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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?
(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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welcome to Section six in our unit on Dynamics in this section, we're going to be looking at some other options for centripetal forces. Previously, we had identified friction, good function as a centripetal force, and we had also looked at things like tension and even normal force. Um, back when we first looked at two dimensional motion and we will review some of these and then also look at some new options for things like gravity that conserve as a centripetal force. Um, so the important thing to remember and this came up in the previous examples is that not always do you have a single force that causes centripetal motion? Think about affairs Will, For example, on affairs wheel, you have all the different spokes coming out. People sitting at the ends of them. You can picture it that way at least. And you know that as you go around in a circle as you go around in a circle, you have multiple forced on you. For example, here you have gravity pushing you down. But then you also have your chair pushing you up. Okay. In fact, your chair is not going to be straight up and down. It's going to be angled a little bit so that it will get you to have some sort of center pointing acceleration and then the why component would cancel. With the gravity up on the top, you'll have gravity down and normal force up such that you would say FN minus F G is equal to M V squared over r. If it were down at the bottom, we have FN up and it would be the same. Over here you have f g down and then you have an FN that points in a little this way and again you could. So, for example, if this is your first case, that's your Newton's second law. In your second case, you would say, given a theater right here that you have f n cosine theta minus M g equals zero and f n signed. The data is equal to M B squared over our because this is your centripetal force. So it's really important that you keep track, not just of I'm thinking that Oh, I was going around in a circle. It's attached to a string tensions. The only thing causing this No, we have to think about normal force and tension and friction and every possible force that could be exerted on this object in order to determine how do these forces add up equal centripetal force? So that's really going to be the focus of the next few videos. Um, is just doing some additional examples that come up Ah, lot and really digging into where this idea of centripetal force comes from. One other issue that I should bring up because it usually comes up about this time an introductory physics craft classes is the idea of centrifugal force as opposed to centripetal. Centripetal is what we've been talking about. This is center pointing force or center pointing motion. Centrifugal force or centrifugal motion is used a lot in colonial speech, but it doesn't necessary mean necessarily mean what everybody thinks it means. Um, you've probably all been in a situation where you're in the back seat of a car and you go around the corner, and as you go around the corner, you're kind of thrown into the person on the outside edge of the car. So if the car is turning this way, you get thrown to the outside edge and you say Oh, wow, That was a lot of centrifugal force. Um, and then someone turns around and says to you in a snarky tone, Centrifugal force doesn't exist. It's a fictitious force. The reason they say that is because there's not actually anything pushing you to cause this toe happen. Um, centrifugal force is, ah, property of inertia, Really, that inertia wants to keep going the direction it has been going, and because you're belted in down here, your hips go in the circle. But there's not any really not enough friction between your back in the back of the seat to keep you from sliding over to the side. And so there's force applied to one part of you. But to the part of you, that force isn't applied to you have a You've tried to take a different path. Um, think of, for example, attendance bar that's tied to a string and going around in a circle. We know that the string is applying this centripetal force here, but if we were to bring out a pair of scissors and cut the string, the ball would go off in a tangential direction. If we cut it here, would go off this direction. If the ball we're over here would come off this direction, it comes off tangential to the motion of the circle. Okay? And this is because that's the direction that inertia wants to go because when we no longer have a force causing an acceleration in this case simply a change in direction when we no longer have that acceleration, this is the direction that we will continue because that's the direction that we were last headed in when the accelerations stopped. Okay, And centrifugal force is kind of related to that. In fact, um, you know, we've talked about these different coordinate systems X y z our state. If I If you go to Newton's second Law and you correctly switch it from X Y Z coordinates to R Theta Phi coordinates, you come up with three different terms in Newton's second law, where appear you really only have one term mass times acceleration. Well, down here, you come up with multiple terms. You have the standard mass times acceleration looking thing. But then you have to other terms, one of which is called the Coriolis Force Corey oldest force, which effects weather and how cloud swirl and things like that. Some people like to say it's responsible. How, for how toilets drain. That's not quite true. Um, so if you had a very large lake and you put a hole in the middle of it, then the Coriolis force might affect the way that it spins around towards the bottom. Um, and then you also have centrifugal force. So it's not so much that centrifugal force is a fictitious force. It's a force that only exists in a rotating reference frame, like the one that we live on being on a rotating planet. Um, so centrifugal force does have some importance when you're going through a rotational motion like this, but it only does it if you switch into this perspective in math on that is technically what centrifugal forces. If we're just talking about this F equals M a, then this is absolutely what you should do. And if your physics teacher tells you it's a it's a fictitious force, just go with that because they're not wrong and that there's nothing pushing or pulling you. It's just the tendency of your inertia. Don't wanna keep going in the same direction it is going in, um, but mathematically what it is. It's a term in Newton's second law when we switch in tow R theta Phi coordinates and when we switch into a rotating reference frame. So that's where some typical force really comes from. Um, it's It's not just something that people make up because they like to squish their brother when they go around the corner. Um, it Israel, It just, uh, is mathematically precise in this terms, whereas we use it to mean something else entirely, which is pretty wrong. It's better to talk about centripetal force and Newton's second law in these terms.
Equilibrium and Elasticity