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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?
(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?
(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?
(I) What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 m/s?
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welcome to our third example video. Looking at the concept of power in this video, we're going to look at an elevator, so an elevator empty has a mass of approximately 1200 kilograms. Um, let's say it's got a couple of people in it, each one playing about 75 kg. So that added another 150. So instead, our total mass here will be more like 1350 kilograms. And the elevator, now an elevator doesn't actually accelerate the entire time is lifting you or dropping you. Instead, it's going to move you with a particular velocity. Okay, so let's say that it is pulling you up with a velocity and that velocity is equal to approximately one meter per second. I want to find out what is the power output of this elevator. Okay, well, first of all, we can find the force. We know we have big mg down, and then we have the force up, which is the force that's doing the work here. So let's go ahead and just call that f. I know that f minus big M G is equal to big M times acceleration if acceleration is equal to zero, then f is simply equal to M G. Now I remember that power can be written as f got it into the that being correct. Then we can say All right, well, I know that power is equal to big M G. Dotted into V. They're going the same direction. So all we have to do is big M, which is 13 50 times 1 m per second times approximately 10 m per second squared. So the power then in this case is going to be about 13,000 500. What? Okay, so this is the power required to move an elevator with two 75 kg people inside eso. This is moving at a constant velocity. We could also have dropped it noticed in that direction, um, that we would have simply had a force up still and MGI and then we would have had Emma here. So all that would have changed is the velocity direction. Okay, if we're using the same magnitude of velocity, we have the same force f dot v as long as it's a constant velocity. Now, if we had an acceleration, then it would be a little bit more of a challenge to handle. So we could say, for example, we have work and we're going to apply some force over some distance and we could go back to our elevator picture. We have big mg down and then we have ah force up and we know that F minus big M G is equal to big M times acceleration or in other words, F is equal to big m times, acceleration plus G. So if we have an acceleration in a constant acceleration and it's up, then we would end up with an F that's greater than big mg. If it's down than it would end up with a force that's less than big M G. And then we could decide the distance. So let's say that it's going to take you up approximately 3 m to the next floor and it's gonna accelerate you the entire distance at 0.1 meters per second. Squared very slowly doesn't wanna rock you around too much. So if that were the case, then we would say Okay, well, our work then is equal to big M times. We'd have 9.8 plus 0.1, so that be 9.9 m per second squared notice. I didn't round to 10 here, so I could be a little more precise. And then I'd multiply that by 3 m. Remember, Mass was approximately equal to 1350 kg. So you can go ahead and plug that in and see how it compares to the previous calculation for work. And then I'd say power is equal to work divided by time. So I need to say the amount of time given 0.1 m per second squared. I know that Delta X is equal to one half 80 squared T then is to Delta X over a square root two can calculate the amount of time plug it in here, calculated amount of work, put it in here and then compare this power to the power we found previously.
Equilibrium and Elasticity
Moment, Impulse, and Collisions
Rotation of Rigid Bodies