Cart 1 moves rightwards toward cart 2 cart 2 is initially...

Cart 1 moves rightwards toward cart 2. Cart 2 is initially stationary. Consider the following two scenarios: (A) The collision is totally inelastic—the two carts stick together and move together to the right. (B) The collision is perfectly elastic—cart 1 bounces backward off of cart 2, moving to the left while cart 2 moves to the right. In both scenarios, cart 1 transfers some magnitude of momentum to cart 2. In which scenario do you think the momentum magnitude gained by cart 2 is greater? Explain your reasoning.

Transcript

00:01 So we have two scenarios here where the first one is totally inelastic.

00:05 The two carts take that after collision, cart 1 is moving to the right and cart 2 initially stationary.

00:11 Then for the second scenario, we have an elastic collision, cart 1 bounces of cart 2, and they both move in opposite directions after collision.

00:24 So we need to know that the change in momentum for the minding of the change of momentum for the two cards is going to be.

00:31 Be equal so delta can write the final momentum to caught two would be called to sorry minus the initial momentum for card two would be called to the insharmamentum for card one minus the final momentum for got one so we could also write it as minus final momentum for got one minus insharmamentum for got one so this is a negative of this and momentum is birth of mass and velocity so this is m to v2 minus m2 um u 2 u 2 u is going to be the initial velocity and v is going to be the final velocity is it go to minus m1 u1 v1 minus m 1 u1 so this is m2 in bracket v2 is equal to m1 in bracket u1 minus v1 so now this is the magnitude of the momentum for cat 2, right? and this is equal to the maximum momentum for card 1.

01:55 So let's find the scenario where the change in momentum for cut 1 is greater.

02:03 So the mass of cart 1 remains the same in both scenarios.

02:08 So what is actually changing is the velocity.

02:11 The final velocity to be precise, which is v1 here.

02:16 The ensure velocity remains the same also.

02:17 So let's look at what happens to the velocities in the two scenarios.

02:23 So in scenario a, we have the two cards stick together and move to the right.

02:30 So the velocity, the final velocity of cart 1 is to the right...