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- [Lecturer] Let's solve
a couple of problems

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on Newton's second law.

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Here's the first one.

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We have an elevator, which is moving up.

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And let's say the mass of the elevator,

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including the passenger
inside, is 1,000 kilograms.

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Now the force, the tension
force of the cable,

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let's say that's about 7,800 newtons,

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our goal is to figure
out what the acceleration

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of this elevator is.

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We're also given that the
gravitational force acting

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on that elevator, including
the passenger over here,

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is about 9,800 newtons.

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So, how do we figure this out?

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Well, the first thing
that comes to my mind is,

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"Hey, we have some forces

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and we have some motion
variables like acceleration.

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What connects forces and motion variables?

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What connects forces and motion?

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Newton's second law.

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So, the first thing I try to do

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before applying Newton second law is I try

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to draw a free body diagram.

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So lemme do that.

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What's the way to draw
a free body diagram?

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We try to get rid of unnecessary details.

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Use a box to represent
your object of interest.

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Our object of interest is this elevator

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and the person over here.

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So, that's our box.

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It's mass is 1,000 kilograms

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and let's draw all the
forces acting on it,

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which are the forces acting on it.

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Well, we have an upward
force that's tension

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and we have a downward force
that's the force of gravity

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and our goal is to calculate
what the acceleration is.

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And how do we do that?

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Well, we use Newton second law,

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which says the acceleration

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should equal the net
force acting on an object

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divided by its mass.

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And of course, since we're
dealing with vectors,

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we can put arrow marks over here.

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The direction of the
acceleration will be the same

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as the direction of the net force.

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Okay, now we can calculate
the net force from this

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and we can calculate, we know the mass,

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so from that we can
calculate the acceleration.

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So why don't you pause the video

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and see if you can plug in the numbers

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and find the acceleration yourself first.

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All right, let's try.

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So our acceleration
would be the net force.

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How do I figure the net force out?

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Well, the total force,

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well they're since in
the opposite direction,

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we'll subtract them.

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So, I'll just take the bigger number.

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So 9,800 newtons, which
is acting downwards.

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We need to take care of the direction.

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From that, I'll subtract
the smaller number,

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that is 7,800 newtons
upwards divided by the mass,

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which is 1,000 kilograms.

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And if you simplify,

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we will get 9,800 minus 7,800 is 2,000.

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Nice numbers, 2000 newtons.

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But what direction is it?

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The downward one wins, right? It's bigger.

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So, the net force will be
in the downward direction.

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It's divided by 1,000 kilograms
and that gives us two.

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So, our acceleration becomes

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two meters per second square downwards.

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Okay, we found our answer,

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but one of the best ways to
gain deeper insights is to try

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and see if this kind of makes sense.

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Can you get a feeling for
what's going on over here?

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Okay, now the first question

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that we could be having
over here is, look,

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the net force is downwards

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because gravity is winning, right?

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So the total force acting on
this elevator is downwards

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and yet the elevator is moving up.

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Why is that? (chuckles)

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Well, remember, force does not dictate

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the direction of motion.

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Force tells you the direction
of acceleration, okay?

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The elevator could be moving,

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objects can be moving
whatever direction it wants.

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When you put a force on it, it tells you

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what direction it should accelerate.

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So that's the key thing.

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So, there is no problem that
the force is acting downwards,

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but the elevator is moving upwards.

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Secondly, what does it mean

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that the acceleration is downwards?

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See, if the net force is downwards,

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the acceleration has to be downward.

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But what does it mean
the elevator is moving up

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and the acceleration is downwards?

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Ooh, this means since the velocity

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and the acceleration is
in the opposite direction,

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this means the elevator is slowing down.

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That's what it means for velocity

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and acceleration to be in
the opposite direction.

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If they're in the same direction,

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it means they're speeding up.

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So, this means our elevator is going up,

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but it is slowing down, which
probably means that, you know,

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it's probably about to stop.

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Maybe this person has probably reached

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his destination or something.

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All right, onto the next problem.

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This time we have a sledge at
rest whose is 70 kilograms.

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Our goal is to push it

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and accelerate to six meters per second

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in about two seconds, let's say,

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so that, you know, it
can nicely slide down

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and we can enjoy the ride.

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Now, there is going to
be some frictional force.

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Even though we're on ice and everything,

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there'll be some frictional force.

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Let's say the friction

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that this ledge will experience
is about 200 newtons.

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The question now is what is
the force with which we have

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to push on it so as to
achieve all of this?

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So how do we figure this out?

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Well, again, the first thing
that comes to my mind is

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that look, we're dealing with
forces and we have motion.

