[Music playing]
No?
Okay, let's just start then.
Alright.
First of all, we need to review some principle
of physic.
So there are few concept that you already
know and one of them is basis of our operation
here.
So let's look at Newton's Law of Motion.
Newton's [writing on board] Law of Motion.
These are all materials that you have learned
in physic.
The first one is very important for us because
you have heard this theory a lot.
And that is when some of the forces apply
to an object is equal to zero, that object,
if it's stationary, remain stationary or it
is moving in a constant velocity's going to
continue with that.
So that is of course, we are in a static class,
nothing is moving.
So we are going to assume everything is not
moving, but some of the forces must be equal
to
Zero.
Zero.
That's Newton's first law.
Newton's second law of course is when some
of the forces are not equal to zero, so what's
going to happen?
It's going, there going to be a motion.
Correct.
And the object is going to accelerate and
that become a dynamic problem.
So some of you immediately want to take your
dynamic course after the static, that's the
subject that is going to be involved, which
is not, of course, a static.
We are not going to use it.
So law number 2 is not applied to us.
And law number 3 that I'm sure some of you
are familiar is that if you have two masses
close to each other, they are going to exert
forces equal and
Opposite.
Opposite, so those two forces are equal and
then [writing on board] a formula is given
for that force which is equal to M1, M2 times
G which is the gravitational force, depends
where you are on air or on moon or where you
are, divided by R square, R being the distance
between the two.
Is that, are we going to use that law number
3?
No, but somehow or some version of it we are
going to use because every time that we have
an object and we cut the object like the leg
of this microphone, we cut the object, the
forces there must be equal and
Opposite.
Opposite in two side of the body.
So in a way, yes or no, but not in this format.
So that's why that not concern me.
So what we are going to talk about constantly
in this class is this.
And the object is in a stationary, not moving
anywhere.
So that's the rule that you have seen it in
physic.
Now there is another point which is very important,
is how do we handle with the number?
Because your calculator goes to 3, 4, 5 digit.
You have 10 to the power of 4 here.
10 there.
However, we have an accuracy procedure that
you should all follow and that is we need,
we need 3 minimum of 3 digit [writing on board]
for every number.
Now 3 digit does not mean 3 decimal point,
everybody get the point.
So I don't mean go to 3 decimal points.
Not at all.
Means for each number no matter how large
or how small it is, you need at least minimum
of 3 digit.
The rest of it you can put 10 to the power
of 6, or 10 to the power of 3 in front of
it.
For example, if you have 367,432 for example
your calculator shows something like that.
This with 3 digit accuracy can be 367 times
10 to the power of 3.
How many digit do I have?
How much you lose here is insignificant, everybody
understand that.
However, if you have 1, this is another example
divided by 3 and you put here point 33, that's
not correct.
Everybody under, because it's not 3 digit
it's only this compared to the original number,
you are losing more here than you are losing
here.
Although this is 432 unit but this is not
comparable.
Everybody understand that.
If you multiplied that number by 10 million,
you can see how much you lose there.
Everybody under, but the number are compared
to each other, not, I mean to each type of
number not the, large number will be never
compared to a small number.
Is that understood?
So anytime you have a sign or co-sign, don't
put point 78 or point 20, you must go to at
least 3 digit, everybody got the idea here.
So 1 over 3 would become equal to 1 over 3
that's right, that become point 33 et cetera,
is 100 over for example 3 become 33 point
3.
So these are correct procedure.
Everyone of them has 3 digit, 3 digit, 3.
So what I'm saying is this.
If you have a large number don't put the large
number down, it's a waste of number.
Use a prefix of 10 to the power of 3, or 10
to the power of 6.
Usually in engineering work we don't use 10
to the power of 4 or 5 or 7 and 8.
In engineering work we always use 10 to the
power of 3 and 6, or 10 to the power of minus
3 and minus 6.
They have name if they were [Inaudible].
Because as we go along we're going to exponate.
Then the other subject that I'm sure you're
aware of half of your problem is metric system.
Half of your problem are in our system.
So you should be familiar to convert one to
another one.
One thing that we are using constantly is
this.
That unit of the mass and unit of the force.
So let, I'm sure you all know that but I have
to mention that.
In metric system unit system of the mass is
kilogram.
Yes or no?
The [Inaudible] of the force, unit of the
force is milton [phonetic] that's right.
Now what's the unit of the force in our system?
Is pound.
[Inaudible] you go to Europe to buy apple
you say two kilogram.
