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- [Voiceover] Let's now tackle part C.

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So they tell us block 3 of mass m sub 3,

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so that's right over here, is added

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to the system as shown below.

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There is no friction between
block 3 and the table.

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Alright, indicate whether the magnitude

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of the acceleration of block 2

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is now larger, smaller, or the same

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as in the original two-block system.

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Explain how you arrived at your answer.

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So let's just think
about the intuition here.

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If you think about the net forces

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on the system itself, they're the same

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as we had before, now the internal forces

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are going to be different, you're actually

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going to have two different tensions now,

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now that you have two different strings

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but the net forces, the ones that are

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causing this thing to accelerate

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in the upward direction
on the left-hand side

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to the right on the top and then downwards

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on the right-hand side,
it's still this though

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the difference in the weights between

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the two blocks but now
that difference in those,

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inbetween the weights of the two blocks

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is moving more mass and we know that force

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is equal to mass times acceleration

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or acceleration is equal to force

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divided by mass and our
force, our net force

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is being, is the differential
between the weights

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or the difference between the weights

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of the block but now we're going

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to be moving more aggregate mass,

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this is going to be m1 plus m2 plus m3

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and so you're going to have
a smaller acceleration.

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And so what you could
write is acceleration,

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acceleration smaller

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because same difference,

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difference in weights,

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in weights,

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between m1 and m2

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is now accelerating more mass,

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accelerating more mass.

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And that's the intuitive
explanation for it

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and if you wanted to
dig a little bit deeper

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you could actually set up free-body

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diagrams for all of these blocks over here

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and you would come to
that same conclusion.

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So let's just do that, just
to feel good about ourselves.

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So what are, on mass 1

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what are going to be the forces?

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Well you're going to have
the force of gravity,

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which is m1g, then you're going to have

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the upward tension pulling upwards

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and it's going to be larger
than the force of gravity,

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we'll do that in a different color,

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so you're going to have, whoops,

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let me do it, alright so you're going

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to have this tension, let's call that T1,

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you're now going to have
two different tensions here

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because you have two different strings.

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Now the tension there is T1, the tension

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over here is also going to be T1

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so I'm going to do the same magnitude, T1.

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Now since block 2 is a larger weight

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than block 1 because it has a larger mass,

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we know that the whole system is going

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to accelerate, is going to accelerate

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on the right-hand side it's
going to accelerate down,

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on the left-hand side it's
going to accelerate up

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and on top it's going to
accelerate to the right.

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And so if the top is
accelerating to the right

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then the tension in this second string

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is going to be larger than the
tension in the first string

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so we do that in another color.

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I'm having trouble drawing straight lines,

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alright so that we could call T2,

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and if that is T2 then

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the tension through,

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so then this is going to be T2 as well

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because the tension through, the magnitude

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of the tension through the entire string

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is going to be the same, and then finally

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we have the weight of the block,

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we have the weight of block 2,

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which is going to be
larger than this tension

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so that is m2g.

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Now I've just drawn all
of the forces that are

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relevant to the magnitude
of the acceleration.

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If I wanted to make a complete

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I guess you could say free-body diagram

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where I'm focusing on m1, m3 and m2,

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there are some more forces acting on m3.

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M3 in the vertical direction,

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you have its weight,
which we could call m3g

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but it's not accelerating downwards

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because the table is exerting force

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on it on an upwards, it's exerting

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an upwards force on it so

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of the same magnitude
offsetting its weight.

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So that's if you wanted to do a more

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complete free-body diagram for it

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but we care about the things that are

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moving in the direction of the accleration

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depending on where we are on the table

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and so we can just use Newton's second law

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like we've used before,
saying the net forces

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in a given direction are equal to the mass

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times the magnitude of the accleration

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in that given direction, so the magnitude

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on that force is equal to mass

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times the magnitude of the acceleration.

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And so we can do that first with block 1,

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so block 1, actually I'm just going to

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do this with specific, so block 1

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I'll do it with this orange color.

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So block 1, what's the net forces?

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Well it is T1 minus m1g,

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that's going to be equal
to mass times acceleration

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so it's going to be m1
times the acceleration.

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Now what about block 3?

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Well block 3 we're
accelerating to the right,

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we're going to have T2,

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we're going to do that
in a different color,

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block 3 we are going to have

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T2 minus T1,

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minus T1 is equal to m

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is equal to m3 and the magnitude

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of the acceleration is
going to be the same.

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Here we're accelerating to the right,

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here we're accelerating up,

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here we're accelerating down,

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but the magnitudes are
going to be the same,

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they're all, I can denote
them with this lower-case a.

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And then finally we can
think about block 3.

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We could say that the net forces,

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well that's m2g minus T2,

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that's going against m2g,

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is equal to m2 times its acceleration

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and now if we want to
solve for acceleration,

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and this will be quite convenient,

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we can just add up all
of the left-hand sides

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to get a new left-hand side, and add up

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all the right-hand sides to
get a new right-hand side,

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we can do that algebraically
because they're all

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this is equal to that,
that is equal to that,

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that is equal to that so if you add up

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these and then you add up those,

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well then the sums are going
to be equal to each other.

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And so what are you going to get?

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So if you add up all of this,

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this T1 is going to cancel out
with the subtracting the T1,

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this T2 is going to cancel out
with the subtracting the T2,

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and you're just going
to be left with an m2g,

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m2g minus m1g,

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minus m1g, m2g minus m1g

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is equal to and just for,

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well let me just write it out

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is equal to m1a plus

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m3a plus m2a.

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Well we could of course factor the a out

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and so let me just write this as

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that's equal to a times m1 plus m2

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plus m3, and then we could divide

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both sides by m1 plus m2 plus m3.

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So let's just do that.

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So m1 plus m2 plus m3,

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m1 plus m2 plus m3,

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these cancel out and so this is your,

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the magnitude of your acceleration.

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And notice you have the
same difference in weights

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that's providing the
net force on the system

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but is now accelerating more mass,

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so you could even say, hey look,

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I have more mass here,

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so more mass to accelerate,

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more mass,

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more mass to accelerate
while I have the same

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net force acting on the system,

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we're not talking about
the internal forces,

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those all canceled out when
I added these equations

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and so if you're taking the same net force

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and you're dividing it by more mass

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you're going to have a smaller,

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smaller acceleration.

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Hopefully that all made sense to you.