So I've got this block of wood here that has a mass of 5 kilograms, and it's sitting on some dirt. And we're 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 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, then 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 newtons on a mass of 5 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 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. 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 contact 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 the force necessary to overcome friction, and then 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 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 is going to be the gravitational field, which is 9.8 meters per second, times 5 kilograms. 9.8 meters per second times 5 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 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 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 going to be equal to 49 newtons times the coefficient of static friction. Or that's 49 newtons times 0.60.
And remember, coefficients of friction are unitless. So the units here are still going to be in newtons. And so this gives us, get out our calculator, this gives us 49 times 0.6 gives us 29.4 newtons.
This is equal to, let me write it, 29.4 newtons. So that's the force necessary to overcome static friction, which we are applying more than enough of. So with 100 newtons, 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 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'm just starting.
I'm going to budge this just for that little moment. 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, I'll have a net force of 100 minus 29.4 to the right. So I'll have a net force of 70.6. So I will have a net force of 70.6.
I could do that in my head. I shouldn't have to look at that. 70.6 Newtonss. 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 Newtons net force in the right direction.
And so just for that moment, you divide it by a 5 kilogram mass. So just for that moment, it'll be accelerating at 14.12 meters per second. So you'll have an acceleration of 14.1.
meters per second squared 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 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 resistance. 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 force, the magnitude of the force of friction, it'll 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 49. You get 49 newtons times 0.55, which is equal to, 49 times 0.55 is equal to 26.95 newtons. So this is equal to 26.95 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 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 newtons going that way, and I have 26.95 newtons going that way. 26.95. 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 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 newtons to the right.
You have 26.95 newtons to the left. 100 minus 26. 0.95, 100 newtons that I'm applying to the right, minus 26.95 newtons, 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 newtons. 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, 73.05 divided by the mass, divided by 5 kilograms, divided by 5 kilograms, gives us 14.61. So the acceleration, the acceleration once we're moving is going to be 14.61 meters per second squared to the right.
So I really want to make sure you understand what's happening here. Because right now, we're going to be moving We always had enough force to start budging it. But right when we budged it, we kind of had to overcome the static friction. For just for a moment, our acceleration was slower. Our acceleration was slower because we're overcoming that static friction.
But once we've 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 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 the 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 newtons.
And so now we are accelerating to the right a little bit at a slightly faster rate, 14.61 meters per second. So right when you budget, accelerate at 14.1 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.