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##### Static and Kinetic Friction Example : Thinking about the coefficients of static and kinetic friction

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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