A line of identical train cars collide inelastically. (They couple.) Three carts are initially
coupled and moving at speed v: the rest are stationary. The three moving cars hit a fourth,
then those four hit a �fth, and so on. This continues until the speed of the "collection" is 1/5
the speed of the initial three carts. How many carts are in the �nal "collection"?
To solve this problem, we need to analyze the conservation of momentum and energy during the collisions.
Let's denote the number of carts in the final "collection" as N. We are given that initially, three carts are moving at speed v and the rest are stationary. So we have:
Initial momentum = Mass of three moving carts * velocity = 3mv
During each collision, the carts couple and move as a single unit. Therefore, the momentum is conserved. After the first collision, the speed of the collection becomes 1/5 of the initial speed. So we have:
Final momentum = Mass of the collection * (1/5 * v)
Since momentum is conserved, we can write:
3mv = N * (1/5 * mv)
Canceling out the mass and v:
3 = N/5
Cross-multiplying:
15 = N
So there are 15 carts in the final "collection".