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# Moments (part 2)

## Video transcript

I'm going to do a couple of more moment of forest problems especially because I think I might have bungled the terminology in the previous video because I kept confusing clockwise with counterclockwise this time I'll try to be more consistent let me draw my lever again my seesaw so that's my seesaw and that is my axis of rotation or my fulcrum or my pivot point whatever you want to call it and let me let me throw a bunch of forces on there so let's say that I have that is a 10 Newton force and it is at a distance of 10 so distance is equal to 10 right this the moment arm distance is 10 let's say that I have a 50 Newton force it's 50 Newtons and it's moment arm distance is equal to 8 all right let's say that I have a 5 Newton force and it's moment arm distance is I don't know 4 the distance is equal to 4 that's enough for that side and let's say I have a I don't know let's say that I have so let's see I have that that's let me just keep going I'm going to randomly let's say I have a I'm gonna switch colors actually now I'm going to keep it all the same color then we'll use colors to differentiate between clockwise and counterclockwise so I don't bungle everything up again so let's say I have a 10 Newton force here and that is and of course these vectors aren't proportional to actually what I drew right 50 Newtons would be huge if I if these were the actual vectors and let's say that that moment arm distance is 3 let me do a couple more and let's say at a moment arm distance of 8 I have a I don't know let's say I have a a clockwise force of I don't know and make up a number 20 Newtons and let's say at a distance of 10 again the distance is equal to 10 I have my mystery force and it's going to act in a counterclockwise direction and I want to know what it needs to be so whenever you do any of these moment of force problems and you know you say well what does a force need to be in order for this this seesaw to not rotate you just say well all the clockwise moments have to equal out of the counterclockwise moments so clockwise clockwise moments equal counterclockwise I'll do them in different colors equal counterclockwise moments so what are all the count what are all the clockwise moments well this clockwise is this direction right that's the way a clock goes so this is clockwise that is clockwise I want to go in this direction right and so this is clockwise so we're all the clockwise moments it's 10 Newton's times its moment arm distance 10 so 10 times 10 plus 5 Newton's times this moment are in distance 4 plus 5 times 4 plus 20 Newtons times its moment arm distance of 8 plus 20 times 8 and that's going to equal the counterclockwise moments and so the ones that the left over ones are counterclockwise so we have 15 Newton's acting downward here and that's counterclockwise and it's at a distance of 8 from the moment arm so 50 times 8 let's see we don't have any other counterclockwise on that side this is counterclockwise right we have 10 Newton's acting in the counterclockwise direction is moment arm distance is 3 plus 10 times 3 and we're assuming our mystery force which is at a distance of 10 is also counterclockwise plus 4 times 10 and now we simplify and I'll just go to a neutral color because the simplification this is just math now 100 plus 20 plus 160 is equal to what's 50 times 8 that's what 400 plus 30 plus 10 and F what is this two and fifty times a ride is 400 okay 100 this is 120 plus 160 is 280 280 right yet 280 is equal to 430 this is a good example plus 10 F I just realized subtract 430 from both sides so what's 430 minus 280 it's 150 right 100 - that's a 330 all right so it's 150 so it's minus 150 is equal to 10 F so f is equal to minus 15 Newtons in the counterclockwise direction so f is minus 15 Newtons in the counterclockwise direction or it means that it is 15 Newtons right we assumed that it was in the counterclockwise direction but when we did the math we got a minus number so excuse me I apologize if I blow out your sneaker your speakers with us nice well anyway we assumed that it was going in the counterclockwise direction but when we did the math we got a negative number so that means it's actually operating in the clockwise direction at 15 Newtons at a distance of 10 from the moment arm hopefully that one was less confusing than the last one so let me do another problem and these actually used to confuse me when I first learned about moments but in some ways they're the most useful ones so let's say that I have some type of let's have a table I'll draw it in wood and it's a wood table that's my table and I have a leg here I have a leg here let's say that you know the the center the center of mass of the top of the table is here right it's at the center and let's say that it has a weight right it has a weight going down I don't know whatever you what's reasonably made kilogram let's say 20 Newtons say it has a weight of 20 Newtons let's say that I place some textbooks on top of this table or box just to make the drawing simpler I didn't want it it undo let's say I place a box there and the box is also let's say the box weighs I don't know this is say it's like 10 let's say it's like 10 kilograms which would be about 100 Newtons so let's say it weighs about 100 Newtons 100 Newtons so what I want to figure out what I need to figure out is how much weight is being put onto each of the legs of the table and this might have not even been obviously a moment problem but you'll see in a second it really is so how do we know that well well both of these legs are supporting the table right whatever that the table