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Aditya P.

(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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Suman Saurav T.

(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

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Keshav S.

00:56

Donald A.

I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?

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So now we come to what are the units of current? Well, in order to give it units, we need to be able to quantify it. How are we going to count what current is? So let's consider some metal wire and we'll consider the simplest case of electrons all of these or electrons. Now we apply some electric field through the wire in this direction, and we get forces on the electrons in this direction and we got a drift velocity to the left. So we get current in this direction as well. How can we count that current? Well, let's consider this to be tie T equals zero, which I'll call t. Not on time. Zero. The elections are exactly where I've drawn them at some later Delta T. Some of these guys will have drifted past this line, and so I've have some kind of total charge moving in some Delta T or what we can say is some amount of charge in some time of tea. And this is the definition of current, and you'll see it has units of columns per second. And since we use current so often we call this Senate the ampere So how big is the typical current? And the answer really is it depends. Remember, we're moving currents around in order harness potential electric energy, our electric potential energy. And so the amount of current we need. It's really gonna depend on what we want to do with it. And so you might have something like your car when you started up. Well, not easy to start up a car, and we'll see something on the order of about 100 peers or more, whereas you might have something like the electronic device in your phone. It does a lot, but it doesn't require that much power. And so, for electron ICS, we might measure something more on the order off Mila amperes. So we see currents can vary greatly, um, depending on what we want to do with them. And it's actually current that poses the dangerous to us as people. And as we learn more about current and resistance, we'll see why that is so we might ask ourselves how big is a typical current, how maney amperes and the answer is it really depends. Remember, we're using current current to accomplish something. We want a harness electrical potential energy. And depending on what we want to do, the amount of energy we need is big or small, and so you can see currents in the hundreds of amperes for some applications down to, say, PICO amperes 10 to the negative. 12. And Peters. We'll discuss this more as we go. But one thing to know is that we know currents could be dangerous, and it's actually current. That is dangerous for us. Electric shock has caused by current electrons flowing, and as we study currents, more and resistance will understand why it is that it could be dangerous or even lethal to humans. So now we have units recurrent. But what does this mean? What is actually happening? So let's consider some piece of wire here. It's got a certain number of charges of charge Q. Within it, we know when we apply an electric field to the right, we'll get some drift velocity to the right, assuming they're positively charged and the electrons will start moving that way. So what is our change in charge? How can we count that? Let's put a barrier here. Well, we know if they're drifting to the right at some time, all the electrons will be over on this side of that barrier and they'll space will be empty. Or in reality, more electrons will come in. But the electrons that were there before will be gone. So let's call this time t zero. And this time DT and T zero is simply zero. So how many elections, Aaron here? Well, it really depends on the material. Often what we do is we use the term little in which is equal, the total electrons divided by the volume of the material. So an his charge density. Great. So we have a charge density. How much charge of we moved through? Well, our charge density is stop. So let's consider what this actually means on a microscopic level. What is current telling us? Well, let's consider here this segment of wire and it goes on in this direction and in that direction. But we're only concerned with this segment right here. Well, it's got some charges in, and we'll just call them charge Q. And if we apply a field to the right, some of these charges are positive. We get some drift velocity of the right and our current is in that direction. So now let's put it very here. So we started at T equals zero with that configuration, and we turn on the electric field after some time. DT. All the charges are over here, so we're only concerned in moving the charges in this section of wire in the middle to the right, we don't worry about what's coming from the left. So how many charges are there? Well, particles, We just have the total number of particles in our material divided by the volume of the material. So this is a particle density. So now we can start to calculate what is our dick and dick is how much is passing through this barrier? Well, how much charge that we have? Well, we know we have a density of that many particles, which you'll notice the units are particles per volume or meter cubed, and they each have a certain charge Q per particle. So, really, now we're dealing with cool apps for meter cube. It's a great we have the cool arms we need for our calculation, but we need to figure out what this meter cubed is. Well, notice how many electrons are in this segment, there's an area A and they traveled this entire distance in a time of VD DT, right? Velocity over time and they're all cleared out. So that must be the length of this material. Now we see we can define our current de que DT as que en a BD are charged sized times the density of particles times the area we're passing through times the velocity of the particles and oftentimes well, right. Is I over a It was cute and BD and this is a charge. Sorry. This is a current density or current per unit area. So we see we have been able to find a microscopic definition of our current and our current density and notice that if these charges are negative and moving to the left, current still goes in the same direction and our current density is still in the same direction. And so oftentimes folks, oh, put absolute values are on the charge so as not to confuse themselves. But it's not necessary. If you're keeping track as long as you know, you just care about the magnitude of the charge and not the sign. Now we said current isn't a vector. The current density can be and we can define it as and que BD Now first off noticed that there is. There are no signs in here, but current density will always follow the electric field. If our charges negative, remember now our Dr philosophy we're using as a vector that's also negative, and so we get the same direction. The reason we treat current density as a vector is we always discuss it in terms off current through a certain point or a certain cross sectional area. And so we'll see current density as a vector often. But recall current itself has never dropped used as a vector and well in this video by making one more observation. We've derived this expression here for the current due to the movement of a chart type of charge. But we've said many types of charges can contribute to current in a single material, and so we can generalize this more as the some of the currents of each type of charge, which we can write as a density for each times to charge for each notice. The area stays the same for each, but the drift velocity also changes for each and in the same way we can write the current density as the some of the individual current densities. Where I over a in some direction is our current density, and you'll see you'll notice here that charges are there positive, moved to the right and so have a positive sign. If that's our positive direction and James positive and each charge that is negative. Well, that have a negative sign on the charge and a negative sign for strip philosophy and still add to our current density, since it has the same sign as a positively charged particle moving to the right.

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