Two structural members b and c are bolted to bracket a...

Two structural members $B$ and $C$ are bolted to bracket $A .$ Knowing that both members are in tension and that $P=10 \mathrm{kN}$ and $Q=15 \mathrm{kN}$, determine graphically the magnitude and direction of the resultant force exerted on the bracket using ( $a$ ) the parallelogram law, $(b)$ the triangle rule.

Transcript

00:01 Here we have two forces, one 10 kiloons at 25 degrees above the horizontal, the other 15 kiloons at 50 degrees below the horizontal.

00:11 We're asked to find the resultant of the two forces graphically using the parallelogram rule and then the triangle rule.

00:18 So because we need to draw these to scale using a ruler and some type of angle gauge, i set my scale to 10 kilonutons is equal to 1 inch.

00:29 So the red vector here of 10 kilonitons is 1 inch long, and the blue vector of 15 kilonitons is 1 .5 inches long.

00:38 So first we're going to use the parallelogram rule, which means we're going to draw a parallelogram using these two vectors as the equal sides.

00:49 So we'll start with the blue, okay, and we'll connect that, the tail of that one to the tip of the 10 kilon -newton force.

01:04 And there's that, and then we'll do the 10 -kill -newton force from the tip of this one, to the tip of that one.

01:20 So there we have our parallelogram, and all we have to do is connect two vertices between both tails to both tips of the other two forces.

01:35 So in there we have our resultant.

01:38 Now all you have to do is get your ruler, measure the length of that resultant force, in this case the green.

01:45 Line and what i got was i got close to two inches so that would be able to a force of 20 kilonutons and then when i measure this angle i get an angle of 22 .6 degrees and there is the result in using the parallelogram rule next we'll use the triangle rule which as you've seen, i've already arranged them...

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