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Rutgers, The State University of New Jersey
(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) 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?
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?
(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?
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welcome to our first example video when we're talking about special centripetal forces, Um, the first concept we're gonna look at Rather, the first physical example is using a game called Tether Ball. If you're not familiar with tether ball, essentially, there's a large post put inside of a tire just in the ground or something, with a rope and a ball tied on the end. And then you hit the ball back and forth to see who can wrap the rope around first. So one person hits the ball clockwise. The other person hits the ball counterclockwise. Okay, eso tether ball is kind of an interesting game in terms of physics. When we look at the free body diagram of that ball, we have force F G pulling it down and then the force F t pulling it towards the center here. And we know because it's going around and around in a circle that we have a centripetal force. Now, looking at this, you should be able to identify at this point that tension forces what's gonna supply the centripetal force but has broken up into two components. So if we get on angle theta here, then we can write inthe e x and Y direction in the Y direction will have noticed here that I have major data from a horizontal angle. So I'm going to say that my in my wide direction I have f t sine theta minus F G is equal to zero as long as the ball is not changing its height in the Y direction and then I have f t cosine. Theta is the only force in this centripetal force direction, which means it will be equal to M b squared over our and so we could do Cem Cem different calculations with this, where we could say things like, Oh, the ball is rotating at a particular speed. What's the force of tension? Um though we can also find force attention simply by finding the angle and saying that force attention is going to be equal to F G divided by sine theta. Given that, then we could take it and plug it in and say we have f g over cosine theta multiplied. But I'm sorry over sine theta, so f g over sine theta multiplied by cosine. Theta is equal to m v squared over r f G is just mg, so we would cancel out on em. Then we could flip things over and we would end up with Tangent of theta is equal to the squared over our Remember that mg over here RG And this would all be to the negative one because we flipped over signing coastline and this side, so that's kind of an interesting result here. Um, it's flipped from before simply because I measured the angle from the x axis and the Y axis. Hopefully, this equation looks familiar to If not, you should go back and watch some of the example videos. But eso all we've done here is we have tanta equals V squared over r g e to the negative one instead of simply be squared over r g. So the tether ball example is a is a nice, simple one. We can calculate all sorts of help little things from it. The point is to make sure you know which direction zahren why, which are in the X and add up the forces in the X in order to find your centripetal force
Equilibrium and Elasticity