A uniform sign of weight Fg and width 2 L hangs from a...

A uniform sign of weight $F_{g}$ and width $2 L$ hangs from a light, horizontal beam hinged at the wall and supported by a cable (Fig. P12.31). Determine (a) the tension in the cable and (b) the components of the reaction force exerted by the wall on the beam in terms of $F_{R}, d, L,$ and $\theta .$

Transcript

00:01 In this problem, we have been given that there is a signboard and the weight of the signboard which acts at the center of mass.

00:08 That is given as fg and the width of the signboard is 2l as shown here.

00:17 It hangs from a beam which is light and that's horizontally placed.

00:22 So there is a cable supporting here and we need to determine the tension that's acting on this cable.

00:28 So let's consider the tension t and we can take the component of this tension, so it will be t sine theta and t cost theta respectively.

00:39 So in order to figure out the tension, we consider the moment about this point, let's say o.

00:45 So the net clockwise moment that will be because of the weight, so that's fg into its perpendicular distance from this point o.

00:54 That's d plus l.

00:55 And this is equal to the total anti -clockwise moment that's because of the perpendicular component of the tension.

01:04 So that will be t -sign theta into its perpendicular distance.

01:08 So that will be d plus 2l.

01:10 So from here we can solve and get the value of the tension that will be fg into d plus l divided by sine theta into d plus 2l.

01:22 And that's the value of this tension force.

01:26 In the next case, we have to figure out the components of the reaction force that's exerted by the wall.

01:33 So let's consider the force fx and fxy that's acting at this point.

01:42 So in this case, if we apply the idea that the total force in the x and y directions are balanced, because the complete system is given to be in equilibrium here...

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