Here you go you say two pound.
Yes or no?
Something wrong there, is that correct.
We are using math which you should use too,
but here it is force.
So in physic or in math classes, they gave
you pound force, pound mass.
Wrong, actually that's we are not going to
use that.
Anytime I want to give you the mass, what's
the unit of mass in our system? Slug, that's
right.
But next I'm going to the [writing on board]
one of the supermarket ask for so many slug
of apples.
Okay, doesn't work.
So what the point is this.
When I give you pound then I give you kilogram,
you have to multiply by G to get the force.
Yes or no?
I have seen a student do that.
I give them the pound which is the unit of,
force, and then this multiplied by G. Don't
do that.
In other work when I want to give you the
mass, I will give you a slug.
Is that correct or not?
So that is the something that I have to clarify.
Now these are the a little bit of principle
of the physic that will be in first two problem.
Also those two problem are very important
for me to see, but one is the conversion of
the unit.
The other one actually I'm very interested
the other one.
The other one do not, I want in the problem
number 5, I want you to find out how many
newton is one pound.
But I want you not use the table.
I want you to use the data that given in the
problem.
How to use that data, please make a note of
that.
In problem number 5 of your handout, use the
data given in the problem to find out how
many newton is equivalent to 1 pound.
That's problem number 5.
Then we go to Chapter 2 which is the getting
of a static.
Of course, in a static we are dealing, in
a static we are dealing with the object load
being applied to that object.
Those load could be weight, could be pool,
could be a spring force, could be contact
force.
Some of them you have already seen in physic
and you have also know that what are the forces
the forces must be [writing on board] vectors.
And vectors have magnitude and direction et
cetera, et cetera.
In this class remember that if you showing
vector you must show something like that or
some [Inaudible].
If it is non-vector you showed or magnitude
you show like that.
This is a sample of the scalar number or non-vector
and that's the vector.
So please be careful.
Many student do not follow that.
Anytime you have a vector of course if you
are writing as a component, it has to have
IJ or K, everybody understand that.
Because each force has two component or three
component, depending whether you are looking
at it at a 2D problem, or a 3D problem.
And that's of course the unit of the force
everybody knows again, is a pound at newton
and now the subject we want to sort of view
together adding vectors together [writing
on board].
Of course you all know that.
In order to add the several forces together,
let's say that I have force F1.
I want to add to force F2.
I will add F3.
You can put few more if you want.
That usually we write it like that in a vector
form.
F1 plus F2 plus F3 equal to R, which form
a polygon.
And that polygon is like that.
You start from a point A, you put F1 there.
And the F2, toe, head, toe, head, F2 there,
and then F3 there and then when you are finished
with all the forces, then you connect the
beginning of the first force to the end of
the last force.
And that will be your R. Is that [Inaudible].
And that R again, our vector, it has a magnitude
and it has a direction and you are supposed
to find out this is the formula.
You have done it.
However, to do that you are going to use two
method.
That's why you see two line of homework there.
The first method is this, so please write
it out.
Two method and each one is specifically learned
for different reason.
One is using, method one is using [writing
on board] sign slash co-sign rules.
Obviously if I want to use sign and co-sign
rule, I have to form a triangle because the
triangle have 3 side in order for me to be
able to use sign rule at co-sign rule.
Everybody familiar with sign rule, co-sign
rule.
Correct?
If not, look at your handout in what page
of two of your handout or three, please take
a look there.
In page yes, in the page four on the bottom
of the page, noticed on the left-hand side
is the, or right, I'm sorry, are the prefixes
for add, from my side, from your side would
be left side.
It's prefixes and the sign rule and co-sign
rule are there and this is the table of conversion
that you may or may not want to use.
However, and the second let me tell you the
second method then we going to give you, I'm
going to give you example.
The second method is using component of the
force which also you are familiar component.
Okay, this one is only good right in front
of this one.
The first one is only good if you have two
forces and you find the result.
And if you are more than two forces, three
or four or five forces, you have to repeat
the process again and again and again, doesn't
work, you know that, so let's get so go through
an example.
Now the example is the class exercise.
So please go to the page that it says Class
Exercise and take a look at the example that
I have given you there.
And this is just a exercise which is similar
to problem 5-2-15, 4-2-15 there on the board.
And look at the problem.
There is a hook there which driven into a
wood, something like that.
There is a force applied there.
There is rope there which represent a force.
It says F2.
And there is a force going in that direction,
F1.
And the angle which mean the two is given
120 degree.
Correct?
