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