Three control rods attached to a lever a b c exert on it the...

Three control rods attached to a lever $A B C$ exert on it the forces shown. ( $a$ ) Replace the three forces with an equivalent force-couple system at $B$. (b) Determine the single force that is equivalent to the force-couple system obtained in part $a$, and specify its point of application on the lever. (Figure cant copy)

Transcript

00:01 3 .89 in this problem there are three forces are acting on the system and we have to replace these three forces by a single equivalent force couple system at point b so for the calculation of equivalent force we can observe one thing that these two forces 20 lb 20 point forces are antipadled to each other and are separated by some distance so these vectors will cancel out each other and they will have no effect on equivalent forces so the only effect on equivalent force will be because of this 48 point force so equivalent force will be 48 now talking about its direction so from horizontal let's say it is making an angle theta so for the calculation of this theta we can do some geometric interpretation here that we can extend this abc line in this direction so this abc line and this direction will be perpendicular to each other so this angle is 55 degree so this angle will be 35 degree and if we draw a horizontal line from point c so in the problem it is given that this is making an angle 30 degree this is mentioned in problem so this angle will also be 30 degree so 48 point force is making an total angle 65 degree with horizontal so theta here comes out to be 65 degree so this was the equivalent force acting at point b now for the calculation of moment so there will be two moment one moment will be caused by these two anti -parallel forces.

02:04 So let's say that moment caused by these anti -parallel forces is m1.

02:08 So and considering the anti -clockwise direction to be positive, so these are causing a clockwise couple.

02:16 So first of all, their sign will be negative.

02:19 Now talking about the magnitude, we have two options.

02:23 Either we can resolve these forces into its perpendicular component or we can draw a perpendicular line between these two line of action.

02:31 So let's draw a perpendicular line between these two line of between these two line of action of the force.

02:41 So if we draw a perpendicular from this line, let's say this is the perpendicular and this is m...

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