Do you see that in your handout, page 6.
Question is, what's the resultant of this
two forces?
Of course since I only have two force, the
result, the polygon of the force has become
a triangle because there's two forces and
only one result.
And therefore the sign rule and co-sign rule
become applicable.
Yes or no.
So there's four that polygon.
You can start, oh, let me give you the magnitude
of forces.
So F1 is given equal to [writing on board]
80 pound.
Notice this is a magnitude, this is a vector.
Notice you should follow the same rule for
all your homework.
And F2 magnitude of F2 is given equal to 60
pound.
And the angle 52.
The weight shown is equal to obviously the
resultant is not 140.
The resultant could be 140 if two line are
along the same line, is that correct or no?
Over here the resultant is something oh let's
find out.
Okay, put the F2 here which on the scale.
And then put F1 there, which on the scale.
But notice that this angle is 120 degrees
so that angle become equal to 60 degree, correct.
And then, as I said here, toe, head, toe,
head, toe, head then the last the first toe
would be at connected to the last head, which
is your R. So your R here is, I can use a
different color, your R here is, Okay, how
do you calculate R?
Of course my sign rule and co-sign, Which
one, sign rule or co-sign rule?
I'm testing your knowledge of the math because
you have lots of math prerequisite for this
course.
And I'll tell you this.
If you are good in math, you become more successful
in this class.
If you are a little bit fuzzy about the principle
of math you need to work on it a little bit,
because lots of concept in this class will
be math-related.
So please be aware of that.
Is that correct or not?
Now, co-sign rule because co-sign rule is
if there is a triangle everybody know that
C is squared equal to A square plus B square
minus 2AB time co-sign the angle between the
two, yes or no?
Here it applicable because I have the value
of F2, yes.
I have the value of F1.
I have this angle, therefore co-sign rule
is applicable.
Therefore this constituted the C, constituted
this AB, you don't have to write it like that.
So R equal to square root of, or C square
equal to the rest which is A square.
You don't have to write the formula because
the formula is in your page 4 or 5 I gave
you, I mentioned before.
But you apply that concept to this problem.
Is it this square and that is square.
This one is 80 square and the other one is,
60 square.
Is that correct or not?
Yes, minus 2 times 80 times 60 times the angle
between the two, which is 60 degrees.
So co-sign of 60 degree and that is your R.
When you solve it with your calculator of
course, R ends up to be, look how I write
the answer, 72 point 1 pound.
How many digit did I use?
Three.
How many digit did I use, I erase it here.
Three digit.
If there is another one, you want to put extra
digit that's okay but you need minimum of
three digit, that's the rule because otherwise
you lose the accuracy of your number.
Extra doesn't matter but it sometimes waste
of time [Inaudible].
Okay, is this finished?
Is the problem finish?
Did you find a resultant?
No.
You need the direction of that.
Yes?
To find a direction of that you need this
angle up [Inaudible] or whatever you call,
is that correct or not?
Yes?
Because each vector has a magnitude and a
direction.
You already find a magnitude and you want
the direction.
Of course for that one you have to use a sign
rule.
Is that correct or now we because we are looking
at the sign rule is this.
Sign of this angle over F2 equal to sign of
60 over R equal to sign of alpha or F1, is
that correct or not?
Yes?
So therefore I can write here either one of
them to solve for alpha so I can write F1.
F1 was how much?
F1 was I can do it in reverse order too, so
let's put it this this way, sign up alpha
over F1 which is 80 is equal to sign of 60
degree which is this angle over magnitude
of R. Magnitude of R we already calculated
to the 72 point 1.
You can put pound here but they eliminate
either way is correct.
So you calculate alpha eventually equal to
73 point 9 degree.
It is not a bad idea that always you have
your calculator with you and then check my
answer if you can quickly.
So then we are in the same place together.
Now, what did we do here?
We find a resultant, yes, a bunch of number.
But for, in [Inaudible] this mean different.
This was a cable that get capacity of how
much?
This is what static is all about.
First few times that you go through the lecture
you think we are talking about a bunch of
arrows going this way and that way like what
you see here.
But really that is not the case.
Every concept that we are talking in this
class, you are going to use in all the engineering
classes in future, including my next class
which is ME 218 which is spanked up material
class and we do lots of operation there.
First every problem I give you there, the
first three step is a static then a start
[Inaudible] up and just going to be repeated
as I said earlier, the static is for everyone
and for everything.
So base of every problem finding the forces
that make our moment of each problem is essential
part of engineering application in future.
