Let's say that I have a ramp made of ice

think maybe a wedge or some type of inclined plane made of ice

we'll make everything of ice in this video so that 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

Let's say on this ramp made of ice I have another block of ice

so this is a block of ice

shiny like ice is shiny

and it is has a mass

it has a mass of 10 kg

and 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 if we're 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

is going to be equal to or at least it's magnitude is 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 98 newtons downward

i just took 10 kg

let me write it out

so the force due to gravity is going to be equal to 10 kg times 9.8 m/s^2 downward

this 9.8 m/s^2 downward 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 the negative 9.8 m/s^2 and that negative is giving you the direction implicitly

because the convention is normally that positive is upward and negative is downward

but we'll just go with this right over here

the magnitude of this vector is 10 times 9.8

which 98 is kg-m/s^2 which is the same thing as newtons

so the magnitude here is 98 newtons and it is pointing downwards

now what we want to do here 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 in the last video that whatever angle this is over here

that is also gonna 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 component of the force of gravity that is perpendicular to the plane

and then there is 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

cause this is perpendicular to the plane and this is parallel to the plane

so they're going to

and it's perpendicular to the plane and 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's magnitude over the hypotenuse is going to be equal to the cosine of 30

or you could say the magnitude of this is 98 times the cosine of 30

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 the surface of the plane

and based on the simple trigonometry

we go into this in little 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 98 sine of 30 degrees

sine of 30 degrees

and this comes straight out of this magnitude

which is the opposite to the angle

over the hypotenuse

opposite over hypotenuse is equal to sine of the angle

we did all work over here

I don't want to keep repeating it but I want to emphasize that this 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 one half

that's just one of those things you learn

you can derive it yourself using 30 60 90 triangles

or actually even equilateral triangles

or you can use a calculator

but it's also one of those of things that you memorize when you take trigonometry

so no kind of magical trick i did here

so if you evaluate this 98 time square root 3 over 2 newtons 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 its direction

it's perpendicular to the plane

but the force the component of gravity that is perpendicular to the 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 the suface of the plane

into surface of 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 to you what direction it's going in

and the component of the force of gravity that is parallel

i drew it down here but i can shift it up here

it's the 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 to the surface of the plane

i always have trouble spelling parallel

parallel to the 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 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 there's this big wedge of ice here that is keeping it from accelerating in that direction

so at least in this dimension there will be no acceleration

when i talk about this dimension 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 perpendicular component of gravity

and that force

you might guess what it's called

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

cause this right here is 49 square roots of 3 into

and so this is 49 square roots of 3 newtons 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 as the contact force

that the in this case that the surface is exerting to keep this block of ice from accelerating in that direction

and we're not talking about accelerating straight toward the center of the earth

we're talking about accelerating in that direction

we broke up the force into kind of the perpendicular direction and the parallel direction

so you have this counteracting normal force

that's why you don't have the block plummeting or accelerating into the plane

now what other forces do we have?

we have the force that's parallel to the surface

and if we assume that there's no friction

and i can assume that there's no friction in this video cause 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

what's 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 (F = ma)

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

parallel downwards to the surface of the plane

so if you divide both by mass

if you divide both of these, if you divided by mass

so that's the same thing as dividing it by 10 kg

dividing by 10 kg

that will give you acceleration

that will give you our acceleration

so acceleration is 49 newtons divided by 10 kg

in that direction

in this direction right over there

49 divided by 10 is 4.9

newtons divided by kg is meters per second squared

so then you get your acceleration is going to be 4.9 m/s^2

maybe i could say parallel

that's two bars or maybe i'll write parallel downwards to surface

to the surface

now i'm gonna leave you there

i'll let you think about another thing that i'll address in the next video

what if you had this just standing still?

it wasn't accelerating downwards

it wasn't accelerating and sliding down

what would be the force that's keeping it in sort of a static state?