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# Force of friction keeping the block stationary

## Video transcript

in the last video we had a 10 kilogram we had a 10 kilogram mass sitting on top of an inclined plane in the plane at a 30-degree angle in order to figure out what would happen to this block we broke down we broke down the force of gravity on this block into the components that are parallel to the surface of the plane and perpendicular to the surface of the plane and for a perpendicular component we got 49 times the square root of 3 Newtons downwards it's 98 times this quantity over here downwards but we said look we don't see this block of ice we don't see it accelerating downwards into this wedge because the wedge is supporting it so there must be a counteracting force that the wedge is exerting on the block and that counteracting force is the normal force out that of the wedge on the block of ice and that is exactly opposite to the force of gravity in this direction the normal force of gravity I guess you could say is the normal force of the wedge and then these completely balance each other out in that normal direction in that perpendicular direction that's why this blocks is not accelerating either in that direction or in this direction over here but the one component of the force of gravity that did not seem to have any offset at least the way we set up the problem in the last video is the force that is or the component that is parallel that is parallel to the surface of the plane and we figured that out to be 49 Newtons it was it was essentially the weight of the block times the sine of this angle we said look if there's no other forces then it would be accelerated in this direction and to figure out how how the rate of acceleration you take the force in that direction divided by the mass of the block and you'd get 4 point 9 meters per second squared now let's say that that wasn't happening let's say you were to look at this system right over here and and the block is just stationary now for the sake of argument let's assume it's not ice on ice let's assume that they're both made out of wood and now of a sudden we have a situation where the block is stationary what would if it's stationary what is necessarily the case well we already says is that it we already determined that if it's not accelerating in this normal direction in this perpendicular direction there must be zero net forces on it but if it's stationary as a whole then there must be zero net forces in this parallel component as well so there must be some force counteracting this 49 Newtons that wants to take it down the slope so there must be some force there must be some force that is counteracting that is counteracting that force the component of gravity that wants to take it down accelerate it down the slope and the question is what is this force we're dealing with a situation now where we're dealing with a stationary block where we're dealing a stationary block a block that is not accelerating so what is that force I think you know from experience maybe what is the difference between a block of wood on top of a block of wood and a block of ice and on top of a block of ice a block of ice on top of a block of Isis much slit more slippery there's no friction between ice and ice but there is friction between wood and wood and to make it a little more tangible maybe we put some sand paper maybe we put some sand paper on this surface over here and then it becomes a little bit clearer the force that is keeping this block from sliding down in this situation is the force of friction is the force of friction and the force of friction will always act in a direction opposite to the motion if there was not any friction so what is the or or the the potential I should say the potential acceleration say the motion the potential acceleration if there was not any friction so what is the force of friction in this case well if this block is completely stationary it's not accelerating down the ramp the force of friction over here is going to be 49 Newtons it's going to be 49 Newtons but it's going to be upwards kind of up the ramp 49 Newtons up up the ramp now what I want to think about and this is something that can be determined experimentally if you if you have blocks and ramps even if you don't have blocks and ramps you as long as you have some way of measuring force you can do this experimental e but an interesting thing that question an interesting question here is well what how much do I have to push on this block until it starts to move down the ramp how much do I have to push on it and let's say you are able to experimentally determine that if you can apply if you can apply another one Newton so let's say that you can if you can apply another one Newton on this so above and beyond the parallel force if you can apply another another I should do it small if I can apply another one Newton if I can apply another one Newton then all of a sudden I can at least get the box to start to start accelerating down not the rate at which you would do naturally but I can just start to nudge it down if I give it another push of one Newton in the parallel direction so what is the total force that it has it so exactly one Newton so the total force at this point that's acting on it in order to just start to budget the total force I'll call this the budging force you'll never hear this in a traditional class f sub B for the budging force the budging force it's in the parallel direction let's say that that is if I'm applying one Newton in this direction and it already has 49 Newtons due to the component of gravity in this direction then my budging force is 50 Newtons and so an interesting thing that you can determine based on the materials that are coming in contact with each other is just just how much force you need to just start to overcome friction in this case it's the budging force that's a term that I made up an interesting ratio which tends to hold for given materials pretty well is the ratio between the amount of force just to budget and the amount of force between the two objects between how much force they are exerting on each other and in this case the amount of force that is being exerted by this by the the the wedge on the block is the normal force it's 49 square roots of three so maybe I should say the magnitude the magnitude of the budging force over the magnitude of the force that is putting these two things in contact in this case it is 49 square roots of 3 Newtons so let me write this I'll write this over the magnitude of the normal force of the normal force and that is 49 square roots of three we call this the coefficient of static-friction the coefficient of static-friction we're going to use this deeply or a little bit more deeply in other problems but it's tends to hold true for different materials so that in the future if you have a different mass but you have this or maybe a different incline but you have the same materials you can given the normal force you could figure out the budging force you can figure out exactly how much force do you need to put if you know this which you usually figure out experimentally so what would be the value in this case you have 50 Newton's over 49 square roots of 3 Newtons so this is let me get my trusty calculator out so I have so I have 50 divided by divided by 40 times the square root of 3 gives me point seven two eldest around two two significant is zero point seven two so this is zero point seven two and then you could use this information right so let me write this down this is the coefficient coefficient coefficients in other word that have trouble spelling coefficient of static-friction static friction we call it the coefficient of static friction because this is what this is this this deals with the ratio of the force of friction relative to the normal force or I guess the the force necessary to just overcome the force of friction just kind of get right over that the most friction that can be applied by kind of the abrasiveness of the two things when the object is stationary and I'll do a whole video on the difference between the how this is different when some when you when an object is stationary to when it's moving a lot of times they are very very very close but for certain materials you have a very you have a at least a noticeably different coefficient of friction when the object is stationary as opposed to when it is moving so I'll leave you there in the next few videos we'll use coefficient of friction or calculate coefficients of friction to do some more problems