Everybody understand that.
So you should take it seriously, you should
spend about 6 to 10 hour depend your resident,
on the set of homework, it's a serious [Inaudible]
but when you do that you will be, at the end
you will be all smart.
Because then you have learned a lot and you
have built your foundation for future courses.
Don't take this lightly.
I have said that, this in previous classes,
so I must mention here too.
Static and strength of material both of them
are fundamental courses.
Not because I'm teaching it but because I'm
fortunate to teach that because however, it's
so important that anybody who get A in static,
and anybody get A in strength of material,
I guarantee I can give you sign signature
that he or she will be a good engineer who's
successful engineer.
Because it's so important to grasp the concept
of the principle that you are set up already
for a much more difficult classes that coming
future, you already have the base there.
However, that means lots of work.
That means you cannot miss classes.
I did not mention that but ask any other class
student from my class, you cannot miss classes.
You have to spend about 6 to 10 hours in every
set of homework.
You need to do the homework by yourself.
You cannot go to somebody else and say what,
how do I do this one?
How do I do, like a blind person you take
the hand, your hand going to be [Inaudible]
you are not learning then.
This is the fact of life.
You need to do it yourself to get the idea.
Doesn't matter, you cannot do 100% is no problem,
nobody actually can do the 100% of the problem.
So any time I see that one student getting
100% in every homework from the beginning
to the end, it worries me because if you get
100% in your quizzes you should get 100% or
90%, I'm sorry, in the homework you should
get 90 or 80% the quizzes as well, yes or
no?
So I see the homework is all there but come
to the quizzes is not showing the result.
Something is missing there.
Everybody, that missing is your either copying
it or you're getting lots of help, which is
okay at the beginning, I didn't say that you
shouldn't get help, you should get help but
you should try first yourself how far you
move put extra force there, go to your note,
goes to your example, et cetera, et cetera,
and then when you need help come to me or
somebody else.
Is that understood?
You need that self help as well.
Therefore, what we did here is engineering
application, look they are very K but here
they're useful but how much was the capacity
of cable?
80 pound.
This cable was 60.
Can I take this two cable replace it with
one cable?
With the same effect?
Yes.
Isn't that cheaper process?
You see that?
So if you are a designer you're designing
something and you want to put it how do you
present that alternative?
So I take this two cable, put one cable in
this direction, everybody understand?
Which has the same effect and the same structure.
It's much cheaper [Inaudible] alternative.
So every problem from now on looks like now
numbers or arrows in future is all engineering
applica, that's the example of.
Now, did you say this, yes?
What did I use here?
Very simple sign rule and co-sign rule.
Let's go to one of my quizzes, let's see whether
you can do the same thing here.
Go to Quiz Number 1.
Sample quizzes.
If you can duplicate this in that problem,
that is the right now you haven't done any
homework so you don't know what I'm talking
about.
But quite frankly, not this one both, they're
both the one before, yeah that's the same
thing actually.
Look at the both.
You see that?
Does look anything like this?
Would you believe conceptually the same?
Now read the question while I'm erasing the
board and tell me what you want to do in order
to solve that problem.
See I haven't said much yet.
I only gave you one little concept here, but
this is a good practice for future.
So if you listen carefully that's what I said
Andy, you listen to me carefully, make a good
note.
And then you will see all the answer that
you want for all your homework is in your
note.
So your best reference is your note, then
it is the book.
That's what I said.
If you don't read the book, don't buy it.
If it's too expensive, however, as I said,
it is a good book, you should have it.
However, your best reference is your note
and example on the [Inaudible] if you make
it good note in class.
That means you should always listen carefully
and if you have any question of course, you
can always ask that.
Now let's look at that other problem.
What's this problem we have here?
It is a boat somehow the engine is out, so
it's not working.
And here is the boat stop here, notice and
you try to get this boat to side up the [Inaudible].
So if you put that little [Inaudible] and
you draw a rope here, put it that way, the
boat will move that way.
Yes or no.
If I put another rope this way and do the
same thing, it will look that way.
But the object of this exercise is not to
move their boat to this bank or to this bank,
to move it along the centerline, yes or no?
Correct?
So what is saying is this, the resultant if
you are going to be in this direction because
we want perhaps two mile down the road down
the river, there is a village or something
we want to take the boat there for repair
or whatever.
Is that correct or not.
Therefore it requires two forces.
What did I call those two forces, so let's
go to the example, okay.
This one is F1 in this direction is force
F1.
