welcome to iect turn line to get a better understanding of how friction works on an inclin plane we're going to have a nonstatic example what we're seeing here is that the net forces along the incline plane are not going to equal zero therefore there's going to be an acceleration we're not going to worry about the acceleration but we do want to find all the various forces the normal force the friction Force the resultant Force we want to find the various angles and yes we want to find the net force along the incline so how do we do that well first of all we realize that we have a load not really a load we have the weight of the object on the incline and we drew it up on top this is simply the weight or mg equal to 100 Newtons coming straight down then we have a force pushing the block of the incline but it's not parall to the incline it's simply parallel to the horizontal it's 20 Newton Force then we realize there's going to be a normal force and let me draw the N over on this side so there's going to be a normal force which is always perpendicular to the surface and then we're going to have a resultant Force which is a combination or a sum of the normal force and the friction Force by definition the friction force is always going to be equal to the normal force times the coefficient in this case it's going to be the static coefficient of friction because it's going to be moving so how do we find the normal force the normal force is a reactionary force that pushes back back it's going to push against the perpendicular component of the weight and it's going to also push against the perpendicular component of the force applied to the block notice we're going to have a perpendicular component to the weight and we're going to have a parallel component to the weight so when we then find the normal force the normal force is going to be equal to the reactionary Force to the perpendicular component of the weight which is the weight times the cosine of theta in this case Theta is going to be 30° that's the angle of the incline and then we have to add to that the perpendicular component of the applied force which is going to be f * the S of theta that will be the normal force now since we know the weight and we know the force and we know the angle we might as well just calculate the normal force so this is going to be equal to the weight which is 100 Newtons time the cine of 30 30° plus the applied force 20 Newt time the S of 30° now that's 866 that would be 86.6 Newtons plus a halftimes this is 10 Newtons so that would be a total of 96.6 Newtons is the normal force the reactionary force of the incline back up against the block from that we should be able to find the friction Force the friction Force is going to be equal to and again we're going to assume that the net force is going to be down the incline which means the friction force will be acting in the opposite direction of the incline and the friction force is going to be equal to the normal force times the coefficient of friction in this case the kinetic coefficient of friction so it'll be 96.6 Newtons time 0.2 and let's see here 96.6 * two we get 193. 2 Newtons 193. 2 Newtons and so that's going to be the friction Force o I'm missing a decimal place how about 19.32 Newtons that's better all right what about the force acting down the incline that's going to be the horizontal component of the weight so the weight times the S of theta which is going to be the parall component of the weight which is equal to 100 Newtons times the S of 30° which is 0.5 so that's a force of 50 Newtons trying to push the block down the incline now we're going to also find the parallel component to the incline of the applied force so that would be the f * the cosine of theta which is 20 newtons time the cosine of 30° that would be 866 that would be uh * 20 866 that would be 17.32 Newtons and now we can calculate the net force we have the friction force acting upward we have the parallel component of the force pushing upward and we have the parall component of the weight acting downward which means that the net force is going to be equal to the pel component acting downward which is 50 newtons that would be in this direction minus the friction Force which is 19.3 Newtons we'll just keep on decimal place and minus the force pushing against the block acting upward a component acting upward which is min -7.3 Newtons so the net force is going to be 50 minus 19.3 - 17.3 equals ha that's going to be [Music] 13.4 Newtons acting down the incline and so therefore we're going to have an acceleration down the incline because there is indeed a net force here what about the angles we have a reactionary Force this way which is going to be a sum of the normal force and the friction Force so let's take this triangle right here and redraw that so we have the friction Force we have the normal force so there's my normal force and then we have the what we call the reactionary force or the resultant force of those two we know the friction force is equal to 19.32 newtons and we knew that the normal force is equal to 96.6 newtons so the normal force equals 96.6 Newtons and let's say we want to find this angle right here which we typically label Fe well we can do that by realizing that this will always be perpendicular we know that this is perpendicular to the incline and the friction force is pal incline so this is a 90° angle which allows us to use the tangent because we know the opposite side and we know the adjacent side so we can say that f is equal to the arct tangent of the opposite side which is the friction Force 19.32 Newtons divided by the adjacent side which is which is the normal force 96.6 Newtons and that gives us an angle let's see here that's 19.32 ID by 96.6 and take the arc tangent of that that would be 11.31 de so that's the angle between the normal force and the resultant or the reactionary Force which is the sum Vector sum of the normal force and the friction Force finally we want to find find the angle between the the vertical and the reactionary Force the angle right here and we call that Alpha and Alpha will be equal to the angle of the incline which is Theta in this case minus Fe now sometimes the the resultant force is acting in a direction like this and we add the two angles in this case it's somewhere in between so we subtract the two angles that means the angle Alpha is going to be equal to 30° minus 11.3 de I'll just keep one decimal place which means that this is equal to 18.7 De and that would be angle between the resultant and the vertical so that's everything you need to know about the situation like this where you don't have a static situation we have something there a net force you calculate the normal force the reactionary Force the angles we need to find the net force which means you need to add this Force right here plus the parall component of the weight and the friction Force add those three forces together to get the net force and that's how it's done