Two forces f 1 and f 2 act at a point as shown in the...

Two forces, F⃗ 1 and F⃗ 2, act at a point, as shown in the picture. (Figure 1) F⃗ 1 has a magnitude of 8.00 N and is directed at an angle of α = 61.0 ∘∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 5.20 N and is directed at an angle of β = 54.1 ∘∘ below the negative x axis in the third quadrant. What is the x component Fx of the resultant force? Express your answer in newtons. What is the y component Fy of the resultant force? Express your answer in newtons. What is the magnitude F of the resultant force? Express your answer in newtons. What is the angle γγ that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative xx axis. Express your answer in degrees.

Transcript

00:01 The information we're given is that there are two forces acting on a point.

00:05 F1 is directed up and to the left and f2 is directed down into the left.

00:12 Okay, so here is the positive x direction and this is the positive y direction.

00:21 Okay, and we're given the forces, magnitudes, and their angles.

00:25 So first we're going to find the x component of the resultant force.

00:29 So we're going to do this by adding, okay, so the x component of the resultant force is equal to the x component of the first force plus the x component of the second force.

00:43 Okay, so we can see that for the first force, the x component points in the negative direction, and it is equal to, okay, so the cosine.

01:07 Of alpha is equal to the x component of force 1 divided by the magnitude of force 1.

01:17 So this means that the x component of force 1 is equal to f1 times cosine alpha.

01:30 Okay, and for f2, we have an x component here that makes an angle beta with the total force.

01:44 Okay, so we see that cosine of beta is equal to the x component divided by the second force.

01:53 So the x component of the second force is equal to f2 times cosine beta.

02:01 Okay, so now i'm going to substitute these into our equation.

02:06 So we have fx, the x component of the resultant force, is equal to f1, cosine alpha.

02:15 Plus f2 cosine beta.

02:21 And i'm sorry, these are all negative signs here, okay, because we know that the x components aren't not there.

02:36 It's over here.

02:40 It's negative, okay, because we can see that the x components are in the negative direction.

02:50 Or actually we can put them here as well.

02:53 So this is negative, which means this is negative, and this is also negative.

03:00 And so this is negative.

03:01 We have to add those negative signs in there because it's not going to be reflected by this.

03:06 The magnitudes here are just absolute values.

03:10 Okay.

03:11 And these cosines aren't going to have a negative sign either.

03:15 So we need to put that negative sign in ourselves.

03:19 Okay, so let's plug in our values to calculate the x component...

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