Determine the magnitude and coordinate direction angles of the resultant force acting at point A

step 1 All right. We've hit the century mark kind of on our problems here. For 100, notice that the ans

Determine the magnitude and coordinate direction angles of...

Key Concepts

Coordinate Direction Angles

Coordinate direction angles are the angles that a vector makes with the coordinate axes. They are used to describe the vector's orientation in space relative to a given coordinate system, typically calculated using the relationships between the vector's components and its magnitude.

Vector Magnitude

The magnitude of a vector, often computed using the Pythagorean theorem in two or three dimensions, represents the size or length of the force. In the context of forces, it quantifies the overall strength of the resultant force.

Vector Addition

Vector addition is the process of combining multiple vectors by summing their corresponding components. This is essential for determining the resultant force when several forces act on a single point, ensuring that both magnitude and direction are accurately accounted for.

Resultant Force

The resultant force is a single force that has the same effect on an object as all the individual forces applied simultaneously. It is obtained by vectorially adding the individual forces, and it provides a comprehensive summary of the net influence acting at the point.

Transcript

00:02 All right.

00:04 We've hit the century mark kind of on our problems here.

00:10 For 100, notice that the answer is not in the back of the book.

00:14 And we need to find the resultant force.

00:17 Oh, my goodness.

00:19 So how do i want to do this? i think that what i'm going to do is i'm going to try to do it the way that seems to be a little easier.

00:38 A little less technical though.

00:45 I'm going to draw it, but i'm going to put some things on the drawing that aren't there on the book's drawing.

00:58 So we've got a point c over here, but the distance out to point c is four.

01:17 It's just four meters.

01:24 So this distance is four meters here.

01:28 This distance is 3 meters, and that is shown.

01:37 All right, and that's the distance to point c.

01:40 The distance to point a is also 3 meters, and then we've also got a point b way out here, and it's showing that this is 2, and this is 4.

02:11 All right, so i think this will work out.

02:16 Got a force here, and i've got a force there.

02:23 Fab is 200.

02:26 Newton's, fac is 150 newton's.

02:34 We've got to figure out the resultant.

02:37 So, first of all, uab, or rather, let's just go to fab, is going to be fab times the vector form of uab.

03:15 Well, in the x direction, it's going to, in the y, direction it's going four and in the z direction it's going three two squared plus four squared plus three squared okay f ac is just going to be f ac times oh wait a minute there should be a negative here positive positive negative okay f ac is going in the negative negative direction and in the negative y direction and in the negative z direction.

04:26 Everything's negative on that one.

04:28 So it's going to go negative 3 in the x direction, negative 4 in the j direction, and negative 3 in the k direction.

05:00 That's it.

05:01 Well, that's not it because now i've got to add them all together.

05:06 What is the square root? you know, these are not going to work out nicely.

05:12 Trying to think of what's the best way to do this now.

05:17 Well, i'm just going to write it down.

05:27 All right.

05:29 200 times 2 over the square root of 2 squared plus 4 squared plus 3 squared.

05:51 That gives me 74 .3.

06:03 4 is the next one.

06:06 4 in the numerator...