams and is rolling at 1.33 m/s to the right, after they collide and stick together due to magnets, the momentum is conserved.

The momentum before the collision will be equal to the momentum after the collision, meaning the velocity of the joined carts can be calculated using conservation of momentum principles. When calculating this, if friction was present, it would be an external force and would affect the total momentum, but in a low-friction scenario, the external forces are negligible, and therefore, the center-of-mass velocity would remain constant.

Answer 2

Yes, if the two carts are moving into opposite directions

Step-by-step 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.