Two 1-kg carts are each moving toward each other at 2 m/s. They collide and each reverses directions, moving in the opposite directions at 2 m/s.

Question

Two 1-kg carts are each moving toward each other at 2 m/s. They collide and each reverses directions, moving in the opposite directions at 2 m/s. Draw a diagram showing the carts before and after the collision.

 

a) Calculate the momentum of each cart before the collision. (Hint: Since they are moving in opposite directions, one momentum will be positive and one will be negative.)

 

b) Calculate the total momentum before the collision.

 

c) Calculate the total momentum after the collision.

 

ANSWER A, B, AND C USING PHYSICS TERMS, EXPLAIN FULLY. THANKS.

Answer 1

Chantelle,

 

This scenario is the opposite of the other I answered. This is a totally elastic collision. The two carts just bounce off of each other. Because they come out with equal but opposite velocity, we know they have come out with the same energy they carried in.  Again, this is conservation of momentum. Because velocity is a vector quantity (direction matters), the momentum is considered positive when moving up or right, and negative when moving left or down.

Pre-collision:

 

Cart 1 ⇒ 1 kg @ 2 m/s       1 kg @ -2 m/s ⇐ Cart 2

           p₁ = 2 kgm/s              p₂ = -2 kgm/s

 

Post-Collision:

 

Cart 1 ⇐ 1 kg @ -2 m/s        1 kg @ 2 m/s ⇒ Cart 2

           p₁ = -2 kgm/s             p₂ = 2 kgm/s

 

 

The total momentum is 0 both before and after because they are equal and opposite.

Answer 2

a) The momentum of each cart is just its mass times its velocity, so 1 kg * 2 m/s = 2 kg m/s. And -2 kg m/s for the other cart.

 

b)Therefore the total momentum is m1v1 + m2v2 = 2 kg m/s + - 2 kg m/s = 0

 

c) 0 because momentum is conserved, meaning the total momentum before the collision is equal to the total momentum after the collision. Also since you have the same numbers as before, they just switched signs, so you now have -2 kg m/s + 2kg m/s = 0.