welcome to electron line now let's take a look and see what happens to the friction forces and the normal forces and the reaction forces when you place an object on an inclined plane now we want to have any additional forces yet Afghan the block that will come later this is simply under the force of gravity as a comparison let's start out with just having a block on a horizontal surface like we did in the previous video we simply have the weight of the block pushing down the normal force pushing back in this case the normal force is equal to the reaction force which is equal to the weight of the block we have a maximum friction force that can exist between the block and the surface which is equal to the normal force times the coefficient of static friction however that's the maximum possible friction force since there's no forces acting in the horizontal direction there's no friction forces in this particular case block is not moving now what happens when we put the block on an inclined plane and there is friction between the block and the surface the angle here is relatively small we can see that the weight of the block acts straight down towards the centre of the earth but we can take the weight of the block and divide it into the perpendicular and parallel components to the surface the perpendicular component is the weight times the cosine of this angle the parallel component is equal to the weight of the block times the sine of the angle notice in this case that the normal force pushing against the block is going to be directed in the same direction as mg cosine theta it's going to be perpendicular to the surface and the normal force is going to be equal to mg cosine theta the reaction force pushes straight up against the weight here notice that the reaction force is the vector sum of the normal force plus the friction force between the block and the surface now the maximum friction force again is going to be equal to the normal force times mu sub s but in this case since mg sine theta the force trying to push the block down the incline is smaller than the maxim friction force the friction force will be limited to the applied force and sine-theta and so this component of the reaction force is mg sine-theta this component is a normal force and that's how we find the reaction force in this particular case what happens when we increase the angle well then this component mg sine-theta begins to increase of course mg cosine theta decreases a little bit now the normal force pushing back against the block is still going to be equal to mg cosine theta now this component of the reaction force is becoming larger and in this case let's say that if we're on the verge of moving mg sine theta will be exactly equal to the maximum friction force which is the normal force mg sine theta times and I'm missing something here mu sub s of course we have to multiply that times the coefficient of static friction if those are equal to each other if this is equal something is not right here let me correct that the maximum friction force I was not right the maximum friction force is going to be mg cosine theta which is the normal force times mu sub s that's the correct equation for the maximum friction force and in this case that is going to be equal to mg sine theta of course at that moment we're on the verge of the block moving if there's any additional force pushing the block down the block will begin to move so let's now move on to the next example here the block is now moving now we can say that mg sine theta is larger than the maximum friction force so once the block begins to move the friction force now becomes equal to the normal force times the coefficient of stead of kinetic friction and so it's going to be mg cosine theta times mu sub K instead of muse of s now in this particular case notice that the reaction force no longer is perpendicular in the same direction as the weight of the block why is that well the reaction force is going to be the sum of the normal force plus this component right here which is actually equal to the actual friction force not the maximum friction force Oh actually it is equal to the maximum friction force but since this is smaller than the mg sine-theta this will be smaller than this and therefore the reaction force now has an angle relative to the vertical to find the angle between the perpendicular the normal force and the reaction force is it let's call this angle fee we can say that the tangent of fee is equal to the ratio of the opposite side to the adjacent side now the opposite side is the friction force which is the normal force times mu sub K and the adjacent side is the normal force when we cancel out the normal forces we can see that the tangent of fee is equal to the coefficient of kinetic friction then to find the angle we take the inverse tangent or the arctangent of the coefficient of kinetic friction and that's how we get the angle again remembering that mg sine theta the force trying to drive the block down the incline is larger than the maximum friction force and therefore the friction force that will exist and therefore the block will accelerate down the incline but what's important to see is that in the first three cases when the block is not moving the reaction force is perpendicular to the earth pointing straight up and in this case you can see that the reaction force is actually at an angle relative to the vertical and that's because this component now is smaller than this component so the reaction force is no longer perpendicular to the surface of the earth or in the vertical direction and so again if we add these pieces of knowledge about friction together in video 1 video 2 video 3 we're beginning to see how this actually works now in the next video we're going to start adding additional forces acting on these blocks of incline and then we can see how we actually add these forces together and try to figure out the reaction force you need to particular case and that's how it's done