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So I have got this block of wood here that has a mass of 5 kilograms

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and it is sitting on some dirt and we are near the surface of the earth

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and the coefficient of static friction between this type of wood and this type of dirt is 0.60

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and the coefficient of kinetic friction between this type of wood and this type of dirt is 0.55

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This was measured by someone else long ago

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or you found it in some type of a book someplace

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And let's say we push on this side of the block with a force of a 100 N

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What is going to happen?

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So the first thing you might realize is if there is no friction

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if this was a completely frictionless boundary and there is

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no air resistance, we are assuming that there is no air resistance in this example

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That in this dimension, in the horizontal dimension

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there would only be one force here, this 100 N force

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It would be completely unbalanced and that would be the net force

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and so you would have a force going in that direction of a 100 N on a mass of 5 kilograms

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Force = Mass times acceleration

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acceleration and force are vector quantities

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So you would have the force divided by the mass

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would give you 20 meters per second of acceleration in the rightward direction

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That is if there were no friction

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but there is friction in this situation

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So let's think about how we'll deal with it

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So the coefficient of friction tells us

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So this right here is the ratio between the magnitude of the force

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that I have called the budging force

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The amount of force you need to apply to get this thing to budge

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to get this thing to start moving. So we can start using the coefficient of kinetic friction

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It's the ratio between that and the magnitude of the force of contact

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between this block and the floor or ground here

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And the magnitude of that force of contact is the same thing

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as the normal force that the ground is applying on the block

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the magnitude of the normal force the ground is applying on the block

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Then once its moving

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then we can say that this is going to be--this will then be equal to

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this over here will be equal to the force of friction

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So this is the force that really overcome friction

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and this over here will be equal to the force of friction

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The magnitude of the force of friction over the force of contact

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the contact force between those two, so over the normal force

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and it makes sense

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that the larger the contact force

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the more that these are being pressed together

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the little at the atomic level, they kind of really get into each others grooves

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the more budging force you would need

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or the more friction force would go against your motion

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And in either situation

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the force of friction is going against your motion

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So even if you push it in that way

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sounds like force of friction is all of a sudden going to help you

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So let's think about what the necessary force will we need

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to overcome the force of friction right here in the static situation

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So the force of gravity on this block

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is going to be the gravitational field which is 9.8 m/s^2 times 5 kilograms

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9.8 m/s times 5 kilograms gives 49 kilogram meters per second or 49 newtons down

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This is the force, the magnitude of the force due to gravity

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the direction is straight down towards the center of the earth

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The normal force, and that force is there because this block is not accelerating downwards

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So there must be some force that completely balances off the force of gravity

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And in this example, it is the normal force

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So it is acting 49 newtons upward

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and so these net out. And that's why this block does not accelerate upwards or downwards

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So what we have is the budge the

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magnitude of the budging force, needs to be equal to, over the magnitude of the normal force

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well this thing right over here is going to be 49 newtons

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Is equal to 0.60

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Or we could say that the magnitude of the budging force

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is equal to 49 newtons times the coefficient of static fiction

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Or that's 49 newtons times 0.60

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And remember coefficient of friction are unitless

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So the units here are still going to be in newtons

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So this 49 times .6 gives us 29.4 newtons

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This is equal to 29.4 newtons

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So that's the force that's started to overcome static friction

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which we are applying more than enough of

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so with a 100 newtons, we would just start to budge it

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and right when we are in just in that moment

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where that thing is just starting to move

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the net force--

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so we have a 100 newtons going in that direction

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and the force of static friction is going to go in this direction--

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maybe I could draw it down here to show it's coming from right over here

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The force of static friction is going to be 29.4 newtons that way

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and so right when I am just starting to budge this

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just when that little movement--

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because once I do that, then all of a sudden it's moving

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and then kinetic friction starts to matter, but just for that moment

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just for that moment I'll have a net force of 100 - 29.4

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to the right, so I have a net force of 70.6 N

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for just a moment while I budge it

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So just exactly while I'm budging it

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While we're overcoming the static friction, we have a 70.6 N net force in the right direction

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And so just for that moment, you divide it by 5 kg mass

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So just for that moment, it will be accelerating at 14.12 m/s^2

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So you'll have an acceleration of 14.1 m/s^2 to the right

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but that will just be for that absolute moment, because once I budge it

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all of a sudden the block will start to be moving

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And once it's moving, the coefficient of kinetic friction starts to matter

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We've got the things out of their little grooves

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and so they're kind of gliding past each other on the top, although there still is resistant

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So once we budge it, we'll have that acceleration for just a moment

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Now all of a sudden, the coefficient of kinetic friction comes to play

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And the force of friction, assuming we're moving

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the magnitude of the force of friction will always go against our movement

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is going to be--remember, our normal force is 49 N

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So we can multiply both sides of this times 49

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We get 49 N times 0.55 which is equal to 26.95 N

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This is the force of friction; this is the magnitude

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and it's going to go against our motions

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So as soon as we start to move in that direction, the force of friction

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is going to be going in that direction

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So once we start moving, assuming that I'm continuing to apply this 100 newtons of force

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what is the net force? So I have 100 N going that way

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and I have 26.95 going that way

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Remember, with vectors, I don't have to draw them here

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I can draw all of their tails start at the center of mass of the

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object. I can draw them whatever, but remember this is acting on the object

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If we want to be precise, we can show it on the center of mass because

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we can view all of these atoms as one collective object

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But anyway, what is the net force now?

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We have 100 N to the right; we have 26.95 to the left

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100 minus 26.95

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100 N that I'm applying to the right

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- 26.95 N which is the force of friction to the left always acting against us

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means that there's a net force to the right of 73.05

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So once we're moving, we have a net force to the right of 73.05 N

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This is the net force and it's acting to the right

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Right after we budge it, how quickly will this accelerate?

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Well, 73.05 divided by the mass, divided by 5 kg, gives us 14.61

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So the acceleration once we're moving is going to be 14.61 m/s squared

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to the right

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So I really want to make sure you understand what's happening here

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We always have enough force to start budging it

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but right when we budged it

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we overcome the static friction for just a moment

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our acceleration was slower

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because we're overcoming that static friction

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but once we budged it and once it's moving

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and assuming that we're continuing to apply a constant force over here

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then all of a sudden, the force of friction since

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we're kind of bump it along the top now and not stuck in their grooves

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we're now using the coefficient of kinetic friction

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And so once it's moving, the net force becomes greater in the rightward direction because

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you can kind of view that force of friction will become less once it starts moving

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And so now the force of friction went down a little bit to 26.95 N

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And so now we're accelerating to right at a slightly faster rate 14.61 m/s^2

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So right when you budge it, it accelerates at 14.1 m/s^2

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but just for a moment, almost unnoticeable moment once it starts moving

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Then you're going to be going to the right with this constant acceleration