Three forces act on the bracket as shown in Figure 1: y 4...

Three forces act on the bracket as shown in Figure 1: y 4 kN F 15° ? 30° x' X 6 kN Figure 1 a) Find the magnitude and direction of F so that the resultant force is direct along the positive x-axis and has a magnitude of 8kN. [10 Marks] b) If F = 5 kN and u = 30°, find the magnitude of the resultant force and its direction, measured counter-clockwise from the positive x-axis. [10 Marks] (CLO1-PLO1:C2) [Total: 20 Marks]

Transcript

00:01 All right, so here we have two forces f1 and f2 acting at a point, and we're trying to resolve them into components that fall along these u and v axes.

00:10 Now careful, because the first thing we should notice is that these axes, u and v, are not 90 degrees apart.

00:15 They're not perpendicular.

00:17 They're actually 75 degrees and 105 degrees, so it's not an even number.

00:21 So it's going to make the trigonometry a little bit more confusing here, but just bear in mind.

00:25 So first, what we should do is try to resolve the forces into one of the axes components.

00:32 So let's go ahead and take a look at v first.

00:35 Let's find the v1 component from f1.

00:38 Well, if we take a look at f1, what we could do is draw a dotted line towards the v axis, and we know that the force is going to be equal to whatever f1 is times cosine, because cosine is adjacent over hypotenuse.

00:53 And in this case, from this angle, the adjacent is the v axis we're looking for.

00:57 So cosine of 30, and that's going to give us approximately 3 .46 kilonewtons.

01:07 Okay, and then let's find the component for v2.

01:10 Well, v2, again, we're going to go ahead and draw a dashed line to the v axis, make that a right triangle.

01:16 And this time, we know if this is 30, this angle is not really going to help us.

01:20 It's not part of the triangle we just made.

01:22 We've got to find this angle.

01:23 Luckily, we know that the whole thing is 105.

01:26 So if 30 is over here, that means 75 is also here.

01:29 So this triangle has an angle of 75, and his component will be f2 cosine of 75 degrees.

01:38 Now keep in mind, this is in the opposite direction of our original v component, so it's going to be negative 1 .55 kilonewtons.

01:47 Okay, on to our u component...

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