Two carts with masses of 4.56 kg and 2.26 kg move toward each other on a frictionless track with speeds of 4.96 m/s and 3.60 m/s respectively.

Question

The carts stick together after colliding head-on. Find the final speed.

Answer 1

This is an example of the conservation of momentum. The total momentum before collision is equal to the total momentum after collision. Also, as the carts stick together, this is an inelastic collision.

As momentum is a vector quantity, let the cart having a mass of 4.56 kg be moving from left to right and is a positive quantity. Conversely, the 2.26 kg cart is moving from left to right and is negative.

The total momentum before collision is then 4.56 kg x 4.96 m/s - 2.26 kg x 3.6 0m/s = + 14.48 kg-m/s to the right.

This before collision momentum is set equal to the total mass after collision x the final velocity or 14.48 kg-m/s = (4.56 + 2.26)kg x V_after.

Solving for V_after = + 2.12 m/s to the right.

Please chem math.