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Video transcript

there are unfortunately quite a few common misconceptions that many people have when they deal with centripetal force problems so in this video we're going to go over some examples to give you some problem-solving strategies that you could use as well as going over a lot of the common misconceptions that people have when they deal with these centripetal motion problems so to start with imagine this example let's say a string is causing a ball to rotate in a circle and to make it simple let's say this ball is tracing out a perfect circle and let's say it's sitting on a perfectly frictionless table so this would be the bird's eye view this is the view from above what it would look like from the side would be something like this you'd have the ball tied to the rope and then you nail some sort of stake in the middle of the table you tie the rope to the stake and then you give the ball a push and the ball is going to take the circular path on the table when we view it from the side but when we view it from above you see this path traced out so this is a bird's eye view that you would see if you were looking down from above the table and this would be the side view so let me ask you this question what force is causing this ball to go in a circle now a lot of people want to answer that question with the centripetal force they'd say that it's the centripetal force that points inward that causes this ball to go in a circle and that's not wrong it's the truth but it's not the whole truth and the reason is that when we say centripetal force all we really mean is a force that's directed toward the center of the circle so saying the force that causes this ball to go on a circle is the centripetal force is a little unsatisfying it'd be like answering the question what force balances the force of gravity while the balls on the table with the answer the upward force I mean yeah we knew it had to be an upward force but that really doesn't tell us what force it is similarly just saying the centripetal force just tells us what direction the force points it doesn't really tell us what type of force this is so to answer this question over here in a better way if someone asks you what force counteracts gravity that keeps the ball from falling through the table instead of saying upward force it'd be better to just say that's the normal force and we could do better over here as well instead of just saying the centripetal force we could say what kind of for this is it's got to be one of the forces that we already know about I mean it's got to be either the force of friction or normal force or tension or the force of gravity the centripetal force isn't a new type of force it's just one of the forces we already know that happens to be pointing toward the center of the circle and that's important because this is our first big common misconception people think the centripetal force is a new kind of force but it's not it's just one of the forces we already know that happen to be pointing toward the center of the circle and that happen to be causing an object to move in a circle so in this case over here what force is it well there's a rope tied to this mass and that rope is going to pull on it and when a rope pulls we call that the force of tension so I'm going to call this the tension so that's a little better now we know what kind of force is acting as the centripetal force now be careful out there sometimes people want to do this they're like oh yeah there's a force of tension and there's also a centripetal force but that's just crazy because this tension is the centripetal force I wouldn't draw it twice anymore then I'd come over to here and say yeah there's a normal force there's also upward force the upward force is the normal force I wouldn't draw it again similarly over here I'm not going to draw the centripetal force twice the tension was the centripetal force I mean it's possible you could have two forces inward maybe there's two ropes and you had a second tension over here pulling inward but you'd better be able to identify what force it is before you draw it don't just call it F centripetal so you might be like yeah yeah I get it the centripetal force is just an extra title we give to a force that happens to point toward the center of the circle but how would I ever solve a problem like this what what strategy do I use I got forces that are up that are down that are in so let me show you how to solve some problems and some things to keep in mind so let me add some numbers in here so let's say I told you this let's say the mass of the ball was two kilograms the ropes length was 0.5 meters and the ball is traveling around the circle at a constant speed of five meters per second so what kind of question might you be asked if given a problem like this a possible question would be well what's the force of tension in the rope and so now's a good time for me to let you in on a little secret the secret to solving centripetal force problems is that you solve them the same way you solve any force problem in other words first you draw a quality force diagram and then you use Newton's second law for one of the directions at a time and if the direction you chose to analyze Newton's second law for didn't get you to where you needed to be just do it again use Newton's second law again for another direction and that'll get you to where you need to be so in other words let's draw a quality force diagram we've got forces but they're kind of all over here this side view is going to better illustrate all the forces involved so we've already got the normal force upward and the force of gravity downward now I'm going to draw this tension pointing inward that's the force that's acting has the centripetal force now we're going to use Newton's second law for one of the directions which direction should we pick well which force do we want to find we want to find this force of tension so even though I could if I wanted to use Newton's second law for this vertical direction the tension doesn't even point that way so I'm not going to bother with that direction first I'm going to see if I can get by with doing this in one step so I'm going to use this horizontal direction and that's going to be the centripetal direction ie into the circle and when we're dealing with this intrapleural force we're going to be dealing with the centripetal acceleration so over here when I use a and set that equal to the net force over mass if I'm going to use the centripetal force I'm going to have to use the centripetal acceleration in other words I'm going to only plug forces that go into radially into the circle here and I'm going to have the radial centripetal acceleration right here and we know the formula for centripetal acceleration that's V squared over R so I'm going to plug V squared over R into the left-hand side that's the thing that's new when we used Newton's second law for just regular forces we just left it as a over here but now when you're using this law for the particular direction that is the centripetal direction you're going to replace a with V squared over R and then I set it equal to the net force in the centripetal direction over the mass so what am I going to plug in up here what forces do I put up here I mean I've got normal force tension gravity a common misconception is that people try to put them all into here that people put the gravitational force the normal force the tension why not but remember if we've selected the centripetal direction centripetal just means pointing toward the center of the sir so I'm only going to plug in forces that are directed in toward the center of the circle and that's not the normal force or the gravitational force these forces do not point inward toward the center of the circle the only force in this case that points toward the center of the circle is the tension force and like we already said that is the centripetal force so over here I'd have V squared over R and that would equal the only force acting as the centripetal force is the tension now should that be positive or negative well we're going to treat inward as positive so 90 forces the point inward are going to be positive is it possible for a centripetal force to be negative