00:01
Okay, workmen are trying to free an suv stuck in the mud.
00:04
Use three ropes that produce the vectors shown in figure for problem two.
00:13
So i don't have the figure, but this looks to be similar, if not identical, to another problem that we have.
00:23
I guess it's kind of a commonly used one.
00:26
It looks something like this.
00:29
So the red dots, right, that's our suv.
00:32
We have a force here, force here, force here, force here, and we'll just call them f1, f2, and f3.
00:46
We're given angles here, theta 1 with respect to the x axis, theta 2 with respect to the y axis, and theta 3 with respect to the negative x axis.
01:01
I'm trying to find the magnitude and direction of the resultant.
01:06
Force.
01:08
So in other words, you have these three separate forces, but if you were to add them all up, what would be the result, right? in other words, if you had like another force, and we'll just pretend it's over here, fr, how big does fr need to be, and in what direction does it need to point to produce the exact same effect as f1 plus f2 plus f3, right? so we're just saying fr, equals vector f1 plus vector f2 plus vector f3.
01:46
F3.
01:48
Okay, so to find the magnitude of fr, fr, we're just going to take the x component of the resulting force, square it, add it to the y component of the resultant force, square it, take the square root, right? so this comes from a triangle, that is the resultant force, has a direction in magnitude, and then if we break down the components to f r y and f r x, right, then to find the magnitude, to find the hypotenuse, you just use the pythagorean theorem.
02:30
Okay.
02:32
Now i guess let's leave that up here.
02:34
And if we want to find the direction, we just say tangent theta, and we'll just use theta, regular theta, not one, two, three, four, whatever, equals opposite.
02:49
So that's the y component over adjacent.
02:52
It's the x component.
02:56
So theta is the inverse tangent of the y component over the x component.
03:04
Okay...