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(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) A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow.What is the skier's change in velocity?
(I) What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?
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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welcome to our first section in Dynamics. In this video, we're going to consider specifically one dimensional dynamics. So the reason we're gonna look at one dimensional dynamics is so we can start to get an idea of what strategies we're gonna use to solve these problems and then be able to expand the complexity of them and one dimensional dynamic. Specifically, we're gonna talk about things that have forces in one direction or 180 degrees from that direction. And then how they react that force, it could be horizontal, could be vertical. It could be slanted is if it's on a Nen climbed plane. All of these are examples of one dimensional dynamics. So that's what we're going to look at here. Remember that we do have a few basic things to keep track of this stuff. We still have our equations from Kinnah Matics, and we still have the underlying assumptions that go with them to remember. For example, that equation requires that acceleration be constant, as does this one. We're going tohave Newton's second law, which we will write as a vector here, though, for this particular case of Wonder National Dynamics, all that a vector means is it's positive direction or negative direction as defined by us. So it's not particularly difficult to keep track of, so we have fewer equations to deal with. When we're talking about a one dimensional situation. We're also going to start looking at some of the forces that we can consider beyond just simply saying, Hey, I push a box this direction and I call that Force F one and or the gravity pulls something down and the floor pushes it back up. The first of these forces that we want to consider is tension, So tension is a force applied by a rope or to rope, depending on your perspective. So, for example, we have a tug of war between two people, and they have a rope that they're holding on to and applying a force in different directions. So this person is pulling to the right, and this person is pulling to the left. So remember, when we draw a free body diagram, it shows up as a point. And if I were to say this is such a situation where they're at, ah, balance here, where each person's applying the same force, then the free body diagram of the rope will look something like this. We have F one and F to just call this person one in person too, and they happen to be equal each other. Now. If I were to draw the forces on each person, then well, what would those be? Well, if the rope is being pulled by person to with the Force F two, it means they're gonna pull back on that person with the Force F two and similar over here. If it's pulled with the Force F one by person, have one and it's not moving. That means the person is being pulled back towards it with a Force F one. So in since F T equals F one, all of these are the same. So what we end up saying instead is that person to experience is a force of tension to the right person. One experiences the same force of tension to the left, and that's how we handle this now, naturally, in this situation, in order for these people to not actually be accelerating in any anywhere, they need countering forces. In this case, they would be forces due to friction, but between their feet and the floor beneath them, and those friction forces would have to balance out in order to prevent any acceleration. But the idea is that attention force Kim pull in different directions. It pulls person to to the right. It pulls person one to the left, and that's okay. They also have the same quantity, meaning that tension is constant in a rope. But look, now that's not 100% true, and we will see that perhaps in Cem Cem rather complex problems. In fact, we may never even touched them in these examples. In this particular video, Siri's because they are so complex and usually require calculus to handle well. And that is because if a we're going to assume that all ropes are massless, unless I say otherwise, all ropes and strings will be massless, and if they are massless, then this condition that tension is constant throughout. It is true. If they are not massless, then it's not necessarily true because we have to compensate for the mass of the rope or the string. And that's a little bit of a difficult, uh, difficult idea toe to keep in your head. But it's an important one that we're going to leave the tension to be constant. But we have to make this assumption that the rope is massless in order to make that in order to say that the tension is constant throughout the rope. So something to know, but maybe not something that we will apply, except in one or two examples through this entire video, Siri's. Now, since we have disability of tension to be constant, we're going to spend a number of problems looking at police, where a rope attaches to objects and through a pulley it's actually able to pull. For example, In this case, we have a box of some mass that's hanging, and then a box of some mass that's sitting on a table. And when we touched the first box here, it's going to start to fall, which is going to start to pull box to. That means that tension in this case, if I were to draw this, I'd have gravity down and tensions on top of the box, so it's going to pull it up against gravity. Meanwhile, over here for this box, tension will be to the right, as opposed to any other direction but notice that we have fear tensions to the right and here, tensions up so police can actually change the direction of attention force. We'll also find out how they can affect the tension force later on, when we consider things like moment of inertia in a couple of sections, but in particular this is the important point. Right now that force of tension can apply. OB can apply forces in different directions on objects, Even if those forces end up being perpendicular to each other. Tension can still do that. So it's something that we definitely need to keep our eye on. We're also going to talk about towards the end of these resisted forces in preparation for videos on friction. Resistive forces are forces that resist any movement, so if a box is not moving, there's no resistance force. But if we attempt to move it, then the resistant four starts to appear. For example, if I were to draw a free body diagram of this box, I would only have vertical forces. But then if I start to push it, I would add in the secondary force, and then if there's friction here, that is when there starts to begin to be a friction force. It wasn't there until we started to cause emotion across it. And this is very important for friction. If velocity is zero of the object across some rough surface, then force of friction is zero. But if velocity is not zero, then we gain this force of friction. Now there is a possibility here that we'll learn about in something called static friction, where it's not entirely true that you have to have a velocity in order to have a force of friction. But generically speaking for this exam, talking about resistive forces in general, that's, uh, that's generically true. All right, so we're gonna move on to our examples here, looking at how we can handle these forces in one dimensional dynamic dynamics. And we're gonna you do it using Arcana, Matics and our Newton's Second Law and also remembering a little bit of calculus
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