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Current time:0:00Total duration:6:46

let's say we take the shoot instead of sitting it on the floor here's one the trips you pull out let's say we take the showings shove it against the wall so walls can exert normal forces just like floors can but when this happens people start to get a little bit concerned starts to get a little bit weird let's say we exert a force so say the force looks like this so here we go let's call this force f4 so here's f4 this force keeps the shoe from falling down but it also pushes the shoe into the wall so again we're going to have a normal force let me give you an angle here let's say this angle right there is Phi and let's say the question we want to ask now we want to know what's the normal force in this case so this one's a little bit weirder but we can still do it the same way we should draw a force diagram first it's always good practice to draw what forces are exerted on the object you're trying to find a force for so we're going to have the normal force but first we should draw the force of gravity gravity is easy gravity always points it down so you got mg straight down we're going to have a normal force here's where people make a mistake we will not draw the normal force up people think that the normal force is always mg we saw that that's not true people also think the normal force is always up but it's not it's usually up because it's in contact with a horizontal surface but now this is in contact with a vertical surface and this word normal in the phrase normal force is not referring to like boring or usual it's referring to normal in the mathematical sense is perpendicular perpendicular to the surface exerting this normal force in this wall that's vertical perpendicular to that wall is coming out of the wall and that's going to be to the right so the wall is going to push to the right on the shoe to keep the shoe from penetrating this wall that's a little bit weird for people is that this normal force is now pushing to the right and I've got one more force I've got my F 4 I'm going to draw this force F 4 looks something like that ok so these are my forces that's it those are the only forces there are I mean we're going to neglect any friction let's just assume the the shoes just sitting there there's no other frictional forces let's say this is it we want to find the normal force what do we do again we're going to use Newton's second law we're going to use a equals the net force in a certain direction this time we're going to use the horizontal direction we're going to use the horizontal direction because the force we want to find our normal force is in the horizontal direction so the acceleration in the X direction is going to be what well you think about this if I'm pushing the shoe into the wall it's probably got no horizontal acceleration even if it was sliding up and down even if there was motion up and down it's probably not penetrating into this wall and is probably not bouncing off of this wall is probably constricted to be only in the plane of this wall so there's going to be no horizontal acceleration and if that doesn't make sense it's because there's no motion in the horizontal direction left or right there's no velocity change at all in this horizontal direction because the shoes is not going to be moving in that horizontal direction and it continues to not move in that horizontal direction so our acceleration horizontally is just zero equals the net force divided by the mass all right the net force in the X direction what we're going to have in the X direction well I've got FM pointing to the right so again that's a positive 4 so I'm going to consider rightward to be positive and I've got this F 4 part of it points to the left so just like before I've got to break this force up I've got to figure out how much of this force points horizontal and how much of this force points vertical to get this F 4 in the x-direction which is what I plug in to this formula pier because I need this component here this is the horizontal force of F 4 not the vertical force so I don't plug the vertical force in anymore because this vertical force is not part of the X direction we're considering Newton's second law for the X direction so to solve for F for X I'm just going to again use sine because this angle the opposite of this angle is F for X I'm going to use sine of theta oh sorry sine of Phi I'm going to take sine of Phi that's going to equal F 4 in the X divided by the total amount F 4 I get F 4 in the X is going to be F 4 times sine of Phi and now I can use this up here but you got to be careful with signs F 4 X points left I'm going to consider that a negative force so if F 4 sine theta represents the nough tude I'll write this as negative F for sine Phi sorry I keep saying theta I mean Phi I multiply both sides by M I'll get 0 again on the left hand side equals I've got FN minus F for sine Phi now when I solve this first F and the normal force I'll get the FN I'll add this F for sine Phi to both sides and I'll get that this normal force is going to equal F for sine Phi and that makes sense it makes sense because what these surfaces are doing the reason why you're getting a normal force is these surfaces are exerting whatever force they have to to prevent any penetration of the surface so if this F for X is pushing in to the surface with F for X all right that's the force we're pushing in with F ends just got to equal that it's got to match that so that there's no acceleration horizontally there were no other forces we could now you know what to do if there were if you wanted to step this up you can add another force here we'll call that f5 that'd be another force this way we'd have another f5 you know how to handle that now you come over to here that's pointing to the left so you do - f5 you come down here this would be a minus f5 you'd add that to both sides that'd be a plus f5 what if we added a vertical force what if we added another vertical force this way to the shoe and we called that f6 well that wouldn't impact the normal force at all this force f6 does not affect how much these surfaces are getting pushed into each other so I wouldn't include that over here at all that's a vertical force it wouldn't affect the normal force this time also no gravity's not even affecting the normal force this time because gravity is exerting a force in the vertical direction and our normal forces in the horizontal direction so long story short normal force is not always mg the normal force will only exist it will only be nonzero when two surfaces are in contact at pushing on each other you can change what the normal force is by adding forces into or out of the surface exert it on that object and if there's a force at an angle when you're finding normal force to make sure you only use the component that in the same direction as the normal force because that's the only one that's going to affect the normal force when you solve using Newton's second law