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(I) What is the weight of a 68-kg astronaut ($a$) on Earth, ($b$) on the Moon ($g =1.7 m/s^2$) ($c$) on Mars ($g = 3.7 \,m/s^2$) ($d$) in outer space traveling with constant velocity?
(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?
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$^2$ ?
(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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So when we start building circuits, we're gonna wanna put multiple components in and even multiple of the same components. When you study this for capacitors, when we discuss those in previous videos, now we'll do the same for resisters. So our first configuration is resistors in parallel. That's simply where our wire breaks into different routes. Any truck carries its own resistor. So here we see part of the circuit with flirt current floating flowing in past point, A breaks into two different pads goes on those parts go through R one and r two. Then they recombine and come out and party point B. Well, we know the current here by conservation of charge, has to equal the current that was coming in. We can't create or destroy charge of everything has to be accounted for. Similarly, whatever these currents are, we know that they must total I two and for the same reason, whatever goes into that junction has to come out of it. The other thing to note is all of this path, which I'm highlighting in blue, is equivalent to point a. So it's at the same potential. Everything here is that whatever we decide to call Va and everything in red Is that the same potential? Whatever we decide to call B B. But we know that this potential difference his b B A. Yeah, And that's because when we draw circuit diagrams, we consider any resistance in the wires to be negligible. And so there's no potential job. We only count that through the resisters themselves. So what we can say is that this v b A equals V R one equals B R two. Now we have everything we need to figure out what is going on because we can redraw this as our points A and B with current going in and the same current coming out what's, um, equivalent resistor in the middle? So if we simply divide our first equation by their various resistance is which are all equal, what we get is that and recall alms law. That be is I R. So what we have here are inverse resistance is, in other words, one over our our equivalents for this which matches this diagram over one over r one equals one over r one plus one over r two. And so we see that resistors in parallel look like capacitors in Siris. The equivalent resistance or the universe of the equivalent resistance is equal to the sum of the inverse is of the individual. Resistance is, of course, we can expand this. However, we want split off into more more paths, and the same principle will hold him. We can do the math and again and again. But what we'll find is I is the sum of I on some uh huh capital. I serve eyes and we just divide everything by B, and what we'll end up with is one over our equivalents is equal to the sum on I of one over R I. So we can put as many resistors as we want in parallel. And this will always hold true. So now, of course, we've looked at resistors in parallel. Let's look at resistors in Siris. So here we have a configuration of resistors in Siris, and the only thing that's important is that the wire between them doesn't splits, doesn't split, doesn't go off into whatever other components, capacitors, resistors. There's just wire between them, and we have some point A on the left. Some point I on the right and the current I going in which, by conservation of charge, must be the current I going out. But of course, since it only goes through the resistor R one at this point will call c. We know this must be I as well. So now what's our equivalent? Resistance. Well, let's draw it like this with points A and B and some equivalent resistor there and some current I well, we know this potential drop BBA We have this potential drop B c A and this one here. BBC So we have some potential difference from A to C and C to be, and that's got a total everything directly from a to B thes air the exact same pictures. So those potential drops must equal each other. So we get the B A equals B C A plus B b c. Of course, they all go or the same current flows through all of them and again, homes. Law shows this is just are equivalent equals r one plus are to and we know we can do the same thing over and over again, adding resistor after resistor. So for resisters in Siris, we could just write the some on I of our So By so resistors in parallel look like capacitors in Siris and resistors in Siris look like capacitors in parallel. As far as the mathematics goes, obviously they do very different things. Now we can start drawing in building circuits, but let's quickly review all the components widow and how we draw them. You will recall a capacitor is drawn like this, or sometimes like that, and this is a capacitor capacitor, right? A straight line is just a wire, and we consider it tohave negligible resistance that is just a resist resistor, and they're usually drawn them well, nicer than I could draw them. And I should mention usually where they can be labeled are or say with their value, for example, the same way we can label a capacitor SC or with its value, perhaps one that affair at, Of course, we also have this symbol, which looks like a capacitor, but with one play bigger than the other. But this is actually our I M. F, and we can label that with E or with its potential, and it's not always drawn in, but sometimes you'll see. Plus and minus. The convention is always at the big plate is thehyperfix intial such that if we go right, we gain 12 volts and if we go left, we lose 12 volts. One more thing to note. Sometimes you'll see the IMF drum like this or like that thes air equivalents. All it means is une IMF with some non negligible internal resistance. Of little are an internal resistance is are usually denoted by little are by convention, so we don't confuse them with the big ours of resistors. So these are the components we studied thus far. There are two instruments will make use off that we draw like this. This is a volt meter and not that kind of meat meter. And of course, this measures changes in potential and we have an amateur or amateur which measures Ambridge or current now two things we should mention. Ideally, a volt meter has infinite resistance. We don't want our currents to go through the volt meter instead of our circuit and of course, already broke my rule. Internal resistance is little are we want all of our current to go through the circuit so we can measure it accurately. And so we'll meters are generally built with extremely large resistance is for this very purpose. So obviously we still have our summing and so we could go back and look at our equation for resisters in Siris are equipped equivalent equals R one plus are too So you can probably guess we don't wanna hook. Ah, Volt meter with a very large resistance up in Siris normally will hook him up in parallel. No, we can rewrite this for the actual value. So what happens if say, are one is a volt meter resistance so well, we make our to negligible if our ones much, much bigger So it's about equal toe are two for our equivalent and that's why we'll use volt meters with very high resistance is and use them in parallel with our circuits. Um, meters, on the other hand, we want to have a very, very low currents. Ah, very low resistance is and ideally, we want internal resistance to be zero. That's because we wanna hook them up in Siris so we could measure the current that's actually going through these components. We don't want to do it in parallel because then we're measuring. We're not measuring what's going through that resistor. We're measuring what happens to make its way through the AM meter
Magnetic Field and Magnetic Forces
Sources of Magnetic field