Exercises 13-15: Three forces ( F1, F2 ), and ( F3 ) cause a...

Exercises 13-15: Three forces ( F_{1}, F_{2} ), and ( F_{3} ) cause a ( 1 mathrm{~kg} ) object to accelerate with the acceleration given. Two of the forces are shown on the free-body diagrams below, but the third is missing. For each, draw and label on the grid the missing third force vector. 13. ( vec{a}=2 hat{imath} mathrm{m} / mathrm{s}^{2} ) 14. ( vec{a}=-3 hat{jmath} mathrm{m} / mathrm{s}^{2} ) 15. The object moves with constant velocity.

Transcript

00:01 In this example, we're going to be working with vector addition, and we're also going to be looking at the relationship between forces and acceleration.

00:07 Okay, so we have three different graphs.

00:09 We have three cases.

00:13 In each case, there are three forces acting on an object.

00:17 Our object will have a constant mass for all three cases, m equals 1 kilogram.

00:24 Okay, so we have three forces acting on this object that give it an acceleration.

00:30 We are shown a graph that has two of those forces drawn in.

00:34 What we wanna do is use the information about the acceleration and the two forces that we have drawn to draw in the third force vector.

00:43 Okay, so here's the first one, and hopefully this will clear things up a little bit.

00:47 I know it's kind of hard to explain.

00:49 So we have this coordinate grid where we have x and y, both of these axes are labeled in newtons.

00:58 Okay, and we have a force, force 1.

01:04 Okay, so this is my force vector 1, f1, and this goes to the point 2, 1.

01:14 Okay, then we have force 2, and this goes to the point, this will be f2.

01:23 This point is negative 2, 2.

01:28 Okay, then we have a third force, f3.

01:31 We don't know where that is yet, but we know for these three forces, the acceleration of my object a equals 2 meters per second squared, and that's in the positive x direction.

01:45 Okay, so i have to sum up all of my forces, my three forces, to give me a total.

01:53 So we're gonna have f1 plus f2 plus f3 has to equal 2 newtons.

02:04 In the positive x direction, all right, we know that our mass is just 1 kilogram, so 2 newtons divided by 1 kilogram is 2 meters per second squared.

02:15 Okay, so what is this third force vector that we need to find? well, let's look at force 2 plus force 1.

02:23 We see the x components are gonna cancel out.

02:27 We're gonna be left with a y component of 3 newtons, so we need to get rid of that.

02:35 So in the negative direction, we need our new force, force 3 needs to go down to negative 3.

02:43 And in the y direction, or sorry, the x direction, we have 0, we want 2.

02:48 So it's gonna be 2, 3.

02:51 Our third force vector, force 3, will look like positive 2, negative 3.

02:58 So this is positive 2.

03:00 Our third force vector is gonna look something like this.

03:03 Force 3, and that goes to positive 2, negative 3.

03:07 Okay, so we're gonna do the exact same thing for the second case...

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