And this direction, it's this rope, each rope
represent a force, F2.
And the angles that went there, this angle
is 30 degree and that angle is 40 degree correct?
I hope this is clear enough.
Yes?
Alright.
What else is given?
Notice the magnitude of R is given equal to
1,500.
The resultant has to be for example, can you
connect the two problems together guys?
And I said it's the same so I have to put
the polygon of forces which are triangle,
yes or no?
Yes.
I know the resultant should be along horizontal
line.
Yes or no?
Correct?
So I have to start somewhere, let's just start
with F2, like the other one.
So I'm starting with F2.
The only problem is that F2 is not known.
So the question you want to put here always
this is the data.
The handout that I gave you one page how to
look at the problem is this.
You always look at the data, these are all
the data is given.
Then you look at the, what is the object of
this exercise?
What are we trying to do?
In this problem we are trying the question
being asked in other words, what is the question?
Magnitude of F1 and F2, reverse of the other
one.
That's only difference between the two is
reverse of the other one.
The other one, F1 and F2 given you want to
find R here, R is given.
You want to find F1 and F2, with a little
twist there [Inaudible] so F1 magnitude and
F2 magnitude are the question that you want
to answer.
So now, in-between the two is the concept.
What concept are we using?
Is concept of sign rule and co-sign.
Is that very simple?
Everybody understand why I apply the same
technique to every other concept that I'm
going to talk the next 10 week but some of
them are very difficult, but that's the same
way.
You learn the concept.
Doesn't matter, it will be applied anyway.
Everybody understand that?
And that is my hope, that I motivate you enough
to look at every problem like that, get the
point and connect those point together, everybody.
And that connection is engineering work.
You go out of college, you sitting in my office,
you are in a consultant office, the project
costs you first of all the project is not
something easy to do, it's 10,000 time more
difficult than like your homework, because
if somebody can do it from the internet or
from the sources available to them they do
it.
They don't come and pay you, yes or no?
When they come to pay you there's something
more difficult that you have.
Then your job as engineer is okay, I know
this much physic, I know this with math, I
know this much static, that much the strength
of material, can I put all of this together
to come at a conclusion that is what I say,
connecting point.
That connecting point is practice through
there, homework.
No here we go.
So F1 is there.
So I don't know the magnitude of that but
I know the direction of that.
The direction of that is at 30 degree, yes
or no?
But it go somewhere or start somewhere it
stop.
So let's assume that's the end of it.
Then at that end I have to put F1 there, yes
or, F1 is going which way?
F1 is going down.
So if this is the horizontal line I have to
put F down in this direction and that angle
is how much, that angle is?
This is the one I draw, it's not in the scale.
Is that correct or no?
Yes?
Okay, where should I end up here?
Some of your homework will not be done like
this.
Here something you may end up here, you may
end up down there as long as you are in this
side.
But none of them is correct except one.
Where should I end up?
Where should be the end of that vector?
Horizontal because the resultant has to be,
Horizontal.
Horizontal.
So I cannot end it here.
If I end up here my resultant looks like that.
If I end here, my resultant look like that.
Because it says the resultant should be horizontal
I want R to be this, therefore, F2 this will
go, only thing different between the two problem
look like that.
Sorry for that mess.
So here is F2 and here is F1.
Now this is 30 degree, this is our first [Inaudible]
degree.
This is 40 degree, so what's that angle?
That angle is? 110, 180 minus 70 degree.
So that angle is 110 degree.
Of course this angle is 40 degree.
Is this exactly what I did a minute ago?
I erased it there.
Is that what you have in your note?
Yes or no?
Yes.
Correct?
So the problem is solved.
Can you solve it?
Okay, so what is the magnus of course here
look what is given.
The magnitude of R is given, so therefore
the angles so you can use actually sign.
You can use sign of reverse of the other ones.
You can do sign of 110 degree over R, over
R which was 1,500 meter, must be equal to,
for example sign of 40 degree over magnitude
of F2.
And write another one F1, and you see the
rest is very simple.
Because you already done your job by coming
up with this polygon or this triangle.
Is that correct or not?
Yes?
Okay, good.
So therefore let me give you the answer.
So you go to the answer so for F2 is become
1,000, F2 become equal to 1,026 newton.
You always have to you can write this at 1,030
have 3 digit if you wish.
And F1 I use 4 digit.
Magnitude of F1 becomes 798 nit [phonetic].
This just was explanation because this is
the first class that hold this conceptual
concept of the subject that I'm teaching you
will be repeated again and again and again.