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What connects forces and
motion? Newton's second law.

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So, the first thing I'll
do is I'm gonna draw

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a free-body diagram.

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Again, I encourage you
to pause the video now

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or anytime later on.

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Whenever you feel more comfortable,

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pause the video and see if
you can complete it yourself.

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Okay, so anyways, let's first try

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to draw a free-body diagram.

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How do we do that?

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Well, again, we'll take
the object of our interest.

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In this case, the object of
our interest is this ledge

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whose mass is 70 kilograms
and just make it a square

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and then draw all the forces acting on it.

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What are the forces acting on it?

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I know there's frictional
force acting backwards

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of 200 newtons, but then I
also have the applied force

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by this person, which I,
we need to figure out.

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This is what we need to calculate.

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That is the applied force.
What are other forces?

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Well, I know that there's
also gravity acting on it

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and then there's a normal
force acting on it upwards.

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But we know that these forces are balanced

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and so they're not going to be useful.

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They're not going to affect
our situation over here.

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So, I'm just gonna draw them over here.

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They're there, of course, but
they're completely balanced.

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They're in the verticals,
they're not gonna affect it,

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so we'll not draw it.

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Okay, now that I have
my free-body diagram,

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let's go ahead and write
down on Newton second law.

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It says acceleration should
always equal the net force,

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which let me draw using pink now.

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Net force divided by the mass.

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Divided by the mass.

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Okay, so what do we do next?

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I need to find this applied force.

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So this means if I can
calculate the net force,

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then I can figure out what
the applied force is, right?

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So, from Newton's second law,

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I just need to figure out
what the net force is.

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For that, I ask myself, do I know m?

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I do. I know that m is 70 kilograms.

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Do I know the acceleration?

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Hmm, it's not given directly,

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but wait a second, I know
the initial velocity,

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I know the final velocity and I know

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that the change in velocity
should happen in two seconds.

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Whoo-hoo!

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That means I can calculate the
acceleration from this data.

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I can plug in and from
that I can figure out

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what the total force is going to be,

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the net force is going to be.

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And from that we can figure out

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what the applied force should be.

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Okay, so if you haven't done this before,

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why don't you now pause the video

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and see if you can put it all together

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and solve the problem?

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Okay, let's do this.

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So, let me first calculate
the acceleration.

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So our acceleration is going

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to be, well how do we figure this out?

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This is the final velocity
minus the initial velocity

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divided by the time taken.

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So, that's going to be, in our case,

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the final velocity is
six meters per second

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to the right minus...

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What's the initial velocity?

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Well, it's zero, it's at rest.

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So there is no initial velocity divided

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by time is two, two seconds.

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That gives us what?

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That gives us six by two is
three meters per second squared

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to the right.

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So I know my acceleration has to be

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to the right, which is
good news. (chuckles)

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It has to be to the right.

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We want this ledge to move to the right.

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So, that makes sense.

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So, we are on the right track over here.

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Okay, now, I can plug in

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and figure out what the
net force is going to be.

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So, if I just simplify that,
so net force is going to be,

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if I rearrange this equation
multiply by m on both sides.

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So I get net force to be
mass times the acceleration.

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And so now I can plug in
for mass and acceleration.

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What do I get? Well I get 70 kilograms.

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That's the mass,

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times the acceleration is three
meters per second squared,

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70 times three, seven times these 21.

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So, this is 210.

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So, I get that my net force is 210 newtons

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to the right of this,

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this acceleration was to the right.

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So, this will also be to the right.

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So, now that I've found my
net force, so my net force,

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the total force will be to the right

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and that is 210 newtons.

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From that, can I calculate
the applied force? Yes.

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So now, first of all,

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I know my applied force should be bigger.

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It has to be bigger

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because my total force
should be towards the right,

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which means if I subtract
the two from this,

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if I subtract this number,
I should get this number.

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That's the net force, all right?

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So now, now that I know all the directions

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and everything, I can
just subtract the numbers.

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So I can now say, "Hey, my net force

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that is 210 newtons should
equal this bigger number,

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the bigger force minus 200 newtons.

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Now, to get applied force,
I just add 200 on both sides

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so that I can get rid of this.

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And look, the applied
force becomes 210 plus 200.

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That is 410 newtons.

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And I already know it's to the right,

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so I know it's direction.

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So if I were to write down its direction,

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it's going to be, oops. (chuckles)

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Okay. Okay.

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I mean, okay, not the most
organized board over here,

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but let me just write it down
a little bit more neatly.

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So 410 newtons to the right.

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That's how much force we need to apply

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for all of this to happen.