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

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Looks like maybe a wedge or
some type of an inclined plane

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made of ice.

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And we'll make everything
of ice in this video

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so that we have
negligible friction.

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So this right here is my ramp.

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It's made of ice.

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And this angle right over here,
let's just go with 30 degrees.

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And let's say on this
ramp made of ice,

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I have another block of ice.

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So this is a block of ice.

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It is a block of ice, it's
shiny like ice is shiny.

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And it has a mass
of 10 kilograms.

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And what I want to do
is think about what's

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going to happen to
this block of ice.

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So first of all, what are
the forces that we know

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are acting on it?

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Well if we're assuming
we're on Earth,

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and we will, and we're
near the surface,

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then there is the
force of gravity.

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There's the force of gravity
acting on this block of ice.

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And the force of
gravity is going

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to be equal to-- it's going to
be in the downward direction,

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and its magnitude is going to
be the mass of the block of ice

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times the gravitational
field times 9.8

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meters per second squared.

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So it's going to be
98 newtons downward.

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So this is 98 newtons downward.

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I just took 10 kilograms.

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Let me write it out.

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So the force due
to gravity is going

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to be equal to 10
kilograms times 9.8

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meters per second
squared downward.

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This 9.8 meters
per second squared

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downward, that is
the field vector

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for the gravitational field
of the surface of the earth,

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I guess is one way
to think about it.

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Sometimes you'll
see the negative 9.8

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meters per second squared.

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And then that negative is giving
you the direction implicitly

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because the
convention is normally

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that positive is upward
and negative is downward.

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We'll just go with
this right over here.

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So the magnitude of
this vector is 10 times

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9.8, which is 98 kilogram
meters per second squared, which

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is the same thing as newtons.

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So the magnitude
here is 98 newtons

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and it is pointing downwards.

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Now what we want to do
is break this vector up

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into the components
that are perpendicular

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and parallel to the
surface of this ramp.

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So let's do that.

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So first, let's think
about perpendicular

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to the surface of the ramp.

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So perpendicular to the
surface of the ramp.

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So this right over
here is a right angle.

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And we saw in the last
video, that whatever

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angle this over here
is, that is also

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going to be this
angle over here.

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So this angle over here is also
going to be a 30-degree angle.

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And we can use that
information to figure out

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the magnitude of this orange
vector right over here.

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And remember, this orange
vector is the component

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of the force of gravity that
is perpendicular to the plane.

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And then there's going to be
some component that is parallel

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to the plane.

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I'll draw that in yellow.

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Some component of
the force of gravity

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that is parallel to the plane.

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And clearly this
is a right angle,

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because this is
perpendicular to the plane.

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And this is parallel
to the plane.

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If it's perpendicular
to the plane,

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it's also perpendicular to
this vector right over here.

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So we can use some
basic trigonometry,

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like we did in the last
video, to figure out

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the magnitude of this orange
and this yellow vector

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right over here.

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This orange vector's
magnitude over the hypotenuse

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is going to be equal
to the cosine of 30.

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Or you could say that
the magnitude of this

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is 98 times the cosine
of 30 degrees newtons.

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98 times the cosine
of 30 degrees newtons.

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And if you want the whole
vector, it's in this direction.

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And the direction going into
the surface of the plane.

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And, based on the
simple trigonometry--

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and we go into this in
a little bit more detail

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in the last video-- we
know that the component

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of this vector that is parallel
to the surface of this plane

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is going to be 98
sine of 30 degrees.

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Sine of 30 degrees.

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Sine of 30 degrees.

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And this comes straight
out of this magnitude,

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which is opposite to the
angle over the hypotenuse.

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Opposite over hypotenuse is
equal to sine of an angle.

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And we did all the
work over here.

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I don't want to
keep repeating it.

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But I always want to emphasize
that this is coming straight

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out of basic
trigonometry, straight out

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of basic trigonometry.

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So once you do that, we know
the different components.

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We can calculate them.

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Cosine of 30 degrees is
square root of 3 over 2.

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Sine of 30 degrees is 1/2.

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That's just one of those
things that you learn

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and you can derive it yourself
using 30-60-90 triangles,

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or actually even
equilateral triangles.

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Or you could use a calculator.

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But it's also one
of those things

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that you memorize when
you take trigonometry.

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So no kind of magical
trick I did here.

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And so if you evaluate this,
98 times the square root

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of 3 over 2 newtons,
tells us that--

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let me write it in that
same orange color--

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the force, the
component of gravity

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that is perpendicular
to the plane.

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And this kind of implicitly
gives us this direction,

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it's perpendicular to the plane.

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But the force
component of gravity

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that's perpendicular
to the plane

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is equal to 98 times
square root of 3 over 2.

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98 divided by 2 is 49.

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So it's equal to 49 times
the square root of 3 newtons.

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And its direction is into
the surface of the plane,

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or downward or, let me just
write, into surface of plane.

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Surface of the plane, or
the surface of the ramp.

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And it's in this
direction over here.

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And I have to do this
because it's a vector.

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I have to tell you what
direction it's going in.

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And the component of the force
of gravity that is parallel.

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The component of the force
of gravity that is parallel,

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I drew it down here, but I
could shift it up over here.

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It's the same exact vector.