it is if there was some force that pointed outward if if for some reason there was another string pulling on the ball outward we would include that force in this calculation and we would include it with a negative sign so forces that are directed out of the circle we're going to count as a negative and forces that are directed into the circle we're going to count as positive in here and if they're not directed into or out of we're not going to include them in this calculation at all now you might object you might say wait a minute there is a force out of the circle this ball wants to go out of the circle there should be a force this way this is often referred to as the centrifugal force and that doesn't really exist so when people say that there's an outward force trying to direct this ball out of the circle they're usually referring to this centrifugal force but this it doesn't exist it turns out this is not a real thing if you're using a good reference frame there is no natural outward force for something going in a circle you might have check you might people wait wait a minute if I let go of this ball it flies out of the circle won't it go flying off this way and no it won't if you let go of the string right now for some reason the string broke at this moment this ball would not veer off that way there's no force pushing it to the right the ball if the string broke would just follow Newton's first law that says it would just travel in a straight line with constant velocity and it would roll off the table so the reason you have to pull on the rope to get the ball to go in a circle is not because there's an outward force but because this ball wants to maintain its velocity it has inertia wants to keep moving in a straight line but you have to keep pulling on it to keep changing the direction of this velocity so even though many people think there's an outward centrifugal force that's just naturally occurring on an object going in a circle there is not so finally we can come back over to here I could put my mass here I can finally solve for my force of tension if I do this I'll multiply both sides by mass and I just get that the force of tension is mass times the speed squared over the radius of the circle and if I plug in my values the mass was two the speed was five and you can't forget to square it you divide by the radius which was 0.5 and you get that the force of tension had to be a hundred Newtons so in this case the force of tension which is the centripetal force is equal to a hundred Newtons now some of you might be thinking hey this was way too much work for what ended up being a really simple problem why do we have to go through all the trouble of stating all of this problem solving strategy and I agree this one was easy but other problems won't be easy if you don't have some sort of problem-solving framework to fall back on you'll be shooting blind and that's a lonely lonely place to be so let's use this same procedure but let's look at a new problem let's say you have this let's say you were riding your bike over a circular Hill so this gray line represents the pavement and it starts off flat but then the pavement veers upward and it creates this concrete hill that you ride over and then down and you ride over to this side and all this purple circle is representing is the fact that if you were to continue this crest of the hill around into a circle it would form this shape so that gives us a way to define what the radius is of this top part of the hill so let's put some numbers in here let's say the radius of this hill was 8 meters let's say the mass of you and your bike together are about a hundred kilograms and let's say you're riding over this hill at six meters per second and let's say I ask you what's the size of the normal force exerted on you and your bike as you ride over the crest of this hill at six meters per second now let me show you what you can't do because most people try to do this they really want to say that the normal force is just going to be equal to the force of gravity therefore since the force of gravity is mg the normal force should just be mg but that can't be right if the force is on an object are balanced and they cancel the object is just going to maintain its velocity size and direction so this object since it's gone to the right this bike would just continue going to the right and it would just hover straight off this hill that'd be awesome but that doesn't happen this bike moves downward it accelerates downward after this moment since it rides down the hill so the downward force has got to be bigger the force of gravity is going to be bigger than the normal force because if it wasn't this bike would just hover off into space so how do you solve this problem we use the same strategy we used before we're going to draw a force diagram but we already did that we're going to use Newton's second law for one of the directions in the direction we're going to pick is the vertical direction now is that vertical direction the centripetal direction yeah it is because look it into the circle is downward because this bike is at the crest of the hill down corresponds to pointing toward the center of the circle and upward corresponds to pointing away radially away from the center of the circle so since I'm dealing with the centripetal direction we plug in the formula for the centripetal acceleration and the part where you have to be most careful is what you plug into the centripetal forces remember that into the circle counts as positive and out of the circle counts as negative so both of these forces normal and gravity are going to be included but only one of them are going to be included with a positive sign think about which one can you figure out which force would be included in here with a positive sign if you said the force of gravity you're right which is weird usually we treat the force of gravity as negative because it points down but for centripetal forces what we care about is into or out of the circle so I'm going to treat gravity has a positive centripetal force gravity is the force pointing toward the center of the circle and the normal force in this case is going to be a negative centripetal force since its directed out of the center of the circle and then we divide by our mass and so if we solve this for the normal force if you do some algebra we'll multiply both sides by M we move over the FN and then move the MV squared to the other side and what we end up getting is mg minus M times V squared over R is equal to the normal force which if we plug in numbers gives us a hundred kilograms times 9.8 minus 100 kilograms times the speed squared that's going to be 6 meters per second squared divided by the radius of the circle we're travelling in which is 8 meters and you end up getting 530 Newtons so the normal force on you and your bike as you ride over this hill is 530 Newtons that is not equal to your weight this is less than your weight the force of gravity on you is going to be M times G that would be about 980 Newton's so you experienced less normal force and this is natural this is what happens when you write over a hill fast you feel slightly weightless as you go over that hill if you've ever gone with a car a little too fast over a hill you feel that oh and your stomach and you're like hey that was cool that was the weightlessness you felt for a moment if you go too fast if you go too fast this normal force will become zero you'll subtract so much MV squared over R here the normal force becomes zero when that happens you do become airborne so be careful driving over those hills if you drive too fast you'll become airborne since your normal force is going to become zero so recapping when you solve centripetal force problems be sure to draw a quality force diagram then use Newton's second law for one of the directions at a time if you use the centripetal direction the direction pointed radially into the circle you can say that the acceleration in that direction is V squared over R but be sure to only plug in forces that are directed radially that is to say forces that are pointing into or out of the circle if they point into the circle they're going to be positive forces and if they point out of the circle they're going to be negative forces