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Static equilibrium and the ladder problem

Added Jan 30, 2019 •

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The narrator explains the diagram and sequential steps for solving a ladder in static equilibrium problem.

Show Transcript

okay infant video going to go over another problem Van Dyke and living in this is of course the ladder problem is that a problem cuz here we have a ladder is a person standing on a ladder the distance from the ground surface the point of act contact between the wall and the ladder the ladder is leaning against this wall is 5.5 m in a we would like to know what is the force of friction between the ground surface in the ladder. Russian forces acting right here if there was no friction the latter Republic slipped down and move out to the right the force of friction opposes the motion so therefore the force of friction points that direction and this is the fourth we're trying to solve for this kind of static classic static equilibrium problem nothing is moving everything you started from there for all the forces must be in equilibrium for the solve this problem going to some of the forces in the X direction to some of the forces in the y direction for this for what are some of the forces in the torch we should draw in the forces first the first thing you should do is draw in the forces there is the force from the person of the weight of the person on the ladder there is actually the weight from the light which we do all right in the center cuz we'll assume louder these two forces are acting in the negative Direction there must be some force acting in the opposite direction for the letters not falling through the ground surface of these two forces are in equilibrium with the other force in the y direction. now we have one force in the X Direction and the right here the ladder is leaning against the wall the wall to the must be some other Force that's keeping the ladder from falling through the wall That's the force on the ladder from the wall so that he is all these are all of the forces that are acting in this problem we have no forces acting all the forces are acting as we don't need to break any of them into their components a piece of information I want to give you that is this distance and this distance and what are those distances for the first one this is Excel for the ladder the X distance for ladder. 1.1 what's the distance between this point the Punta Canta collateral the ground surface and extension the line of action of the force due to the ladder so that's one point one we this one is obviously from this point to the intersection the ground surface with the line of action of the force from the person and these are for the ladder some of the forces the next step for senior directions to positive force in the wall points in the positive direction to friction Force points in the negative Direction so we're just going to put down the force from the Walmart equals zero two forces point in an egg the normal horse minus the force on the person might support from a lot of people zero and then that works now we're going to choose this point to be our axis of rotation these two forces a normal force and friction force act right after seven nation but that's what they produce no torque their lever arm R20 for the number for sanitation for so we're not going to sign those up but these other three forces the ladder the person and the wall they produce so we're going to send those three stop Botetourt from those three forces now you'll notice that this force and the force moonlighter this direction down and if they were to act by themselves these. Lighter to rotate in a counterclockwise Direction forces that cause objects to rotate in a counterclockwise Direction produced positive plus the DART bus depart from the person now this force is acting on Costco ladder to rotate forces that cause objects to rotate in a clockwise Direction produced from the wall and that is also important things here you'll notice for the X forces Force next Direction with only two of them and they're acting in opposite direction so that means the force from the wall in the force of friction must be equal in magnitude but opposite in direction of this is important point because you're not actually going to solve for the fortune the wall we're not going to solve for the force of friction we're going to solve equations for the force from the wall we know the force from the wall and the force of friction equal in magnitude but opposite in direction so we can solve for this I don't know this is the same connect to this the same okay now the wife forces were not going to use we're not have to solve for the normal force we already know the force on the person we already know that forceful about it cuz we're giving them a standing know what G-Force but if you were a splint you would just know that this normal force is equal to the sum of these two forces they were not used to this problem equation is equal to RF sine Theta what is are the straight-line distance from the axis of rotation measured along this radio. tell me about the kitchen of force so for example for the force from ladder is the distance from this point this is our axis of rotation to where the force is applied so that's alright the straight-line distance app is the force what is Theta Theta is the angle always the angle between the radio vector and the force Vector between the radio Vector angle in this problem if we want to calculate the torque we're not giving our we're not giving these distances when I give him a lot of Hangover can't calculate those using trig functions we're not giving our we're also not giving that we don't know what this angle is okay we are given the forces at least two of the three you need but even though we're not given are not going to stay till we are given to something else and that is here and for the force in the ladder this is our lever arm the person this is the lever arm and when we calculate our times the sine of theta you get the lever arm even though we're not given we are giving a lever arms the lever arm in this case is the are that is perpendicular to the line of action of the force so I'm going to rewrite this equation as the lever on the force and that's happened, definition people use the clutch lever arm times the force give me a lever arm the forces we can calculate the torque equation and apply it to these Three Dwarfs to write down that the lever arm for the purse for the person X the force the person that's why I'll give us the truck this is the lever arm and the force plus the lever arm from the ladder times the force in the lab minus the leather warhorse X the wall force this law is perpendicular alarm for the wall force 5.5 m no drop equal to zero now we actually have three six eight things here and if you think about it we know seven of the eight arms we don't know this Force but because we know everything except that forced we can saw previews before that foreskin therefore we know and then we'll know that the friction force is equal to the wall so I told you before we're not going to solve the fraction for 3 Horsemen's Outlet all right to do that in the next life here's our equation for person torque wall and this is our fork for the tuning fork person Park ladder and torque wall I'm going to solve this equation for the force from the wall that is simply the force from the wall move this over to the other side / the letter on from the wall you get that to torque the person what's the torque from the ladder / the torque from / lever arm from the wall force will give us the W so we're just something on a plug all those values this is the lever on the person this is the force lever arm for the ladder this is the force divided by the lever arm for the wall force and if you do all of that you get that the force from the wall is 247 noon once again the force from the wall is equal to the friction force of that meet the friction forces episode 247 new and there you go we did it okay now I'm maybe that's kind of a lot to do but if you just follow those steps step by step draw right down the forces sum up the Torx substitute your values in be careful with your negative in your positive signs and you should be able to do that thank you very much for watching hope you found that video helpful if you did you can do one or all the following three things you can subscribe to my YouTube channel get all my excellent physics chemistry and math videos you can't give me a thumbs up this video and you can also leave in like pugs come in, thank you very much watching will see 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Uploaded by Debra Hood.

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Static equilibrium and the ladder problem

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