mr.p: Good morning.
Today I'm going to show you how to use a data table
to make it easier to solve vector addition problems.
Here we go.
Bo: Hey guys.
Billy: Hey, Bo.
Bobby: Hi, Bo.
♫ (lyrics) Flipping Physics ♫
mr.p: Last time we did a vector addition problem where
we added the displacement vectors A, B, and C
together to figure out our resultant vector, R.
Vector B was neither directly in the X direction,
nor directly in the Y direction,
so we needed to break Vector B into
its components in the X and Y directions.
Once we did that, we redrew our vector diagram,
and we had a right triangle, so we were able to use
SOH CAH TOA and the Pythagorean Theorem
to figure out our resultant vector.
Now I did have to draw the vector diagrams a little bit
smaller this time, in order to make more space on the board,
and what we're gonna do now is we're gonna
look at the same problem, using a data table.
In the first column,
we have the names of the vectors,
A, B, C, and R, the resultant vector,
or the total displacement vector.
In the next two columns we have the components
of each of the vectors in the X and Y directions,
and both of those are in centimeters.
Bo, Vector A is 50.0 centimeters East,
could you please tell me what is
the component of Vector A in the X direction?
Bo: That would be 50 centimeters.
mr.p: And Bo, what is the component
of Vector A in the Y direction?
Bo: That would be 50 centimeters.
mr.p: Actually, Bo, the component of Vector A in the
X direction is 50 centimeters, but the component
of Vector A in the Y direction is not also 50 centimeters.
Who can tell me what the component is
of Vector A in the Y direction?
Billy: Vector A is only in the X direction, so it doesn't have
a Y component, so the Y component of Vector A is zero.
mr.p: Correct, Vector A is only in the X direction,
therefore it has no component in the Y direction,
therefore the Y component is going to be equal to zero.
Bobby, Vector C is 30.0 centimeters North.
Please give me the X and Y components of Vector C.
Bobby: Vector C is only in the Y direction, so its X component
is zero, and its Y component is 30 centimeters.
Bo: Hey, Bobby, why isn't he writing
"centimeters" on the numbers in the data table?
Bobby: Oh, he wrote the dimensions at the top
of the column in the column label,
right where it says, "Centimeters".
That applies to the whole column, so he wouldn't
have to write it on every number in the column.
Bo: Oh right, yeah that makes sense, thanks.
Bobby: You're welcome.
mr.p: And Billy, could you please give
me the components of Vector B?
Billy: Those are already written on the board, actually.
B in the X direction is 22.943 centimeters,
and B in the Y directions is 32.766 centimeters.
mr.p: You are correct, we already figured out
the components of Vector B in the X and Y directions.
Notice that all of the numbers are positive,
because all of our components were either north or east.
If any of the components had either been
south or west, they would be negative.
Bo: What do you guys do in your club?
Billy: Well in physics club,
we talk about physics,
properties of physics.
mr.p: Notice how easy this makes it to find
the components of our resultant vector.
The resultant vector in the X direction is just the
summation of all the components in the X direction.
You just add everything in this column:
50 plus 32.766, plus 0 is 82.766 centimeters.
And we can add all the components in the Y direction,
to figure out the resultant vector in the Y direction:
0 plus 22.943 plus 30 is 52.943 centimeters.
And you can see that the components of Vector R
add up to to the same resultant vector
as we solved for in our previous lesson.
In summary, using a data table can make
solving vector addition problems much easier.
Now it might not have seemed like it made this one
much easier, because this was a rather simple problem,
but as the vector addition problems get more and more
complicated, you will discover that using a data table
definitely makes them much easier to solve.
Thank you very much for learning with me today.
I enjoyed learning with you.