Elastic Collision: Determining Final Speeds of Carts
What are the final speeds of Cart #1, Cart #2, and Cart #3 after the elastic collision?
(a) What is the final speed of Cart #1?
(b) What are the final speeds of Cart #2 and Cart #3?
Answer:
(a) The final speed of Cart #1 is v0 to the right.
(b) The final speed of Cart #2 is v0 to the right, while the final speed of Cart #3 is 0 as it comes to a stop.
After analyzing the situation of the elastic collision between the three carts on the air track, we can determine the final speeds of each cart using the principles of conservation of momentum and kinetic energy.
Given the masses of the carts as m1 = 6m, m2 = 2m, and m3 = m, with Cart #1 initially given a velocity v0 to the right and the other carts at rest, we find that:
(a) Final Speed of Cart #1 (v1):By applying the conservation of momentum, we determine that the final speed of Cart #1 (v1) remains v0 to the right, retaining its initial velocity.
(b) Final Speed of Cart #2 (v2) and Cart #3 (v3):For Cart #2 and Cart #3, we find that Cart #2 also moves at a final velocity v0 to the right, while Cart #3 comes to a stop with a final speed of 0.
This analysis showcases the conservation of momentum and the outcomes of elastic collisions, highlighting how each cart behaves after the collision.