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(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
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to this point in our videos, we've introduced a few of the separate different components that go into circuitry. For example, we have R E M F, which can be drawn on Li like this or with an internal resistance. Of course, this is a new energy source. It keeps providing energy to our secretary so we can keep ah, current running. So a battery is a good example of an e. M f. You also introduce capacitors by sea, which store energy, and we've introduced resistors and resistors. Use energy or or, as we might say, often say they dissipated. And we've looked at some basic circuits, such as ones that have just MFC and resistors and seeing the energy and and power dissipation related in such a circuit. So now we're gonna start building more complex circuits. But we're going to concern ourselves only with D C or direct Current's and direct current basically means that energy will only flow in what currents will only flow in one direction. It doesn't change with time now. This varies to a C or alternating current, which is what comes out of the sockets in your house in alternating current at one time current flows in one direction, and over time it gradually changes and it doesn't flip directions. It oscillates. But for now, we're only gonna worry about director in circuits. And these are the types that run off of E. M. F's batteries, something that provides ah, positive terminal and a negative terminal and so current we know will flow away from the positive terminal sample. Here's a bridge circuit. Now we're gonna gonna wanna be able to analyze this. And as we can see, we've got many branching paths and we have some techniques we've developed this far. But we're gonna look at a couple more called Kerchiefs Rules. This is named after a German physicist who developed these techniques. So first we define terms. A junction is any point. We're three or more wires meet, so we would have a junction here. We have one wire here, one there and one there, and we have many junctions in this circuit. As you can see, we have a total of four. The second definition is that of a loop, and that is any closed path. So here we have many loops we have in red. We have the loop along this path. We also have these two loops here, and these were kind of like the constituent loops. But of course, we also have the entire outer perimeter, which is its own loop. And you see, we can actually draw many, many loops in blue. I'll draw this one, just keep it separate from the others. We have the loop that follows this path, and so any close path that you can draw is a loop. And the existence of many, many loops actually helps us with very complex circuits, because we'll need to develop formulas that will help us solve for different values. And the more loops we have, the marble ah formulas will have and the more unknowns we consult for. So now that we know our definitions, we can look at the actual rules. The first rule is the sum of all currents into a junction zero, and I stress this word into when we draw a junction. It doesn't matter how complex we draw it. We can buy church austral. We can define all these currents going inward, and we have I 1234 and five. So I one plus I to plus I three plus I four plus I five equals zero, which means some of these currents are going to be negative. And that's fine. A negative current, which we will run into all the time as we do. Calculations just means we drew it in the wrong direction. So let's assume that I, too and I five are actually negative here later on. After we know this, we can, if we want, redraw our junction in the correct directions with the current in the correct directions. And this is okay when we're working through these problems, it doesn't matter if you get negative currents, as long as you're consistent and everything. And when you get to the end of the problem, if you've done it correctly, then those negative currents will be consistently negative. And then if you re draw your currents, you can You can put the currents in the directions. They should be going now. We also should add If you draw a junction like this, you should be using negative signs in your some because you'll notice this simply means that I to plus I three equal I one which we know by conservation of charge and that is the basis of this rule. If the some of the current into a loop wasn't zero, well, then we're creating charge at this one specific point. More and more charge over time, and we cannot create charge because, of course, conservation. So now, Kirchoff second rule, which involves loops, tells us the some of potential changes around a closed loop must equal zero. And like kerchiefs, first rule came from the conservation of charge. This comes from conservation of energy. So let's taken example. We're going to start here behind our battery, and we're going to ignore pretend it has no internal resistance. It's r e m f has a certain potential as we go around. Well, we go from low potential toe high potential. So our Delta V I'm gonna add them all up is E. Now we go this way and we'll claim that the current runs like this or we're interested in this loop. So now we cross this Well, we're gonna have a potential change going across the across the resistor, so we'll go like that and then we'll take this loop and we'll call it Artie. We have another potential change across the resistor and then we come back this way and end up back where we started. Well, whatever the potential was here, we just call it be not when we started. That better be the potential when we ended. If not, we have created or destroyed energy or another way of thinking it is if we go around and be not, is greater. Well, we have more potential energy than we had before, so we've created energy. And if we go around and come back and be not is less than it was, well, we have less potential energy than we had before, and we can't possibly keep a circuit running forever are in any kind of steady state because that will dissipate our current. So we see that when you go around any of these closed loops and do the math, all of these potential changes or zero we can take more complicated loops. But we must always remember to balance all of our potential changes and stated most more simply in this circuit we have basically two kinds of components ones that supply energy and others that use it. And obviously our MFC are examples components that supply energy and resistors use it. Capacitors also use it by storing it. So as we go around the loop, all the energy we create our way supply to our circuit we had better use.
Magnetic Field and Magnetic Forces
Sources of Magnetic field