https://youtu.be/EkHcBaEHsBs
PHYS 1101: Lecture Eighteen, Part One
Welcome to lecture 18. We’re onto a new tool now that we call momentum or momentum conservation. These mathematical tools are going to be extremely useful for handling what I’ll call abrupt events. This would be, for example, throwing a ball, catching a ball, an explosion, a collision. If we don’t care about the details during this abrupt event, but we just want to know the overall consequences. Momentum considerations are going to be a really quick, useful notion to help us work that out. There’s three main parts to it; most of which we’re going to be introduced to today, and then we’ll follow up with some more specific examples in the next lecture.
The first bullet here is the notion of what momentum is in the first place. Every object has momentum. We use small p to denote that. The momentum is a vector. It’s given by, not just the velocity of the object, but the mass or measure of the inertia as well. Momentum is mass times velocity. Direction of momentum is the same as direction of velocity. The magnitude is going to be the product of the speed and the mass. As I say, it’s going to be useful when we have these abrupt events in our problem.
You want to make two distinctions to decide which of two momentum tools you want to use. The first distinction is; are you just focusing on one of the objects in this collision and how it responds?
If that’s the case, you’ll see that this is our starting equation, where we’re going to be looking at the average force on the object during the collision. And it turns out, mathematically, that average force is equal to, or it’s the cause of the momentum to change. P final minus P initial would be the momentum just before the abrupt event, and P final would be the momentum just after. The final minus the initial, you’ll recognize that we call that the change. That’s the change in the momentum. And this whole numerator, the change, the Δ momentum, the change in momentum, is given a specific name; impulse with a symbol capital J. The arrow over the top indicates that this is a vector. It’s a vector that points in the direction, not of P final or P initial, but the ΔP. Just like we learned with a V final and a V initial, that the vector, ΔV, could point in a different direction. It’s the change. ΔP is what I have to add to P zero vector in order to get P final. This average force causes the momentum to change, but the magnitude is represented by dividing then by the duration of the collision, the time between P final and P initial. That’s one main tool when the focus is on a simple object.
A lot of cases though will find it’s useful to consider both objects as a group that are interacting in this abrupt event. If these two objects are isolated, meaning the only significant forces during this abrupt event are those that they exert on each other – usually it’s two objects we’re going to be considering. If the only significant forces are this interaction between the objects, then we’re going to consider them as a group. We’re going to think of them as somewhat isolated and look just at these two objects. And what we’ll find is that we can consider adding the momentum together of both of these objects just before the collision, adding the momentum together after the collision. And if there were no other outside forces on these objects, if I only have this interaction between them, then the force on the left side will become zero. This gives me what’s called momentum conservation then. Zero equals the change in the total momentum. We’re going to see more about what this means and how to apply it, but this gives you a big picture at least of where we’re headed.
Here’s a quick warm up question for you, again, just bringing up past material and asking it in a different way. I’ve got another one of these hockey pucks that’s moving along. This one is headed due north. It’s moving on a frictionless surface. You’re looking down at it. You see it moving the direction the compass points. It receives a brief whack to the north. What’s the puck trajectory after it receives this brief force in the north direction?