https://youtu.be/Epg4AGC447Y
PHYS 1101: Lecture Sixteen, Part Four
Now we’re ready to look at our problem-solving steps. I’m only going to propose very small changes in those. And then we’re going to move right into doing examples.
So our problem-solving steps. When we’re faced with a problem where there’s a discussion, there’s the language in the problem that’s suggesting we need to make a connection between speeds and position changes of an object. The position change could be a vertical height change or it could be just a horizontal position change. Either case, if we’re asked to kind of compare or connect speeds and positions, we want to start with or consider energy conservation as a means to solve the problem.
This now is our new starting equation. This will work for all of the problems I’m going to show you today and all of the examples we did last lecture, too.
The name of the game then is starting with this general equation and customizing it to the problem. So we’re going to go in there and take a close look at the left side of this equation. What do I have to plug in to that left side to customize it to my problem? And then the same thing for the right.
So all the steps–they’re very similar. Object is the first thing you have to focus on or decide what object are you going to consider whose energy is changing, that work’s being done on.
When you think about the left side of the equation, you go through the same steps to calculate the work that every force does. The only difference now is that you leave out the contribution due to the gravitational force. Okay? So when you add them up, you will represent the work from every force, except gravity.
Comments for the right side of the equation. You need to substitute in the kinetic energy and the potential energy values at the initial instance and the final instance. Kinetic energy is always one half mb squared. And potential energy is always mgh.
What’s the height at those instances? What’s the speed at those instances? That’s what you need to get the right values for ke and pe. The rest of the steps are the same.
Once I’ve thought about that a bit. I’ve got a sketch of the scenario drawn, so I can clearly think about speeds, heights, altitudes, etc. I’m ready to make a list of my knowns and decide what variable it is I want to focus on. I have to pick a mathematical variable that ultimately will show up in my starting equation as I customize that equation to this particular problem.
Once you start doing that customization, you just, as we’ve come to know, you need to just patiently work toward the appearance of this variable that you want into this equation as you start substituting into it. And then you need to just solve for that. So work through the algebra until you isolate that variable.