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$\bullet$ $\bullet$ Riding a loop-the-loop.A car in an amusement parkride travels without frictionalong the track shown in theaccompanying figure, startingfrom rest at point $A$ . If the loopthe car is currently on has aradius of $20.0 \mathrm{m},$ find theminimum height $h$ so that the car will not fall off the trackat the top of the circular part of the loop.
50 $\mathrm{m}$
Physics 101 Mechanics
Chapter 7
Work and Energ
Physics Basics
Applying Newton's Laws
Kinetic Energy
Potential Energy
Energy Conservation
Cornell University
Hope College
University of Winnipeg
Lectures
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So we have a car which is going through the track and then it's falling a circular loop. So to successfully complete the new, we should know that the centripetal acceleration, which is acting on the car at this point should be equal to the gravitation force protecting on the car. So if we call the centripetal acceleration as and B squared over R, then that should be equal to the preparation force. So from here, we can see that at this point, the velocity he should be equal to. So let's get it off. M Firsts official vehicle tow squared off. G times are where is the radius? So radius that's denoted by big R Right now we need to figure out the height or the minimum the max way. We need to figure out the height for that. The car can successfully complete the look. So in that case, we can use the conservation of energy at this point and that point and then we can solve for the required height. So, conservation of energy at point a key plus que you eh? We don't have any other form of force present here because the track is friction this and at this point will have Can't be a plus newbie. Now hear the initial velocity of the car is zero. So the zero and using that we can see that kind of energy will be zero here. But they're really potential energy because we have a height. So that's m times g times h A. And in here we'll have potential energy and kind of energy as well. So for Connecticut midget will be half off M v b. So let's call the velocity at this point, Phoebe, and we can see that TV is equal to fee, which we figured out in this part. That and then we'll have the potential energy. So we have the hiders hp. So the pension and you will be empty hb right now from here, if we saw for ah, the S O first for we can do is we can replace this guy over here and then we'll solve for H A. So let's first get rid off this EMS. Then finally, we see that h ey will be equal to M G times twice off art plus half off M g big r divided by m times C. It is five by two, Clark. So that means the height must be a tte least. Aah! 2.5 times are and we know that our is 20 meters. So the height H a will be 2.5 times 20 leaders. That is 50 meters action. Thank you.
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