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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?
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