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Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

McMaster University

03:02

Averell H.

(II) Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is $3.6 \times 10^5$ kg how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

0:00

Suman Saurav T.

(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?

01:40

Keshav S.

01:24

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Welcome to our fourth example video Considering kinetic energy in this video, we'll ask ourselves, What if we have a function ffx? We'll say it's equal to some constant C times X squared and we want to extract from this. What is our velocity? Are changing velocity going to be, um, we're going to say that we have a new initial velocity equal to two meters per second and we're going to do this over a distance of 10 m from 0 to 10 m. So when we go to calculate this, then we say All right, well, I know Delta K. It's equal to integral of f d. X, so that's the integral of C X squared d X. We want to do it in the range from 0 m, 10 m. We have a delta K over here c x squared dx. So when we plugged that in, we'll end up with one third c x cubed, evaluated from 0 m to 10 m. 0 m will be zero. Therefore, our Delta K is equal to one third see time's 10 m cube and in order to find our K final, remember, we have dealt K is K final minus K initial. We know that K initial is equal to one half MV not squared. So we have one half MV Final squared is equal to one half m v not squared, plus one third C times 10 meters cubed and we can solve from there for V final. So it works again much the same way as it did when we had velocity and position and acceleration, except that we're integrating with respect to position instead of with respect to time. And that's really the only difference here between working with, uh, this equation versus the Kinnah Matics that we were using in the past.

Potential Energy

Equilibrium and Elasticity

Energy Conservation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

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