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# Static and kinetic friction example

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So I have got this block of wood here that has a mass of 5 kilograms and it is sitting on some dirt and we are near the surface of the earth and the coefficient of static friction between this type of wood and this type of dirt is 0.60 and the coefficient of kinetic friction between this type of wood and this type of dirt is 0.55 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 a 100 N What is going to happen? So the first thing you might realize is if there is no friction if this was a completely frictionless boundary and there is no air resistance, 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, this 100 N force It would be completely unbalanced and that would be the net force and so you would have a force going in that direction of a 100 N on a mass of 5 kilograms Force = Mass times acceleration acceleration and force are vector quantities So you would have the force divided by the mass would give you 20 meters per second of acceleration in the rightward direction That is 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 have called the budging force The amount of force you need to apply to get this thing to budge to get this thing to start moving. So we can start using the coefficient of kinetic friction It's the ratio between that and the magnitude of the force of contact between this block and the floor or ground here And the magnitude of that force of contact is the same thing as the normal force that the ground is applying on the block the magnitude of the normal force the ground is applying on the block Then once its moving then we can say that this is going to be--this will then be equal to this over here will be equal to the force of friction So this is the force that really overcome friction and this over here will be equal to the force of friction The magnitude of the force of friction over the force of contact the contact force between those two, so over the normal force and it makes sense that 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 others 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 in that way sounds like force of friction is all of a sudden going to help you So let's think about what the necessary force will we need to overcome the force of friction right here in the static situation So the force of gravity on this block is going to be the gravitational field which is 9.8 m/s^2 times 5 kilograms 9.8 m/s times 5 kilograms gives 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 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 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 budge the magnitude of the budging force, needs to be equal to, over the magnitude of the normal force well this thing right over here is going to be 49 newtons Is equal to 0.60 Or we could say that the magnitude of the budging force is equal to 49 newtons times the coefficient of static fiction Or that's 49 newtons times 0.60 And remember coefficient of friction are unitless So the units here are still going to be in newtons So this 49 times .6 gives us 29.4 newtons This is equal to 29.4 newtons So that's the force that's started to overcome static friction which we are applying more than enough of so with a 100 newtons, we would just start to budge it and right when we are in just in that moment where that thing is just starting to move the net force-- so we have a 100 newtons going in that direction and the force of static friction is going to go in this direction-- maybe I could draw it down here to show it's coming from right over here The force of static friction is going to be 29.4 newtons that way and so right when I am just starting to budge this just when that little movement-- because once I do that, then all of a sudden it's moving and then kinetic friction starts to matter, but just for that moment just for that moment I'll have a net force of 100 - 29.4 to the right, so I have a net force of 70.6 N for just a moment while I budge it So just exactly while I'm budging it While we're overcoming the static friction, we have a 70.6 N net force in the right direction And so just for that moment, you divide it by 5 kg mass So just for that moment, it will be accelerating at 14.12 m/s^2 So you'll have an acceleration of 14.1 m/s^2 to the right but that will just be for that absolute moment, because once I budge it 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've got the things out of their little grooves and so they're kind of gliding past each other on the top, although there still is resistant So once we budge it, we'll have that acceleration for just a moment Now all of a sudden, the coefficient of kinetic friction comes to play And the force of friction, assuming we're moving the magnitude of the force of friction will always go against our movement is going to be--remember, our normal force is 49 N So we can multiply both sides of this times 49 We get 49 N times 0.55 which is equal to 26.95 N This is the force of friction; this is the magnitude and it's going to go against our motions So as soon as we start to move in that direction, the force of friction is going to be going in that direction So once we start moving, assuming that I'm continuing to apply this 100 newtons of force what is the net force? So I have 100 N going that way and I have 26.95 going that way Remember, with vectors, I don't have to draw them here I can draw all of their tails start at the center of mass of the object. I can draw them whatever, but remember this is acting on the object If we want to be precise, we can show it 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? We have 100 N to the right; we have 26.95 to the left 100 minus 26.95 100 N that I'm applying to the right - 26.95 N which is the force of friction to the left always acting against us means that there's a net force to the right of 73.05 So once we're moving, we have a net force to the right of 73.05 N This is the net force and it's acting to the right Right after we budge it, how quickly will this accelerate? Well, 73.05 divided by the mass, divided by 5 kg, gives us 14.61 So the acceleration once we're moving is going to be 14.61 m/s squared to the right So I really want to make sure you understand what's happening here We always have enough force to start budging it but right when we budged it we overcome the static friction for just a moment our acceleration was slower because we're overcoming that static friction but once we budged it 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 bump it along the top now and 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 can kind of view that force of friction will become less once it starts moving And so now the force of friction went down a little bit to 26.95 N And so now we're accelerating to right at a slightly faster rate 14.61 m/s^2 So right when you budge it, it accelerates at 14.1 m/s^2 but just for a moment, almost unnoticeable moment once it starts moving Then you're going to be going to the right with this constant acceleration