Specify where its line of action intersects member ab...

Name: specify where its line of action intersects member ab measured from point a express your answer to three significant figures and include the appropriate units d 230 ft submit previous answer 77787
Uploaded: 2023-05-03T22:15:14-08:00
Duration: 11 min 17 s
Channel: Emily Anderson
Description: specify where its line of action intersects member ab measured from point a express your answer to three significant figures and include the appropriate units d 230 ft submit previous answer 77787

Specify where its line of action intersects member $AB$, measured from point $A$. Express your answer to three significant figures and include the appropriate units. $d = 2.30$ ft Submit Previous Answers Request Answer Incorrect; Try Again; 5 attempts remaining Provide Feedback Figure 2.5 ft 3 ft B 2 ft $F_1$ 4 ft $F_2$ 1 of 1 45° $F_3$

Transcript

00:01 In this example, we have a rod attached to a wall.

00:06 It's being supported by three forces, by three supports.

00:10 So here's our wall, and we have this little wall plate here.

00:17 And we have attached to this a rod.

00:21 It's free to rotate here about this point a.

00:26 We have three forces acting on it.

00:28 We have f1, okay, that's in the vertical direction.

00:34 And that's a distance of three feet away from the wall.

00:39 We have force f2 that acts at the end.

00:44 Here, let me draw this in a different color.

00:48 Force 2 acts at the end of the rod, a distance of nine feet total from the wall.

01:01 So this distance here is nine feet, okay? this is f2, okay, and that acts at some angle of theta with respect to the horizontal.

01:18 Then we have our last force, force 3, that acts in between.

01:25 Let's make that a different color, 2.

01:27 Okay, so this is in between force 1 and force 2.

01:32 We have force 3, okay? this acts at some angle with respect to the horizontal, and we're given that the angle is the same as the triangle that has sides 5, 4, and 3.

01:48 So we'll find that angle in just a second, okay? and this force acts at a distance of six feet from the wall.

02:00 Okay, we want to replace these three forces with one force, one resultant force.

02:05 So first thing we're going to do is take the sum of the forces.

02:12 Then we want to find where it's going to act, where it's going to intersect with this red rod.

02:18 I'll just call that rod a.

02:20 We'll call that rod ab, okay? so rod ab.

02:25 Where will this force be located? okay, so we're going to need to use forces, and we're going to need to use torques to determine that location.

02:36 So first, let's get some numbers so we can actually start doing the problem.

02:41 Okay, i have the magnitudes of force 1, 2, and 3.

02:46 Okay, force 1 equals 240 newtons.

02:53 Actually, no, sorry, we're working in pounds.

02:56 So 240 pounds for that force, okay? force 2 has a magnitude of 60 pounds.

03:07 Okay, and that angle is theta equals 30 degrees.

03:12 That's with respect to the vertical.

03:14 Then my third force has a magnitude of 140 pounds.

03:20 Okay, and that is, let's find this angle here.

03:23 So we know that cosine of that angle is equal to 4 over 5.

03:29 Okay, so that angle theta, i'll call that theta.

03:32 This will be theta 2, this will be theta 3.