You need to do one problem properly, 50 other
problem look the same to you.
When you don't learn it, that's where the
problem start.
Then anytime you look at it, it still is a
mystery, don't want to solve that mystery
one for yourself.
That's why it's so important so in other words,
don't work for that 5 point, please.
Work for the other 55 point by doing your
homework yourself.
That was my idea [Inaudible] and I stress
this note, you don't know how important this
is until you ask other student who have been
successful in this class.
Everyone of them without exception will write
to you, do the homework do it yourself.
I hope you have read all their comment, yes
or no, for some of you.
Is that what they say?
More or less?
Alright, okay.
Now, this is now here, these two, three problem
is that subject.
There are new sign and co-sign.
This is the rest of the material we are going
to talk about which are component of the force
that we are very familiar with as well, but
let's go over that for review.
Don't want anybody, anything to be left out.
And that, now we are talking of component
of forces.
Okay.
In general, let's talk about in general and
then we make it more specific.
In general, if you have a force here and you
have two line here, line one and line two
and you want to project that F over line one
and line two, you have done that in the past
in physic classes.
At the end of this vector you drive, I mean
or you draw a line parallel to L2 and also
you draw a line parallel to L1, is that correct
or no?
And this force here include become F1 and
this force here become F2.
These are the two component of F overline
F1 and F2.
Look at this polygon of the forces because
this side and this side are equal.
Yes or no?
But if this is F2 this must F2 as well.
So look F1 plus F2 equal to F. Is that correct
or not?
So here you go vector once, F equal to F1
plus F2 in general.
There is a handout problem there that I don't
have time to do it.
There are some homework assignment that there
is a cable [Inaudible] force and you want
to project that over two line.
You use that triangle, either triangle.
You know where [Inaudible] upper one if you
have the data given to you.
Is that correct, like what I used here.
Because if you look at it that's the same
problem.
F1 plus F2 equal to F, so you use side rule,
co-sign rule, you can solve it.
But this is the component of the force over
two arbitrary line.
In many cases those are not arbitrary line.
Those are X and Y axis, which we call it cartesian
component, yes or no.
So therefore incident of that if your two
line L1 and L2 become X, sorry, X, R, and
Y axis and this is your F vector, the same
is applied.
So all you have to do, draw a line here parallel
to Y axis.
Draw a line parallel to there, X axis.
And then the way we do it because I draw that
loose on this is FX as a vector, yes or no?
And this is?
F1.
Okay, following four below that you have seen
it in physic applies from now on to every
problem.
I'm going to erase this because I need larger
area.
So I'm erasing this and like all the component
there.
First of all look what I, the way I have writing.
So please distinguish between the vector and
the skater number [phonetic] or non-vector.
So please write it to follow.
If I write F equal to F1 plus F2, is that
a correct statement or not?
Obviously it is.
Is that correct or not?
Because that's the sum of the two vector right?
However, we know from the past that a unit
vector, okay, what's the unit vector now?
Let's explain that, everybody knows what the
unit vector is but I'm going to put on the
side here another idea that you already know.
Okay, this is a vector.
Let's say you, which had a magnitude of 3
time.
Yes?
This is a vector, unit vector, unit vector
obviously from in this book we are going to
call it "landa" and magnitude of the landa
is one-half.
Yes?
And this is landa, this is you.
Look at the size of it.
This is one pound and this three pounds.
So three of this fits into that, yes or no?
So your forwarder that you have seen in the
past is like that.
Each vector equal to if I want to apply this,
this is three times of this.
We call three times landa, yes or no?
Yes?
U equal to three landa, correct?
So therefore each vector equal to each magnitude
times X, times its unit vector.
Are we going to use this formula?
Believe me, 2, 300 time in this class so please
remember that.
Each vector equal to its magnitude times a
unit vector.
Unit vector has a magnitude of one.
This is in this direction of course I'll talk
about X and Y again in a minute.
So that formula is one of the formula constantly
being used and then reverse of that.
Sometime I give you the vector and I give
it your magnitude.
You want to find a direction, how do you find
that?
Labbed out [phonetic] the direction of the
vector, equal to what?
The vector itself divided by its magnitude.
So this two formula is going to be applied
to all the rest of the problem, their problem
line 3, 4, and 5.
Is that correct or not?
Off to here you use sign and rule.
This one is physic.
This one are sign and co-sign rule.
This all of that, all those, in some of this
in the book.
