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so I've got this block of wood here that has a mass of five kilograms and it's sitting on some dirt and the code the n-word near the surface of the earth and the coefficient of static friction between this type of wood and this type of dirt is zero point six zero and the coefficient of kinetic friction between this type of wood and this type of dirt is zero point five five this was measured by someone else long ago or you found it in some type of a book someplace and let's say we push on this side of the block with a force of 100 Newtons what is going to happen so the first thing you might realize is if there was no friction if this was a completely frictionless boundary and there's no air resistance and we are assuming that there is no air resistance in this example that in this dimension in the horizontal dimension there would only be one force here there would be 100 Newton force it would be completely unbalanced that would be the net force and so you would have a force going in that direction of 100 Newton's on a mass of five kilograms force is equal to mass times acceleration acceleration and force are vector quantities and so you would have the force divided by the mass would give you 20 20 meters per second of acceleration in the rightward direction that's if there were no friction but there is friction in this situation so let's think about how we'll deal with it so the coefficient of friction tells us so this right here is the ratio between the magnitude of the force that I've called the budging force the amount of force you need to apply just to get this thing to budge just to get this thing to start moving so we can start using the coefficient of kinetic friction if the it's the ratio between that and the magnitude of the force of contact between this block and the floor or the ground here and the magnitude of that force of contract is the same thing as the normal force that the ground is applying on the block the magnitude of the normal force that the ground is applying on the block then once it's moving then we could say that this is going to be that this will then be equal to this over here will be equal to the force of friction so this is this is the force necessary overcome friction and then this over here will be equal to the force of friction the magnitude of the force of friction over over the force of contact contact force between those two so over the normal force and it makes sense that the larger the larger the contact force the more that these are being pressed together the little at the atomic level they kind of really get into each other's grooves the more budging force you would need or the more friction force would go against your motion and in either situation the force of friction is going against your motion so even if you push it on that way it's not like force of friction is all of a sudden going to help you so let's think about what the necessary force we need to do to overcome the force of friction right here in the static situation so the force of gravity on this block the force of gravity on this block is going to be the gravitational field which is 9.8 meters per second times five kilograms 9.8 meters per second times five kilograms gives us 49 kilogram meters per second or 49 Newtons down this is the force the magnitude of the force due to gravity the direction is straight down towards the center of the earth the normal force and that force is there because this this block is not accelerating downwards so there must be some force that completely balances off the force of gravity and in this example it is a normal force it is the normal force so it is acting 49 Newtons upward and so these net out and that's why this block does not accelerate upwards or downwards so what we have is the budget the magnitude of the budging force needs to be equal over the magnitude of the normal force well this thing right over here is going to be 49 Newtons is equal to zero point six zero or we could say or we could say that the magnitude of the budging force is going to be equal to 49 Newtons times the coefficient of static friction or that's 49 Newtons 49 Newtons 49 Newtons times zero point six zero zero point six zero and remember coefficients of friction are unitless so the unit's here are still going to be in Newtons and so this gives us get out our calculator this gives us 49 times point six gives us 29 point four Newtons this is equal to it 29.4 Newton's 29.4 Newton's so that's the force necessary to overcome static friction which we are applying more than enough of so with a hundred Newton's we will just start to budget and right when we're just at that moment where the thing is just starting to move the net force so we have 100 Newton's going in that direction and the force of static friction is going to go in this direction maybe I could draw it down here so it's coming from right over here the force of static friction is going to be twenty nine point four Newton's that way and so right when I'm just starting to budge this just for that little you know moment it's not because once I do that then all of a sudden it's moving and then static friction or sorry kinetic friction starts to matter but just for that moment just for that moment I'll have a net force of one hundred minus twenty nine point four to the right so I'll have a net force of 70 point six so I will have a net force of what 70 what did I just write there 70 point six I could do that in my head I shouldn't have to look at that 70 point 6 Newton's for just a moment for just a moment while I budget so just exactly while I'm budging it while we're overcoming the static friction we have a 76 seventy point six Newton net force in the right direction and so just for that moment you divided by a five kilogram mass five kilogram mass so just for that moment it'll be accelerating at fourteen point one two meters per second so you'll have an acceleration of fourteen point one meters per second squared to the right but that will just be for that absolute moment because once I budget all of a sudden the block will start to be moving and once it's moving the coefficient of kinetic friction starts to matter we got the things out of there little grooves and so they're kind of gliding past each other on the top although there still is resistance so once we budget will have the exertion for just a moment now a sudden the coefficient of kinetic friction comes to play and the force of friction assuming we're moving the force the magnitude of the force of friction it will always go against our movement is going to be remember our normal force we already said is 49 Newtons so it's 49 we multiply both sides of this times four nine you get 49 Newton's times 0.55 which is equal to 49 times 0.55 is equal to 26 point nine five Newtons so this is equal to twenty six point nine five Newtons this is the force of friction this is the magnitude and it's going to go against our motion so as soon as we start to move in that direction the force of friction is going to be going is going to be going in that direction so once we start moving assuming that I'm continuing to apply this hundred Newton's of force what is the net force so 100 Newton's going that way and I have twenty six point nine five Newton's going that way twenty six point nine five and remember with vectors I don't have to draw them here I could draw all of them so all of their tails start at the the center of mass of this object I could draw them whenever but remember this is acting on the object so it's usually if you want to be precise you would show it acting on the center of mass because we can view all of these atoms as one collective object but anyway what is the net force now well you have 100 Newton's to the right you have twenty six point nine five Newton's to the left one hundred minus twenty six point nine five hundred Newton's that I'm applying to the right minus twenty six point nine five Newton's which is the force of friction to the left always acting against us means that there's a net force to the right of seventy three point zero five so once we're moving we have a net force to the right of seventy three point zero five Newtons this is this is the net force this is the net force and it's acting to the right so what is going to be once right after we budget how quickly will this accelerate well seventy three point zero five divided by the mass divided by five kilograms divided by five kilograms gives us 14 point six one so the acceleration the acceleration once we're moving is going to be fourteen point six one meters per second squared to the right to the right so I really want to make sure you understand what's happening here it took us right we always had enough force to start budging it but right when we budged it that that kind of had to overcome the static friction for just for a moment our acceleration was slower our acceleration will are because we're overcoming that static friction but once we've budgeted and once it's moving and assuming that we're continuing to apply a constant force over here then all of a sudden the force of friction since we're kind of kind of bumping along the top now and it's not stuck in their grooves we're now using the coefficient of kinetic friction and so once it's moving the net force becomes greater in the rightward direction because you could kind of view it as a force of friction is will become less once it starts moving and so now the force of friction went down a little bit to twenty six point nine five Newtons and so now we are accelerating to the right a little bit at a slightly faster eight fourteen point six one meters per second so right when you budget accelerate at fourteen point one meters per second but just for a moment almost an unnoticeable moment once it starts moving then you're going to be going to the right with this constant acceleration

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