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I will now introduce you to
the concept of tension.

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So tension is really just the
force that exists either

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within or applied by
a string or wire.

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It's usually lifting something
or pulling on something.

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So let's say I had a weight.

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Let's say I have
a weight here.

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And let's say it's
100 Newtons.

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And it's suspended from this
wire, which is right here.

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Let's say it's attached to
the ceiling right there.

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Well we already know that the
force-- if we're on this

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planet that this weight is being
pull down by gravity.

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So we already know that there's
a downward force on

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this weight, which is
a force of gravity.

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And that equals 100 Newtons.

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But we also know that this
weight isn't accelerating,

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it's actually stationary.

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It also has no velocity.

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But the important thing is
it's not accelerating.

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But given that, we know that the
net force on it must be 0

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by Newton's laws.

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So what is the counteracting
force?

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You didn't have to know about
tension to say well, the

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string's pulling on it.

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The string is what's keeping
the weight from falling.

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So the force that the string or
this wire applies on this

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weight you can view as
the force of tension.

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Another way to think about it
is that's also the force

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that's within the wire.

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And that is going to exactly
offset the force of gravity on

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this weight.

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And that's what keeps this point
right here stationery

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and keeps it from
accelerating.

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That's pretty straightforward.

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Tension, it's just the
force of a string.

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And just so you can
conceptualize it, on a guitar,

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the more you pull on some of
those higher-- what was it?

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The really thin strings that
sound higher pitched.

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The more you pull on it,
the higher the tension.

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It actually creates a
higher pitched note.

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So you've dealt with
tension a lot.

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I think actually when they sell
wires or strings they'll

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probably tell you the tension
that that wire or string can

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support, which is important if
you're going to build a bridge

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or a swing or something.

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So tension is something that
should be hopefully, a little

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bit intuitive to you.

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So let's, with that fairly
simple example done, let's

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create a slightly more
complicated example.

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So let's take the same weight.

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Instead of making the
ceiling here, let's

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add two more strings.

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Let's add this green string.

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Green string there.

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And it's attached to the
ceiling up here.

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That's the ceiling now.

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And let's see.

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This is the wall.

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And let's say there's another
string right here

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attached to the wall.

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So my question to you is, what
is the tension in these two

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strings So let's call
this T1 and T2.

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Well like the first problem,
this point right here, this

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red point, is stationary.

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It's not accelerating in
either the left/right

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directions and it's not
accelerating in the up/down

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directions.

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So we know that the net forces
in both the x and y

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dimensions must be 0.

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My second question to
you is, what is

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going to be the offset?

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Because we know already that
at this point right here,

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there's going to be a downward
force, which is the force of

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gravity again.

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The weight of this
whole thing.

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We can assume that the wires
have no weight for simplicity.

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So we know that there's going
to be a downward force here,

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this is the force of
gravity, right?

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The whole weight of this entire
object of weight plus

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wire is pulling down.

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So what is going to be the
upward force here?

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Well let's look at each
of the wires.

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This second wire, T2, or we
could call it w2, I guess.

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The second wire is just
pulling to the left.

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It has no y components.

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It's not lifting up at all.

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So it's just pulling
to the left.

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So all of the upward lifting,
all of that's going to occur

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from this first wire, from T1.

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So we know that the y component
of T1, so let's

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call-- so if we say that
this vector here.

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Let me do it in a
different color.

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Because I know when I draw these
diagrams it starts to

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get confusing.

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Let me actually use
the line tool.

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So I have this.

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Let me make a thicker line.

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So we have this vector
here, which is T1.

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And we would need to figure
out what that is.

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And then we have the other
vector, which is its y

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component, and I'll draw
that like here.

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This is its y component.

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We could call this T1 sub y.

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And then of course, it has an
x component too, and I'll do

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that in-- let's see.

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I'll do that in red.

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Once again, this is just
breaking up a force into its

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component vectors like we've--
a vector force into its x and

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y components like we've been
doing in the last several

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problems. And these are just
trigonometry problems, right?

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We could actually now, visually
see that this is T

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sub 1 x and this is
T sub 1 sub y.

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Oh, and I forgot to give you an
important property of this

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problem that you needed to
know before solving it.

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Is that the angle that the
first wire forms with the

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ceiling, this is 30 degrees.

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So if that is 30 degrees, we
also know that this is a

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parallel line to this.

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So if this is 30 degrees,
this is also

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going to be 30 degrees.

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So this angle right here is also
going to be 30 degrees.

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And that's from our-- you know,
we know about parallel

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lines and alternate
interior angles.

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We could have done
it the other way.

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We could have said that if this
angle is 30 degrees, this

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angle is 60 degrees.

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This is a right angle,
so this is also 30.

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But that's just review
of geometry

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that you already know.

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But anyway, we know that this
angle is 30 degrees, so what's

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its y component?

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Well the y component,
let's see.

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What involves the hypotenuse
and the opposite side?

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Let me write soh cah toa at the
top because this is really

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just trigonometry.

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soh cah toa in blood red.

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So what involves the opposite
and the hypotenuse?

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So opposite over hypotenuse.

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So that we know the sine-- let
me switch to the sine of 30

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degrees is equal to T1 sub y
over the tension in the string

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going in this direction.

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So if we solve for T1 sub y we
get T1 sine of 30 degrees is

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equal to T1 sub y.

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And what did we just say
before we kind of

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dived into the math?

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We said all of the lifting on
this point is being done by

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the y component of T1.

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Because T2 is not doing any
lifting up or down, it's only

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pulling to the left.

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So the entire component that's
keeping this object up,

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keeping it from falling
is the y component of

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this tension vector.

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So that has to equal the force
of gravity pulling down.

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This has to equal the
force of gravity.

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That has to equal this
or this point.

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So that's 100 Newtons.

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And I really want to hit this
point home because it might be

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a little confusing to you.

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We just said, this point
is stationery.

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It's not moving up or down.

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It's not accelerating
up or down.

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And so we know that there's a
downward force of 100 Newtons,

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so there must be an upward force
that's being provided by

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these two wires.

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This wire is providing
no upward force.

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So all of the upward force must
be the y component or the

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upward component of this force
vector on the first wire.

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So given that, we can now solve
for the tension in this

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first wire because we have
T1-- what's sine of 30?

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Sine of 30 degrees, in case you
haven't memorized it, sine

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of 30 degrees is 1/2.

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So T1 times 1/2 is equal
to 100 Newtons.

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Divide both sides by 1/2
and you get T1 is

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equal to 200 Newtons.

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So now we've got to figure out
what the tension in this

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second wire is.

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And we also, there's
another clue here.

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This point isn't moving left
or right, it's stationary.

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So we know that whatever the
tension in this wire must be,

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it must be being offset by a
tension or some other force in

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the opposite direction.

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And that force in the opposite
direction is the x component

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of the first wire's tension.

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So it's this.

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So T2 is equal to the
x component of the

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first wire's tension.

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And what's the x component?

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Well, it's going to be the
tension in the first wire, 200

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Newtons times the cosine
of 30 degrees.

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It's adjacent over hypotenuse.

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And that's square root
of 3 over 2.

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So it's 200 times the square
root of 3 over 2, which equals

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100 square root of 3.

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So the tension in this wire is
100 square root of 3, which

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completely offsets to the left
and the x component of this

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wire is 100 square root of
3 Newtons to the right.

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Hopefully I didn't
confuse you.

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See you in the next video.