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07:43

Kathleen T.

(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

04:15

(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?

04:27

Kai C.

(I) A 110-kg tackler moving at 2.5 ms meets head-on (and holds on to) an 82-kg halfback moving at 5.0 m/s. What will be their mutual speed immediately after the collision?

03:38

Keshav S.

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welcome to our fourth and final example video. Looking at two dimensional dynamics in this video, we're going to consider a car that travels around a banked curve. So something like this, we have a car that wants to go around it. Eso notice this is centripetal motion because the car is going to be going around a central axis here in the middle. And so we do have a centripetal motion, but it's a little different from what we've seen before. One of the reasons this is an interesting problem, because if I if I consider cut away the inclined plane here with the car on it, we might instantly be tempted to say, Oh, let's tilt our X and Y axes because that's what we've always done with inclined planes. This would be a mistake. Don't do it, because if we leave our X and Y axis alone the horizontal and vertical, it means that the centripetal force will all be in the X axis, and that could be really, really helpful is we'll see here in a moment. So when I draw my free body diagram here, put in the silhouette of my inclined plane. Okay, it's I have F g down and then I have normal force. Now there's other things I could add and I could put in a friction force, though For the time being, I'm going to say that Mu is equal to zero. Um, and I might have a force that's causing me to drive around faster and faster that we're going to save. For the moment that VT is constant, we maintain a constant velocity going around this circle. Okay, so this is true if this is true and we want to be going around the banked curve in such a way that we never drift down towards the bottom or risk flying off the top. So we want to maintain a constant position there as we go around. Um then if we want to do that, we have a couple of conditions. We say, Okay, I need motion in the Y to be equal zero. So V y must be equal to zero, which means or rather that a Y must be equal to zero. All right, knowing that then we can say if we set up Newton's second law, we have FN, remember, we've got to right, put in our right triangle here. FN Cosine theta is in the UAE and in the X direction We only have f n sine theta because that's the opposing side up here. So f n science data is going to be equal to Arsene trip. It'll force it is the only force in this centripetal force direction. Therefore, that is the total of the sum of all forces in this centripetal force direction. So we had EFS and and science data equals M V squared of our in the Y direction. We have FN cosine theta is equal to m g again that started out as fn cosine theta minus M g is equal to m A. But Emma zero so I can quickly write it out this way. Now, in order to solve for this problem and get a final relationship, let's say were given data. We want to find out how fast to drive around this curve. Then what I can do is use one of the techniques I showed in the math review videos, which is I can say fn signed data equals M v squared over r. And I'm going to divide this equation by my wife equation FN CoSine data and M. G. M's Cancel FN's cancel sign over Coziness Tangent and I'm Left with Tan Theta is equal to V squared over RG. So if I want to solve for the speed at which I should go around this banked curve safely, I have square root of RG tangent of data. On the other hand, I could have said Saul for tangent of data ourselves for the angle. If I'm going at a particular velocity, and we could have done that instead on that's how they actually designed banked curves, they say, Here's this speed them and for going around this banked curve. Given the speed limit and a range of possible conditions for the road, How much should we bank the curve? And they're able to do that? Or they could also talk about how large should the radius be. Both are ways that they can our numbers that they can manipulate in their design in order to come up with a safe road for us

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