[Inaudible] problem in the book they are using
sign and co-sign.
I suggest you not use it and use component.
Do not follow the Solution Manual, you know
that.
Just use your own initiative.
Anyhow, now everybody knows the unit vector
and all the X axis we call it "I."
The unit vector on Y axis we call it "J."
Therefore the following formula is all applied
to some of your homework and that is this.
F1, sorry here I should change not to X because
you see F1 and F2 here, I should use FX add
to the dimension that I make I call it FX,
XY, not F1, F2.
So that is equal to FX plus FY, yes or no?
However, FX is equal to its magnitude using
this technique times a unit vector, correct?
And FY become equal to FY magnitude time unit
vector there.
So simplifying the two together so I'm putting
this in the equation one so F become equal
to FXI plus FYJ.
This is magnitude direction, magnitude direction.
Of course the direction has a vector, so this
is another form that you have used a lot in
this.
Now, if I give you this angle [Inaudible]
obviously FX equal to what?
FX equal to FX magnitude wise, equal to F
time co-sign off, [Inaudible] this is co-sign,
this is sign.
Everybody agree?
Yes?
Are you with me?
FX equal to [Inaudible] you have [Inaudible]
in the past, this is nothing to do with static
yet.
I'm reviewing some of the principle of math.
If X equal to, equal to F time what?
Co-sign of?
Tater [phonetic] FY equal to what?
F time, Sign tater.
In this class I have seen this happen.
I hope none of you are in this category, I
have seen a student have a problem trying
to find out sign and co-sign.
This is odd to me why it's odd, because you
are going to talk about so much math in the
higher level and you are still stuck there
on the bottom that you don't know which one
is sign, which one is co-sign.
We have lots of problem to resolve, is that
correct or not?
It means in other words, your math should
be a little bit more advanced than that, so
I don't want that formula some of you RHD,
I don't know yet what that is in order to
find sign and co-sign, you don't have time
to do that.
It is adjacent is always equal to co-sign.
The front is always sign as simple as that,
is that correct or not?
So therefore, I'm sure you know what I'm talking
about.
This is F co-sign and this F sign, correct?
You put it there so you sit, again, you put
it back in that equation.
This is one-fourth, this is the second fourth,
and this is the third fourth that you are
seeing a lot of that equal to F time co-sign
tater.
I plus F sign tater.
J, sorry, and since F become a common factor
so I can bring it out, so write it as co-sign
tater.
I plus sign tater J. Each vector these are
component along the I and J, however when
I get this as common factor this is magnitude,
this must be what?
This must be,
Direction.
Direction.
Although you were using love sign, co-sign
and tater and sign tater but remember this
because next week we are going to go to 3D
problem and you are going to reverse this.
And that's very com, the reason on old exam
explaining something very simple that you
already know that to you to look at it a little
bit different in order to find out what I'm
going to do for 3D problem, which is, well
it's very simple but you have to idea here
with one angle.
I can use what, co-sign and sign, everybody
understand that, to express my lambda.
In other words, write it down in your note,
this must be according to this equation each
vector equal to magnitude and direction.
This is the vector, this is the magnitude,
this must be there direction.
Therefore this is landa, so write something
new for yourself.
Landa X actually equal to co-sign of tater
and landa Y is equal to sign of tater and
everybody knows that landa X is square plus
lambda Y square is equal to?
1.
1 because that co-sign is tater is square
[Inaudible] because that's the reason.
Is that correct or not?
Yes.
We use this format for 2D which is obvious
because many of you have used it this way.
But we expand that into a 3D problem for [Inaudible].
We keep this in mind until we get there, is
that correct or no?
Yes?
Now, when we add the vectors together this
is the representation of the vector.
These are the formula which I keep using here
and there.
This is the represention of the vector there,
then we want to add this vector together.
Now let's add these two vector together in
a separate format and see what we end up with
a formula whether I have time to do example
of that we leave it for next time, but let's
put it this way.
I have here, let's do a simple example.
Let's say here we have an XY coordinate.
Here we go.
Let's say we have here a vector going like
that which has a component of let's say 5
and 3.
So it has 5 I and 3 J going [Inaudible] is
that correct or no?
Yes?
And let's have another, this is [Inaudible]
so if I write F1 here and that [Inaudible]
everybody see is 5 I plus 3 J, give it a unit
of [Inaudible].
I can change it to newton.
Then let's look at another vector here, F2
which has here let's say 3 and 6.
Okay?
How do you represent two vector if two of
course is equal to 3 I plus 6 J?