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The component of
gravity that is parallel

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to the surface of the plane
is 98 times sine of 30.

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That's 98 times 1/2,
which is 49 newtons.

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And it's going in that
direction, or parallel

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to the surface of the plane.

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Parallel, I always have
trouble spelling parallel.

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Parallel to-- don't even
know if I spelled it right--

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surface of the plane.

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So what's going to happen here?

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Well, if these were the
only forces acting on it.

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So if we had a net force
going into the surface

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of the plane of 49 square
roots of 3 newtons.

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If this was the only force
acting in this dimension

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or in the dimension that is
perpendicular to the surface

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of the plane, what would happen?

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Well, then the block
would just accelerate.

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At least just due to this force
it would accelerate downward.

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It would accelerate into
the surface of the plane.

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But we know it's not
going to accelerate.

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We know that there's this
big wedge of ice here

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that is keeping it from
accelerating in that direction.

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So at least in this dimension,
there will be no acceleration.

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When I talk about
this dimension,

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I'm talking about in
the direction that

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is perpendicular to the
surface of the plane.

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There will be no acceleration
because this wedge is here.

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So the wedge is exerting a force
that completely counteracts

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the force, the perpendicular
component of gravity.

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And that force.

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You might guess
what it's called.

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So the wedge is
exerting a force, just

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like that, that's going
to be 98 newtons upward.

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The wedge is going to
be exerting a force that

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is 49 square roots of 3,
because this right here

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is 49 square roots
of 3 newtons into.

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And so this is 49 square
roots of 3 newtons out

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of the surface,
out of the surface.

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And this is the normal force.

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It is the force
perpendicular to the surface

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that essentially, you could
kind of view as the contact

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force that the, in this case,
that the surface is exerting

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to keep this block of ice from
accelerating in that direction.

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We're not talking about
accelerating straight

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towards the center of the earth.

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We're talking about
accelerating in that direction.

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We broke up the force into kind
of the perpendicular direction

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and the parallel direction.

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So you have this
counteracting normal force.

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And that's why you don't
have the block plummeting

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or accelerating into the plane.

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Now what other
forces do we have?

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Well, we have the force that's
parallel to the surface.

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And if we assume that
there's no friction--

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

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because we are assuming
that it is ice on ice-- what

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is going to happen?

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There's no counteracting
force to this 49 newtons.

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49 newtons parallel downwards,
I should say parallel downwards,

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to the surface of the plane.

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So what's going to happen?

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Well, it's going to
accelerate in that direction.

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You have force is equal to
mass times acceleration.

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00:09:02,060 --> 00:09:06,640
Force is equal to mass
times acceleration.

199
00:09:06,640 --> 00:09:10,990
Or you divide both sides by
mass, you get force over mass

200
00:09:10,990 --> 00:09:13,820
is equal to acceleration.

201
00:09:13,820 --> 00:09:18,310
Over here, our
force is 49 newtons

202
00:09:18,310 --> 00:09:20,030
in that direction,
parallel downwards

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00:09:20,030 --> 00:09:21,920
to the surface of the plane.

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00:09:21,920 --> 00:09:24,050
And so if you
divide both by mass,

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00:09:24,050 --> 00:09:27,460
if you divide both
of these by mass.

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00:09:27,460 --> 00:09:31,150
So that's the same thing as
dividing it by 10 kilograms,

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00:09:31,150 --> 00:09:33,676
dividing by 10 kilograms, that
will give you acceleration.

208
00:09:33,676 --> 00:09:36,380


209
00:09:36,380 --> 00:09:39,130
That will give you
our acceleration.

210
00:09:39,130 --> 00:09:41,100
So acceleration is
49 newtons divided

211
00:09:41,100 --> 00:09:44,960
by 10 kilograms
in that direction,

212
00:09:44,960 --> 00:09:47,540
in this direction
right over there.

213
00:09:47,540 --> 00:09:50,720
And 49 divided by
10 is 4.9, and then

214
00:09:50,720 --> 00:09:54,900
newtons divided by kilograms
is meters per second squared.

215
00:09:54,900 --> 00:09:56,890
So then you get
your acceleration.

216
00:09:56,890 --> 00:10:02,810
Your acceleration is going to be
4.9 meters per second squared.

217
00:10:02,810 --> 00:10:05,760
And maybe I could say parallel.

218
00:10:05,760 --> 00:10:06,790
That's two bars.

219
00:10:06,790 --> 00:10:09,560
Or maybe I'll write parallel.

220
00:10:09,560 --> 00:10:16,845
Parallel downwards
to the surface.

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00:10:16,845 --> 00:10:18,640
Now I'm going to
leave you there,

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00:10:18,640 --> 00:10:20,790
and I'll let you think
about another thing

223
00:10:20,790 --> 00:10:22,850
that I'll address in
the next video is,

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00:10:22,850 --> 00:10:24,980
what if you had this
just standing still?

225
00:10:24,980 --> 00:10:26,890
If it wasn't
accelerating downwards,

226
00:10:26,890 --> 00:10:29,120
if it wasn't accelerating
and sliding down,

227
00:10:29,120 --> 00:10:31,980
what would be the
force that's keeping it

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00:10:31,980 --> 00:10:33,700
in a kind of a static state?

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00:10:33,700 --> 00:00:00,000
We'll think about that
in the next video.