CONSERVATION OF MOMENTUM 2. Two gliders are on a...

CONSERVATION OF MOMENTUM 2. Two gliders are on a frictionless, level air track. Initially, glider A moves toward the right and glider B is at rest. After the collision, glider A has reversed direction and moves toward the left. The combined system of both gliders is denoted as system C. Initial direction of motion A B m_A = 1/4 m_B Track is frictionless The mass of glider A is one fourth the mass of glider B. a. Draw an arrow to represent the direction of the initial velocity (before the collision) of the center of mass of system C. If the initial velocity of the center of mass is zero, state that explicitly. Explain. Direction of v_cm, i b. Draw an arrow for each glider to represent the direction of the change in velocity from before to after the collision. Explain how you determined your answer. Direction of change in velocity Glider A Glider B Is the magnitude of the change in velocity vector for glider A greater than, less than, or equal to the magnitude of the change in velocity vector for glider B? Explain. c. Draw an arrow to represent the direction of the final velocity (after the collision) of the center of mass of system C. Explain how you determined your answer. Direction of v_cm, f d. Consider the following incorrect statement: ?Glider B will move to the right after this collision, but it would move faster if glider A were to come to a stop, giving glider B all its momentum.? Describe what is incorrect about this statement and explain how you can tell.

Transcript

00:01 Okay, so we've got some conservation of momentum happening here.

00:04 There's a block a, which is one -fourth the mass of b.

00:10 So let's just to make things simple here, say that a is one kilogram, and b is four kilograms.

00:18 That's just a made -up number, but it gives you the same ratio, which i think will be helpful for describing this here.

00:26 And initially, a is in motion with some velocity to the right, and b is at rest with no velocity.

00:35 For part a, we want to know about the velocity of the center of mass of the system.

00:39 So there's probably a couple different ways to think about this, but one way to think about it is the total mass of the system is five kilograms, right? one of those kilograms is moving to the right, four of them are not moving at all.

00:54 So one -fifth of the system mass is moving to the right.

00:58 So the way that i would answer, part a here, is a small arrow to the right for the center of mass.

01:07 Velocity center mass is to the right.

01:12 If they didn't ask for this, but if they asked you, it would be one -fifth of the size of v, because one -fifth of the total system mass is to the right.

01:20 You just need to draw an arrow to the right, though, on this.

01:28 Okay, for b, we want to know about the change in velocity before and after the collision.

01:36 Okay, so what do they tell us here? well, i can tell you that what's going to happen is a is going to bounce back and b is going to bounce forward.

01:53 We know that because this is going to be presumably an elastic collision.

02:01 It's okay.

02:01 It says it at the top.

02:02 I'm sorry.

02:03 A is a reverse direction to move toward the left.

02:06 B is going to be moving toward the right.

02:07 All right.

02:08 So the change in velocity.

02:10 So let's see here.

02:11 Glider a was initially going to the right.

02:16 Now it's going to the left.

02:17 So what happened here? there was a change in velocity to the left.

02:22 Let's put some numbers on this.

02:23 Let's say that a had a velocity of positive 1, and then at the end it had a velocity of negative 1.

02:29 What do you have to add to positive 1 to get negative 1? the change in velocity would be negative 2 in that case, negative 2.

02:39 So do we need to say negative 2? no, but you want to say something like this for glider a, that the change in velocity is to the left.

02:49 For glider b, the change in velocity is to the right.

02:54 It starts with a velocity of zero.

02:56 It's going to end with a velocity to the right.

03:00 Okay, and so our change is going to be just a velocity to the right.

03:03 It's going to be, and this is the next part, it's going to be a smaller change for b because it has a bigger mass, and a bigger change for a because it has a smaller mass.

03:14 Okay, so they're not asking you for equations here, but it might be helpful to just think about the equations.

03:18 The equation for momentum, momentum of a before the collision equals momentum of a after the collision plus momentum of b after the collision.

03:30 I'm going to add in b before the collision as well.

03:33 So if a was one kilogram, if a was one kilogram and moving at one meter per second, then it had a momentum of one.

03:48 B is four kilograms, but it was at rest.

03:52 Before the collision.

03:54 So no momentum...

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