so let's look at this simple moment

problem we have a teeter-totter of two

people sitting on it the big persons a

thousand Newtons and the small person is

five hundred Newtons they're sitting two

meters away from the middle then the

question is how far away does the big

person have to sit well let's draw

Freebody diagram first of all oops

like this free body diagram of the plank

that they're sitting on so first of all

we have our coordinate axes we have x

and y and we're gonna have 500 Newton's

pushing down right here we're gonna have

a thousand Newton's pushing down

somewhere over on the other side and in

the middle we'll have this reaction

force is what we call out pushing up on

it preventing this whole thing from

dropping down to the ground I know just

to make our lives easier let's put on

some distances here we have two meters

and we have X meters and we're gonna

call this point here this point in the

middle let's just call this point a

alright so our first static equilibrium

we have sum of forces in the X Direction

has to be equal to zero well there's no

forces in the X direction they're all

pointing in the positive or negative Y

direction so that condition is satisfied

we have sum of forces in the Y direction

must equal zero for static equilibrium

so we can solve for what F is but we'll

see we won't actually need this for this

problem so we will have negative 1,000

Newtons minus 500 Newtons plus F is

going to be equal to zero so we'll find

that F just by moving these over to the

other side will equal 1,500 Newtons

alright so now that's satisfied lastly

for static equilibrium in two dimensions

we need to some of whom moments about

some point to be easy to be equal to

zero so some of the moments say about a

and we'll say that this is going to be

the positive direction you can choose

are there sort of rotation for positive

but just make sure you pick one

direction and stick with it all right so

this has to also equal zero and if you

recall the formula for our moments one

of the formulas that we can use

you know the moment about a is equal to

just the force times the distance okay

perpendicular distance but these are all

these are all up and down so this is

gonna be easy

alright so let's go ahead and do this so

if it's gonna cause a clockwise rotation

around this point a will define that as

positive so we have two meters times 500

Newtons now this is gonna be positive

value because if we're pushing here it's

gonna want to rotate this way around

point a okay so now we're gonna have

minus X meters times 1000 dajun's I know

this is - because it's causing this

counterclockwise rotation which is

opposite to what we said is positive so

that's why the minus sign is there and

this is going to equal zero for static

equilibrium so we simply have 1,000

Newton meters move this over to the

other side is equal to X meters times a

thousand Newtons now just drop that's a

thousand I now just divide both sides by

that thousand Newtons and we'll find

that X has to equal one meter now this

makes sense because our our equation

here for moments is it's directly

proportional to force and distance so

for example if you double your if you

double your force or your weight then

that means you're gonna have to be half

as far away from this point to create

the same moment as if you were this guy

sitting twice as far about half is half

as heavy