Newton's First Law Exercises 17, 18, and 19 show two of the three forces acting on an object in equilibrium. Redraw the diagram, showing all three forces. Label the third force F3.

Question

Diagram showing two forces Fa and Fb acting on an object, with a yellow dot at the center.

Accepted Answer

Hey, everyone in this problem, we have a diagram that shows a ball in equilibrium. We have two forces applied on the ball that are shown. And there's a third force that we need to draw on this diagram. We're gonna label it F C in order to complete the diagram. So we have our two forces fa and F B fa points down to the left in quadrant three and F B points down to the right in quadrant four. Now we're told that this ball is in equilibrium. What we know about equilibrium is that the sum of the forces in the X direction must be equal to zero and the sum of the forces in the Y direction must be equal to zero. OK. So I've just written them out here. So we have some room to work with these. Now, let's start with the X direction. OK. The sum of the forces in the X direction is gonna be the force A in the X direction, pull off the force be in the next direction plus the four C in the extraction. And all of those X components added up has to equal zero. Now fa and F B, what we can see is that they're the same distance away from the vertical axis. OK. So they have the same magnitude of that X component but they're in opposite directions. OK. So the X component of force A is equal to negative the X component of force B. OK. Equal in magnitude opposite in science. So if we substitute this into our equation, we have that negative F B X plus F B X plus F C X is equal to zero. OK. Those first two terms add to zero and we're just left with the X component of this force C is going to be equal to zero. OK. So we could see that from the diagram in order to be an equilibrium, we need to have the X components adding up to zero. Yeah, the X component of A and B have the same magnitude but opposite signs. So those are gonna add to zero, which means that the X component of our new force must be zero. OK? So it's gonna lie along the Y axis. Now let's switch over to the Y component from our diagram. We can see that FA and F B both have a negative Y component. So we expect that our force F C is going to have a positive Y component to counteract those. OK. And it's gonna be have to be twice the vertical distance of FA and F B since we have to sum them together. So same thing, we're gonna do this using the equation mathematically. OK? We understand it conceptually, we've just talked about it. Now, let's see how the math works out. Now, these two forces point the same distance downwards. OK? And they have the same sign, they're both below the X axis. They're both in the negative Y direction. So when we have the sum of forces in the Y direction, we have the Y component of force A plus the Y component of force B ask the Y component of four C not as equal to zero. Now, we've just said that the Y component of force A is equal to the Y component of four B. So we can substitute that in and we have that two multiplied by the Y component of force A plus the Y component of four C is equal to zero. And so the Y component of four C must be equal to negative two multiplied by the Y component of force A. OK. And so this tells us all of that information we talked about when we looked at the graph, OK? It's negative. The Y component of force A, OK. Force A is pointing downwards. So that means it's gonna be pointing upwards which is what we expected and it's two times OK. So it's a larger magnitude, it is bigger which again we expected so that we could counteract both of those downward acting forces. So we go to our diagram. Now we are going to draw in green, this force F C, the X component is zero. So it's on the Y axis and it has a larger Y component than those original vectors that are pointing downwards. And so F C is going to look something like this. A large arrow pointing straight upwards. That's it for this one. Thanks everyone for watching. I hope this video helped.

Newton's First Law Exercises 17, 18, and 19 show two of the three forces acting on an object in equilibrium. Redraw the diagram, showing all three forces. Label the third force F3.

Verified Solution

Key Concepts

Newton's First Law of Motion

Equilibrium

Vector Addition