is exert exerting downwards the leg is exerting upwards right so that's that's the amount of force that each of the each of the legs are holding so what we do is we pick an axe so let's let's just pick this leg just because it I don't know I'm picking it arbitrarily right let's pick this leg let's pick an arbitrary axis of rotation well let's put pick this is our axis of rotation now why do I pick that as the axis of rotation because think of it this way if this if this leg started pushing more than it needed to the whole table would rotate in the counterclockwise direction or the other way if this leg started to weaken and started to buckle and couldn't hold its force the table would rotate down this way and it would rotate around the other leg assuming that the other leg doesn't fail we're assuming that this leg just you know it's just going to do its job and it's not going to move one way or the other but this leg that that's why we're thinking about that way if it was week the whole table would rotate in the clockwise direction and if it was somehow exerting extra force which we know a leg can't but let's see if it was a spring or something like that then the whole table would would rotate in the counterclockwise direction so once we set that up we can actually we can actually we can actually set this up as a moment problem so what is the force of the leg so the the whole table is exerting some type of some type of without if this leg wasn't here the whole table would have a net clockwise moment right the whole table would tilt down and fall down like that so the leg must be exerting a counter clockwise moment in order to keep it stationary so the leg must be exerting a force upward right here the force of the leg right and we know that we know that from basic physics right there's some force coming down here and the leg is is doing an equal opera's upwards so what is that force of the leg and one thing I should have told you is all of the distances let's say that this distance between this leg and the book let's say that that is one meter or the box let's say that this distance let's say that between the leg and the center of mass is 2 meters and so this is also 2 meters okay so we can now set this up as a moment problem so remember all of the clockwise moments have to equal all of the counterclockwise moments so what are all of the clockwise moments what are all of the things that want to make the table rotate this way right or this way well if that leg the leg is the only thing keeping it from doing that so everything else is essentially a clockwise moment so we have this 100 Newtons and it is one meter away it's moment arm distance is 1 so we have so these are all the clockwise moments 100 times 1 right it's 100 Newton's acting downwards in the clockwise direction clockwise moment it's 1 meter away plus we have the center of mass at the top of the table which is 20 Newton's plus 20 Newtons and that is 2 meters away from our designated axe so twenty times two and you might say oh well but isn't this leg exerting some force well sure it is but it's distance from the are designated axis is zero so it's it's moment of force is zero right any negative is exerting a million pounds or a million Newtons it's it's moment of force or torque would be zero because it's at its its moment arm distance is zero so we can ignore it which makes things simple so those were the only clockwise moments and what's the counter clockwise moment well that's going to be the force exerted by this leg right that's what's keeping the whole thing from rotating so it's the force of the leg times its distance from our axis well this is a total of 4 meters which we set here times 4 meters right and so we can just solve we get 100 plus 40 so we get 140 is equal to the force of the leg times 4 so what's 142 see 4 goes into hundred forty third let's see it goes into it 3 30 30 35 times my math is not so good for is that right 4 times 30 is 120 120 plus 20 right so the force of the leg is 35 Newtons upwards right so and since this isn't moving we know that the downward force right here must be 35 Newtons and so there's a couple of ways we can think about it if if this leg is supporting 35 Newtons right and we have a total weight here of 120 Newton's right our total weight the way to the top of the table plus the bookshelf that's a hundred 20 Newtons so the balance of this must be supported by something or someone so the balance of it is going to be supported by this leg so it's 120 minus 35 is what or my phone is ringing I'm sure it's 120 minus 35 is 120 minus 30 is 90 and then 90 minus 5 is 85 Newtons so disconcerting when my phone rings I have trouble focusing anyway probably because my phone sounds like a freight train anyway so there you go using and this this type of problem is actually key to as you can imagine build bridge builders or furniture manufacturers or civil engineers who are bridge builders or architects because you actually have to figure out well if I design something a certain way I have to figure out how much weight each of you know the supporting structures will have to support and using this and as you can imagine why is why is this one supporting more weight why is this like supporting more weight than that like well because this book is which is 100 Newtons which is a significant amount of the total weight is much closer to this leg than it is to this leg right if we put it to the center there they would balance and then if we push it further to the right then this leg would start bearing more of the weight anyway hopefully found that interesting and hopefully I didn't confuse you and I will see you in future videos