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University of Washington

Simon Fraser University

Hope College

University of Sheffield

01:40

Keshav S.

(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?

03:04

Kai C.

(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?

01:24

(I) What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?

0:00

Aditya P.

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come to our first example video. Looking at two dimensional dynamics in this video, we're going to consider the problem of projectile motion in two dimensional dynamic. So looking at any particular point here, if I were to draw the forces on this object, I would have an f. G. But then I would also have a drag force that would be tangential to the path year. It would be tangential to the path because velocity is also tangential to the path except in the direction it's going so drag force will be in the opposite direction. Eso we need to do then, is when we say all right, well, I need my ex direction and my Why direction here, Um, if I'm trying to find acceleration because I want to find velocity is a function of time or something like that, or how why and X are related to each other, I would say, is equal to f over em. And remember, this is an F net, so that's gonna be equal to one over m times. The net force in the X direction. Well, the only force in the X direction is the X component of the drag force. Meanwhile, in the Y direction will have a Y is equal to net forces in the UAE, divided by M which is one over m times. What do we have here? We have two forces. We have F g, which is down. So that's negative, F g. And then we also have a drag force. So we say f drag. So why? Okay, now notice The X direction for F drag is always going to be negative. So we can just put in the negative here for the Y direction and will actually occasionally be positive. So we need to keep a nigh on that and make sure that we get something consistent as we go across the entire motion of the project. I should mention that because of drag forces, projectile motion tends to look more like this. Then it does like a parabolic arc which would look more like that, Um, the reason being the drag forces. Of course. Now, if you have a small, heavy object, it will generally ignore this because we have this one over m here. And so the drag force in the extraction will be especially small. Um, but if you have a small white object, for example, then it wouldn't really matter because it's so light that you still get significant effect due to drag. Okay, s. So let's go ahead and plug this in here for drag forces. Remember, the significant one was one half see row A b squared. And we have to multiply this whole thing by cosine of data because we want an X component. Meanwhile, for why we have one over m times negative f g minus f drag and the why so f dragon the Why then, is going to be equal to one half see row a V squared times sign of data. Now, remember that the sign of data is going to be equal to B y, and the cosine of data is gonna be equal to forgot. My negative again is gonna be equal to V X. We also know that the the magnitude of is equal to the square root of B X squared plus b y squared. So thinking about that and separating out the V squared term to have a V sign data and Avi coastline data and then a separate V, we can actually write the a X is equal to negative 1/2 m time. See row a times V x times the square root of V X squared plus v y squared because we have the magnitude of e and then V X is equal to v cosign data. And then for a why we have negative will go and put the negative in front one over m times mg here minus one half see row a and then similarly v y times the square root of the X squared plus b y squared. I hope so. I put the negative in the front here. Okay, notice here then that V y okay will occasionally be positive. OK, it'll be positive on the way here and then on the way back it'll be negative, which will combine with this negative to make this a positive force. So are signs work out and these are two equations that we need for acceleration in the X and acceleration in the UAE

Work

Kinetic Energy

Potential Energy

Equilibrium and Elasticity

Energy Conservation

04:34

04:09

04:39