<Lecture HW 9 Problem 12.36 You want to hang a 11-kg sign...

<Lecture HW 9 Problem 12.36 You want to hang a 11-kg sign that advertises your new business. To do this, you use a pivot to attach the base of a 7.0-kg beam to a wall (Figure 1). You then attach a cable to the beam and to the wall in such a way that the cable and beam are perpendicular to each other. The beam is 1.5 m long and makes an angle of 37° with the vertical. You hang the sign from the end of the beam to which the cable is attached. Part A What must be the minimum tensile strength of the cable (the minimum amount of tension it can sustain) if it is not to snap? Express your answer with the appropriate units. Figure 1 of 1 $T = $ Value Units Submit Request Answer Part B Complete previous part(s) 37° pivot

Transcript

00:01 Okay, in this problem we have a sign that is being attached to this beam, and the beam is, has a cable attached to it in the wall so that the beam doesn't rotate.

00:21 It looks something like this.

00:23 Here's our wall.

00:25 Here's our beam.

00:28 There's our cable.

00:30 And from the cable, you hang your sign.

00:37 Okay, so and then this angle here is theta, this angle here is 90 degrees.

00:49 Okay, and we want to know what is the minimum tensile strength or the minimum amount of tension it can sustain, so it does not snap.

01:05 Okay, well, for this problem, usually when you have like some stuff hanging and you want to find a force tensile strength you're gonna want to look at the forces so the forces in the forces in the y and then you want to look at the torque or the moments whatever you want to call them and usually between three of these things you can find what you need so for this to not snap what has to be true all of our forces need to be balanced so nothing's moving and it's not rotating so we want the torque to be balanced as well okay let's draw us some free body diagram here so i'm going to draw this again over here because the angles are the trickiest thing in my opinion so there's our tension t we have our sign we'll just call it m that mass m times g we have the weight of the rock the weight of the rod, i'm going to actually draw these really long for trigonomic reasons.

02:28 So the mass of the beam, we'll call m sub b, and it times gravity.

02:34 The mass of the beam, you can always draw gravity acting through the center of mass of something.

02:40 So if you take your beam, you go halfway along, that's the center of mass of our beam because it's uniform density.

02:48 So the gravitational force is acting through the center of mass.

02:55 Okay, and then we also have, at this pivot point, we have some, i like to use r.

03:00 We have a reaction force in the y and in the x, because there's some forces acting on that pivot point.

03:07 Okay, there's our forces.

03:10 Now let's figure out some angles because we're going to use x and y coordinates.

03:16 And some of these forces are not in x or well they're not in just x or just y they're in both okay so well it's just the tension actually tension force let's see if we can break down the tension force we okay so if we call that our triangle there we could make let's think for just a second this angle is 90 degrees.

04:03 Okay.

04:09 Let's see here.

04:17 Okay, so that would make this angle.

04:19 Yeah, that angle's theta.

04:21 It's probably easier to look at it on this other drawing.

04:25 If we break it down like this, this angle down here's theta, which means this one is not, which means this one is.

04:33 That's usually the way i do it.

04:36 Okay.

04:38 So there's our angle theta.

04:39 It turns out we're not actually going to need it, but it's good practice to draw it.

04:44 And then if we're looking at our gravitational forces, it's good to draw the angle theta there too.

04:52 So theta and theta.

04:56 Okay.

04:59 So let's do some of the forces in the x equals zero...

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