https://youtu.be/HYttX4v96gA
PHYS 1101: Lecture Fifteen, Part Four
So here are the steps to help you solving these energy conservation problems, problems, let me remind you, where it’s asking you to connect — I’ll put this in quotes — “speed and position.” If you see those words, give it a try. Try to apply energy conservation and this tool to solving the problem. Odds are it will be a very convenient tool, easy to use for you.
Here’s the starting equation: the name of the game is write this equation down, and now customize it to this particular problem. And by doing so, you will arrive at the value that you’re asked to find. You can determine what the tension in the line is, or what the final speed is, etc. It’s all about sticking with the starting equation that defines the constraints on the problem, that defines the basic physics at the heart of it.
As always, our first step is be sure you’ve decided what the single object is that you want to focus on. Have a good sketch of that scene. What’s the displacement? What’s this initial instant and the final instant that you’re supposed to consider?
Okay, after you’ve done that, start thinking about your main equation. Let’s just start on the left side, and see what we can determine or figure out about the network that got done in this problem. Well, to do that, first draw a free-body diagram for that object, because you’ll want to consider the possible work that every force does, from start to finish, from initial to final.
Draw the displacement vector, because you’re going to have to be able to identify the part of the force and the direction it is. You do that by following this step, that I’ve got here in the second bullet: for every force, draw them together like I’ve shown you, like hands on a clock. Label your angle here in between, and for every force simply calculate force times distance.
You’re only going to take the part of the force that’s in the direction of motion, and then you’ll multiply by the distance. You do that for every force, and then you simply add them up. Many will be 0 if the force is perpendicular to s. Some could be positive, some could be negative. Again, if F is in the direction that’s contributing to motion in the direction of s then it’s going to be positive work. If F is opposing that motion, it’s going to end up doing negative work. You’ve got to add up all contributions.
After you’ve done that, you’ve thought about the left side of your starting equation, now let’s give some thought to the right. The right side is ignoring all details in between initial and final instances, and all you’re doing is calculating the kinetic energy at that last instant, and calculating the kinetic energy at the beginning instant. No details about what’s in between. One way to think about this equation is that the left side captures the energy that gets added to or taken away during the motion from start to finish. The right side of the equation kind of sandwiches the beginning and the end, and says what change in energy you saw.
Okay, so in order to calculate these kinetic energies, all you have to do is think about the speed at the final instant and the initial instant, and the mass, so where you’re given the mass of the object. The next step, as usual, make a list of the variables that you know and again, very importantly, you’ve got to pick a variable to focus on. What’s the variable that represents the physical quantity that you need to determine? Because it’s the variable for that that’s going to show up, or be defined, in this equation.
And then you just start plugging it into this equation, as we’ve usually done. It’s all about sticking with this main equation, and you keep substituting things in for it as you start customizing it to this particular problem. And then you just wait patiently. Whatever variable you need, it will show up in the equation, and you need to then just do your algebra to focus on it and solve for it. And then, do a quick check. See if the answer makes sense.