Correct?
Okay, where is the resultant?
Like what we did earlier.
Where is the resultant.
This is a [Inaudible] I'm trying to form a
polygon, I started from 0, toe, head, toe,
head, yes?
So this is only 2.
So I'm putting the result and now this must
be the resultant R. [Inaudible], okay.
This is what is the concept of we are using
in this problem number 31, 40, and 41?
R equal to F1 and plus F2.
The black plus black equal to the green.
Yes or no?
Correct?
Vector wise, these are the vector.
This is not number.
Number doesn't match that.
Everybody I show you that is that vector because
that means the polygon in this case triangle.
Is that correct or not?
Yes?
Notice if this is more than 2 or 3, you cannot
use this vector.
You have to use a component, need that correct.
So there is two different method here.
Here I'm still using the triangle.
Anyhow, now look at the RX.
Is this from here to here, if I draw a line
here from here down here, what's RX equal?
Equal 5 plus
3.
3.
Yes or no?
Yes.
So please write it down.
This is equal to R, is equal to RX.
I plus RY J pound, these are all have to do
with a pound.
By looking at this problem I have to get F1X
plus F2 X and add it together.
Yes or no?
So therefore RX become equal to F1X plus F2X,
you have many more, or from now on we showing
it like that.
Summation of all the forces in X [Inaudible].
Which for our problem become what?
3 plus 5 equal to 8, yes or no?
So write it in this format.
So RX is summation, doesn't matter whether
FX is positive or negative, [Inaudible] then
come back, so doesn't, two of them are positive.
One of them are?
Negative.
But the resultant my resultant has a component
along the X equal to F1X, F2X, F3X, F4X, it
doesn't matter how many is there.
Is that correct or not?
Which is from now on is this formula.
So these are the concept you have to use.
RX equal to summation of FX in magnus.
Correct or not?
Yes?
What is RY now equal to?
Notice RY equal to R4, this is 3, this is
3 I should use different number.
This is 3 and 6.
It is?
9.
9.
So what I'm doing here, so RY is equal to,
I'm going to have to repeat that RY is summation
of the forces in the Y direction.
So these two formula will be handy from now
we have to solve for summation of FY.
This become two equation independent [Inaudible].
Now let's go back to the boat.
Could I have used this vector instead of triangle
method?
But [Inaudible] it says what did it say?
It said the resultant of the forces are horizontal.
What does it mean?
Summation of FY must be equal to zero.
This is the conclusion that you have to come
up with.
So sometime some of your homework assignment
this summation is horizontal, that gives you
a data.
If the summation is vertical that means that
[Inaudible] in other words this is part of
analysis if they go show you that you discover
that through the homework, yes or no.
Now what we are saying is this.
If I want my resultant, which is the green
one to be the vertical, this is RR.
No matter how many vector I have they should
start here going there, going there, going
there, yes or no.
In order to be resultant if I'm going here
4 and 4 forward, I should be coming 3 and
5 backward to make it equal to
Zero.
So summation of the forces along the X must
be equal to ?
Zero.
Which gives me a formula to use.
Is that correct or not?
Use that.
So this is when resultant's vertical or when
the resultant is horizontal, like that, again
look what happen here, depend again, depend
how many vector you have you kind of have
to be 2 or more, but depends how many you
have you may have something like that.
But then you should end up like that.
That means no matter how much you go up, you
come the same amount down.
The result must be equal to, [Inaudible].
Now if I tell you like question number one
the sum of all the forces equal to zero, then
what's going to happen?
Which is remember?
Newton's first laws.
R must be equal to [Inaudible] so then what?
[Inaudible] both of them must be equal to
zero, yes?
I already told you this one you just write
it down, this one needs sigma F, X must be
equal to zero, yes or no?
Correct?
In order R to be vertical, sigma of X must
be equal to?
Zero.
Zero.
This one, since R is horizontal write it down,
it's a picture [Inaudible].
This one requires sigma F, Y to be equal to
zero.
Right?
What I said, let's do that next time.
We are out of time anyway, so that is the
[Inaudible] what I'm going to do, I'm going
to use one or two examples here similar to
the composite and immediately move to next
class we move to equilibrium of particle.
Equilibrium of particle according to Newton
laws must some of the forces must be equal
to
Zero.
Zero or must be equal to
Zero.
[Inaudible] equation but zero, both of them.
So that is [Inaudible].
Thank you very much guys.
Thank you again.
Alright.
I don't need the syla
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