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# Ice accelerating down an incline

## Video transcript

let's say that I have a ramp made of ice sake maybe a wedge or some type of an inclined plane made of ice and make everything of ice in this video so we have negligible friction so this right here is my ramp it's made of ice and this angle right over here let's just go with 30 degrees and let's say on this ramp made of ice I have another block of ice so this is a block of ice it is a block of ice it's shiny like ice is shiny and it has a mass it has a mass of 10 kilograms and what I want to do is think about what's going to happen to this block of ice so first of all what are the forces that we know are acting on it well we're for you if we are assuming we're on earth and we will and we're near the surface then there is the force of gravity there's the force of gravity acting on this block of ice and the force of gravity the force of gravity is going to be equal to its going to or at least its magnitude it's going to be in the downward direction and it's magnitude is going to be the mass of the block of ice times the gravitational field times 9.8 meters per second squared so it's going to be 98 Newtons downward so this is 98 Newtons downward I just took 10 kilograms let me write it out so the force due to gravity is going to be equal to 10 kilograms times 9.8 meters per second squared downward downward this 9.8 meters per second squared downward that is the that is the field vector for the gravitational field near the surface of the earth I guess is one way to think about it sometimes you'll see that a negative 9.8 meters per second squared and then that negative is giving you the direction implicitly because we the convention is normally that positive is upward negative is downward but we'll just go with this right over here so the magnitude of this vector is 10 times 9.8 which is 98 kilogram meters per second squared which the same thing as Newtons so the magnitude here is 98 Newtons and it is pointing downwards now what we want to do is break this vector up into the components that are perpendicular and parallel to the surface of this ramp so let's do that so first let's think about perpendicular to the surface of the ramp so perpendicular to the surface of the ramp so this right over here is a right angle and we saw on the last video that whatever angle this is over here is that is also going to be this angle over here so this angle over here is also going to be a 30-degree angle and we can use that information to figure out the magnitude of this orange vector right over here and remember this orange vector is the is the component of the force of gravity do that is perpendicular to the plane and then there's going to be some component that is parallel to the plane I'll draw that in yellow some component of the force of gravity that is parallel to the plane and clearly this is a right angle because this is perpendicular to the plane and this is parallel to the plane so they're going to in this perpendicular plane it's also perpendicular to this vector right over here so we can use some basic trigonometry like we did in the last video to figure out the magnitude of this orange and this yellow vector right over here this orange vector is magnitude over the hypotenuse is going to be equal to the cosine of 30 or you could say that the magnitude of this is 9898 times the cosine of 30 times the cosine of 30 degrees Newtons 98 times the cosine of 30 degrees Newtons and if you want the whole vector it's in this direction in the direction going into into the surface of the plane and based on the simple trigonometry and we go into this into a little bit more detail in the last video we know that the component of this vector that is parallel to the surface of this plane is going to be ninety eight ninety eight sine of thirty degrees sine of thirty degrees sine of thirty degrees and this comes straight out of this magnitude which is the OP which is opposite to the angle over the hypotenuse opposite over hypotenuse is equal to sine of an angle and we did all the work over you don't want to keep repeating it but I always want to emphasize that this is coming straight out of basic trigonometry straight out of basic trigonometry so once you do that we know the different components we can calculate them cosine of 30 degrees is square root of 3 over 2 sine of 30 degrees is 1/2 that's just one of those things that you learn and you can derive it yourself using 30-60-90 triangles or actually even equilateral triangles or you could use a calculator but it's also one of those things that you memorize when you take trigonometry so no no kind of magical trick I did here and so if you evaluate this 98 times the square root of 3 over 2 Newton's tells us that let me write it in that same orange color the force the component of gravity that is perpendicular to the plane and this kind of implicitly gives us this direction it's perpendicular to the plane but the force component of gravity this perpendicular plane is equal to 98 times square root of 3 over 2 98 divided by 2 is 49 so it's equal to 49 times the square root of 3 Newtons and it's Direction is into the surface of the plane or downward or let me just write into into surface of plane surface of the plane or the surface of the ramp and it's in this direction over here and I have to do this because it's a vector I have to tell you what direction it's going in and the component of the force of gravity that is parallel the component of the force of gravity that's parallel I drew it down here but I can just shift it up over here same exact vector the component of gravity that is parallel to the surface of the plane is 98 times sine of 30 that's 98 times one-half which is 49 Newtons and it's going in that direction or parallel to the surface of the plane parallel I always have trouble spelling parallel parallel to don't even know if I spelled it right surface of the plane so what's going to happen here well if these were the only forces acting on it so if we had a net force going into the surface of the plane of 49 square roots of 3 Newtons if this was the only force acting in this dimension or in the dimension that is perpendicular to the surface of the plane what would happen well then the block would just accelerate at least just due to this force it would accelerate downward it would accelerate into the surface of the plane but we know it's not going to accelerate we know that there's this big wedge of ice here that is keeping it from accelerating in that direction so the it's at least in this dimension there will be no acceleration when I talk about this dimension I'm talking about I'm talking about in the direction that is perpendicular to the surface of the plane there will be no acceleration because this wedge is here so the wedge is exerting a force that completely counteracts the force the the perpendicular component of gravity in that force you might guess what it's called so this the wedge is exerting a force just like that that's going to be 98 Newtons upward so I will call it the wedge is going to be exerting a force that is 98 oh sorry not 98 49 square roots of 3 because this right here is 49 square roots of 3 Newtons into and so this is 49 square roots of 3 Newtons out of out of the surface out of the surface and this is the normal force it is the force perpendicular to the surface that is essentially you can kind of view is it's the contact force that the perp that the that the in this case that the surface is exerting to keep this block of ice from accelerating in that direction we're not talking about accelerating straight towards the center there's we're talking about accelerating in that direction we broke up the force into into kind of this the perpendicular direction and the parallel direction so you have this counteracting normal force and that's why that's why you don't have that's why you don't have the but the block plummeting or accelerating into the plane now what other forces do we have well we have the force that's parallel parallel to the surface and if we assume that there's no friction and I can assume that there's no friction in this in this video because we are assuming that it is ice on ice what is going to happen there is no counteracting force to this 49 Newtons 49 Newtons parallel downwards I should say parallel downwards to the surface of the plane so what going to happen well it's going to accelerate in that direction you have force is equal to mass times acceleration force is equal to mass times acceleration or you divide both sides by mass you get force over mass is equal to acceleration over here our force is 49 Newtons in that direction in that direction parallel downwards to the surface of the plane and so if you divide both by mass if you divide both of these if you divide it by mass so that's the same thing as dividing it by 10 kilograms dividing by 10 kilograms that will give you acceleration that will give you that will give you our acceleration so acceleration is 49 Newton's divided by 10 kilograms in that direction in the in this in this this direction right over there and 49 divided by 10 is 4.9 and the Newton's divided by kilograms is meters per second squared so then you get your acceleration your acceleration is going to be 4.9 m/s squared and maybe I could say parallel parallel that's what that's two bars or maybe I'll write parallel parallel downwards downwards to surface to the surface now I'm going to leave you there and I'll let you think about another thing that I'll address in the next video is what if you had this just standing still if it wasn't accelerating downwards if it wasn't accelerating and sliding down what would what would be the force that's keeping it in a kind of a static State we'll think about that in the next video