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Welcome back.

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We just finished this problem
with the pulleys and the

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inclined plane.

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And I just wanted to do one
final thing on this problem

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just because I think
it's interesting.

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And then we can move onto
what seems like

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a pretty fun problem.

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So the last thing I want to
figure out is, we figured out

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that this 20 kilo-- actually,
the whole system will

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accelerate up and to
the right at 4.13

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meters per second squared.

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And then the second part of this
question is, what is the

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tension in this rope
or this wire?

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And at first you might say,
this is complicated.

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You know, this thing isn't
static anymore.

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The thing is actually
accelerating.

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How do I do it?

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Well this is how you
think about it.

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Just pick one part
of the system.

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Let's say that all we could see
was this 20 kilogram mass.

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So let's say all we could see
was this 20 kilogram mass.

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And we know it's suspended
from a wire.

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And we also know that this
20 kilogram mass is not

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accelerating as fast
as it would if

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the wire wasn't there.

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It's accelerating only at
4.13 meters per second.

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If the wire wasn't there, it'd
be accelerating at 9.8 meters

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per second, the acceleration
of gravity.

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So the wire must be exerting
some upward

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force on the object.

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And that is the force
of tension.

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That is what's slowing-- that's
what's moderating its

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acceleration from being 9.8
meters per second squared to

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being 4.13 meters per
second squared.

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So essentially, what is the
net force on this object?

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On just this object?

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Well the net force is-- and
you can ignore what I said

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before about the net force
in all the other places.

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But we know that the object
is accelerating downwards.

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Well, we know it's 20 kilograms.
So that's its mass.

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And we know that it's
accelerating downwards at 4.13

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meters per second squared.

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So the net force, 20 times--
see, times 20 is 82-- let's

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just say 83 Newtons.

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83 Newtons down.

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We know that the net force
is 83 Newtons down.

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We also know that the tension
force plus the force of

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gravity-- and what's the
force of gravity?

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The force of gravity is just
the weight of the object.

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So the force of tension, which
goes up, plus the weight of --

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the force of gravity is equal
to the net force.

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And the way I set this up,
tension's going to be a

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negative number.

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Just because I'm saying
positive numbers are

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downwards, so a negative number
would be upwards.

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So tension will be what
is 83 minus 196?

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Minus 196 is equal to
minus 113 Newtons.

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And the only reason why I got a
negative number is because I

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used positive numbers
for downwards.

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So minus 113 Newtons downwards,
which is the same

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thing as 113 Newtons upwards.

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And so that is the tension
in the rope.

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And you could have done the same
thing on this side of the

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problem, although it would
have been-- well, yeah.

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You could have done the
exact same thing on

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this side of the problem.

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You would've said, well what
would it have accelerated

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naturally if there wasn't some
force of tension on this rope

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going backwards?

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And then you're saying, oh,
well, we know it would have

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gone in this direction at some
acceleration, but instead it's

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going in the other direction.

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So you use that.

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You figure out the net force,
and then you say the tension

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plus all of these forces have
to equal the net force.

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And then you should solve
for the tension.

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And it would be the
same tension.

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Now we will do a fun and
somewhat simple, but maybe

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instructive problem.

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So I have a pie.

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This is the pie.

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This is parallel.

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And I have my hand.

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You can tell that my destiny
was really to be a great

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artist. This is my hand.

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And I'm holding a pie, and I'm
looking to smash this pie into

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this individual's face.

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I actually was a, I was the
newspaper cartoonist in high

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school, so I have some
minor-- but anyway.

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Let's make it a bald man.

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Well anyway, I shouldn't be
focusing on the drawing.

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He has a moustache.

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Anyway, I'm looking to throw
this pie into this guy's face.

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And the problem is, I need to
figure out how fast do I need

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to accelerate this pie for
it to not fall down?

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Right?

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Because what's happening?

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Well there's the force of
gravity on this pie.

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There's a force of gravity on
this pie and if I don't

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accelerate it fast enough, it's
just going to slide down.

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And I'll never be able
to, It'll never

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reach the guy's face.

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So I don't want this pie
to slide down at all.

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How fast do I have
to push on it?

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Well, we know that the
coefficient of friction-- you

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don't know this, but I know
that the coefficient of

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friction between my hand and
the pie, the coefficient of

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friction is equal to 0.8.

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So given that, how fast do
I have to accelerate it?

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Well let's see what's
happening.

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So we have the force of
gravity pulling down.

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So let's say that the mass
of the pie is m.

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m equals mass.

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So what is the force of gravity

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pulling down on the pie?

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Well the force of gravity is
just equal to m times 9.8.

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Right?

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The force of gravity is
equal to m times 9.8.

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In order for this pie to not
move down, what do we know

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about the net forces
on that pie?

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Well we know the net forces
on that pie have to be 0.

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So what would be the
offsetting force?

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Well, it would be the
force of friction.

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So we would have a force of
friction acting upwards.

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Right?

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Because the force of friction
always acts opposite to the

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direction that the thing
would move otherwise.

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So essentially, our force of
friction has to be greater

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than, roughly, greater
than or equal to.

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Because if it's greater than,
it's not like the pie is going

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to move up.

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Friction by itself will never
move something, it'll just

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keep something from
being moved.

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But let's just figure
out the minimum.

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I won't do the whole
inequalities.

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The force of friction has to
be equal similarly, to 9.8

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times the mass of the pie.

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So if the coefficient of
friction is 0.8, what is the

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force that I have to apply?

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Well, the force I have to apply
in this case is going to

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be the normal force, right?

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That's normal to the
bottom of the pie.

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Right?

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My hand is now like the
surface of the ramp.

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So this is the normal force.

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And we know that the force of
friction is equal to the

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coefficient of friction times
the normal force.

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I'm going to switch colors
because this is getting

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monotonous.

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And the force of friction,
we know has to be

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9.8 times the mass.

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So 9.8 meters per second
times the mass.

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9.8m is the force of friction.

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And that has to equal to
coefficient of friction times

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the normal force.

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And remember, the normal force
is essentially the force that

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I'm pushing the pie with.

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And we know this is 0.8, so we
have 9.8 times the mass--

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that's not meters, that's the
mass-- is equal to 0.8 times

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the normal force.

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So you have the normal force is
equal to 9.8 times the mass

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divided by 0.8.

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What's 9.8 divided by 0.8?

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9.8 divided by 0.8 is
equal to 12.25.

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So the normal force that
I have to apply is

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12.25 times the mass.

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So that's the force
I'm applying.

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It's time the mass.

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We don't know the
mass of the pie.

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So how fast am I accelerating
the pie?

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Well, force is equal to mass
times acceleration.

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This is the force, 12.25m--
that's the force-- is equal to

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the mass times the

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acceleration of the pie, right?

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And it's the same pie that we're
dealing with the whole

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time, so it's still m.

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And you can take out m from both
sides of the equation.

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So the acceleration, the rate at
which I have to change the

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velocity, or the acceleration
that I have to apply to the

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pie is 12.25 meters per
second squared.

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And so actually, I have to apply
more than 1g, right?

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Because g is the force
of gravity.

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And gravity accelerates
something at 9.8 seconds-- 9.8

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meters per second squared.

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So I have to do something at
12-- I have to push and

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accelerate the pie at 12.25
meters per second squared.

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So it's something a little over
1g in order for that pie

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to not fall and in order for my
normal force to provide a

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force of friction so that
the pie can reach

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this bald man's face.

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I will see you in
the next video.

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