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# Loop de loop answer part 1

## Video transcript

what I want to do now is figure out what's the minimum speed that the car has to be at the top of this loop loop in order to stay on the track in order to stay in the circular motion in order to not fall down like this and I think we can all appreciate that that is the most difficult part of the loop-de-loop at least in the bottom half right over here the track itself is actually what's providing the the the centripetal force to keep it going in a circle but when you get to the top you now have to you now have gravity that is pulling down on the car almost completely and the car will have to maintain some minimum speed in order to stay in a circular in order to stay in this circular path so let's figure out what that minimum speed is and to help figure that out we have to figure out what the radius of this loop the loop actually is it actually does not look like a perfect circle based on this little screenshot that I got here it looks a little bit elliptical but it looks like the curve the the radius of curvature right over here is actually smaller than the radius of the curvature of the entire loop-de-loop that this if you made this into a circle it would actually be maybe even a slightly smaller circle but let's just assume for the sake of our arguments right over here for the sake of our argument right over here that this thing is a perfect circle and if it was a perfect circle let's think about what that minimum velocity would have to be up here at the top of the loop the loop so we know that the magnitude of your centripetal acceleration is going to be equal to your speed squared divided by the radius of your of the circle that you are going around now at this point right over here at the top which is going to be the hardest point the magnitude of our acceleration this is going to be 9.81 m/s^2 and the radius we can estimate I copied and pasted the car and it looks like I can get it to stack on itself four times to get the radius of this circle right over here and I looked it up on the web in a car about this size is going to be about 1.5 meters high from the bottom of the tires the top of the car and so it looks like just eyeballing it based on these copying and pasting of the cars that the radius of this loop the loop right over here is six meters so this right over here is six meters so you multiply both sides by six meters actually we could keep it just in the variables so let me just rewrite it just to manipulate it so we can solve for V we have V squared over R is equal to a and then you multiply both sides by r you get V squared is equal to a times R and then you take the principal square root of both sides you get V is equal to the principal square root of a times R and then if we plug in these numbers this velocity that we have to have in order to stay in the circle is going to be the square root of nine point eight one meters per second squared meters per second squared times six meters times six meters and you can verify that these units workout meters times meters is meter squared per second squared you take the square root of that you're going to get meters per second let's get our calculator out to actually calculate this so we are going to get the principal square root of nine point eight one times six meters it gives us now here's our drum roll seven point six seven I'll just round to three significant digits seven point six seven meters per second squared and significant digits the whole conversation because this is just a very very rough approximation I'm not able to measure this that accurately at all but I get a roughly seven point I'll just round seven point seven meters per second so this is approximately seven point seven meters per second and just to give a sense of how that translates into units that we're used to when we're driving cars we can convert 7.7 m/s seven point seven meters per second if we want to say how many meters we go in an hour well there's 3,600 3,600 seconds in an hour and if you want to convert that into kilometers this will be in meters you divide by a thousand one kilometer is equal to 1000 is equal to 1000 meters and you see here the unit's cancel out you have meters meters seconds seconds you're left with kilometers per hour so let's actually calculate this and so we get our previous answer we want to multiply it times 3600 to figure out how many meters in an hour and then you divide by a thousand to convert it to kilometers per hour so you divide by a thousand and we get 27.6 km/h so this is equal to twenty seven point six kilometers per hour which is surprisingly slow I would have thought that it would have to be much much much faster but it turns out it does not have to be much much faster only twenty seven point six kilometers per hour now the important thing to keep in mind is this is just fast enough at this point to maintain the circular motion but if this were a perfect circle right over here and you were going in exactly 27.6 km/h you would not have much traction with the road and if you don't have much traction with the road the car might slip and might not be able to actually maintain its speed so you definitely want to be a good bit you might you want your speed to be a good bit larger than this in order to keep a nice margin of safety in order to especially have traction with the actual loop-de-loop and to be able to maintain your speed now what I want to do in the next video is actually time the car to figure out how long does it take it to do this loop-de-loop and we're going to assume that it's a circle and we're going to figure it out and we're going to figure out how fast it's actual average velocity was over the course of this loop the loop