in this video I'll again talk about the box is on an inclined plane and the box is sliding down the inclined plane and there's a friction between the box and the inclined planes so we have a friction between this box and they decline flame and we need to find out what is the acceleration of the block along the incline point so the coefficient of friction between the mass and the they decline plane is point to remember it does not have any unit and this is called the coefficient of kinetic friction and the finger angle is Theta and we need to also find out if the box is sliding down the inclined plane and ready to reach it at the end of the inclined plane what is the speed or the velocity at this point and this distance is given which is 2 meter and the mass of the block is 10 kilogram in order to solve this problem the first thing we need to do is draw the Freebody diagram so let's do the Freebody diagram first thing we'll start with the weight what is the direction of the weight remember the direction of the weight is always down water all right that's the direction of the weight and this angle is Theta so perpendicular so our goal again is to dissolve this force or into two components the one is a parallel to the inclined plane and the other is perpendicular to the inclined plane we call the parallel to the inclined plane x axis and perpendicular come as along perpendicular the y axis if this angle is Theta this angle is also theta so perpendicular to the surface will be mg cosine theta and parallel to the surface this is mg then it'll be mg sine theta so if you want to understand why this one is so what other videos and I'll just give you a little bit int it's a closer to the angle so eel is all this cosine theta and further from the angle this is the further from the this angle will be all this sine theta the normal force then there's another force which is the normal force the normal force is acting perpendicular to this surface which is M and is there a and as there is a friction between the surface between these two surface then there is a friction force and the friction force is always opposite to the motion and as the object is trying to slide down along this direction the friction force will be in the opposite direction this way does the friction force and here I'm calling this friction float as FK and the K stands for the kinetic friction kinetic friction so when the object is in motion we call that as a kinetic friction so we'll have now resolved all the forces into two rectangular components along x axis and along y axis so let's find out first what is the friction force so let's take a look along the Y Direction first along the Y direction we have two forces the normal force and the mg cosine theta and as the object is not moving along this y direction this force the N and mg cosine theta has to be equal because it is not moving along this direction so this force and this force must be equal and opposite that's exactly what I have written here M is equal to mg cosine theta the mass is given 10 G value is 10.8 cosine theta is 30 degree so plugging this value gives me the normal force to be eighty four point nine Newton or 85 Newton the kinetic friction is given by F K is nu K times M this is the kinetic friction this is the equation for calculating the kinetic friction or friction force whenever I write down the italic F that was it is a kinetic kinetic kinetic friction and mu K value between the two surface is point two and the normal force we just calculated is eighty four point nine so if we plug in it gives me the key net the kinetic force or the frictional force to be a 17 Newton which is in the district self so now let's take a look at the along the X direction along this way what is the total force along this direction we are going to write down the Newton's second law of motion which is F X the XS stands for the net force along the x axis is equal to mass times acceleration the mass and at this force F X force so just take a look here along this direction we have two forces one is mg sine theta which is downwards and this one is upward FK so and the sine theta minus FK and now we have mass times acceleration we already have calculated F K here which is 70 Newton or you can just plug in this value here FK would be mu times mg cosine theta why I am telling this one because the masses will cancels out so the thing to remember is this exploitation does not depend upon the mass that's the beautiful things to remember the acceleration does not depend upon the mass okay so the worst is I mean just plug in all the values and you'll get a three point two meter per second square that's the acceleration down the inclined plane and remember this acceleration does not depend upon T the mass all right so now let's calculate the velocity when it comes to the end of the inclined plane or at this point the velocity so you're going to use the kinematic equations VA squared is equal to u s squared plus 2 s and V is the final velocity where we want to find out the velocity U is the initial velocity a is the acceleration and s is the distance we do not know this velocity but we know the U because the object is starting from rest here the object is is starting from rest at this point and it is said the velocity of the box at the end of the slop so if it is starts from the rest so at this point is the velocity is zero this is you know 2 a is 3.2 the distance s is given which is 2 meter so we plug in what I get is 3.58 meter per second that is the speed of the of the block when it arrives at the hand of the slope sometimes here are intentionally used speed and the velocity because the motion is in a straight line so is perfectly okay now Harlan does it take to whisk to the ground so in order to calculate that we're going to use this equation V is equal to u plus AP V is the final velocity which we already calculated 3.58 U is the initial velocity as the object is starting from rest this is zero acceleration we calculated which is three point two and the time we wanted to calculate the time so if I solve for the time we get one point one two second so the time to come to the end of the slope is one point one two second so this is it from this video again if you have any questions write down your questions in the comment section below and do not forget to like share & subscribe the channel thank you