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Problem 53 Medium Difficulty

ssm Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?

Answer

100 $\mathrm{N}$

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Video Transcript

in this question. We have three forces that are acting on an object that is supposed to move with constant velocity. So remember that constant velocity means zero acceleration. We've standing mind. We proceed to apply Newton's second law. So let me choose my reference frame as being these one. Everything that is pointing up on the Y direction is positive, and everything that is pointing right on the X direction is positive too. Them we have fine Newton's second law on each of those directions. On the wider action we have the following The net force on that direction must be equal to zero because the acceleration is it close to zero. Now, what is the net force in the Y direction? Well, there are two forces these 18 years on force and a portion off this force F on that portion off the force F is these one. It is the Y component off that force and then we also have the X component. But for the vertical direction, we have 18 you times minus the vertical component off the force f these physicals zero So half component Wife, is it close to 80 Newtons? Now we proceed to calculate the next component, the X component off that force F. For that, we have to apply Newton's second law on the X direction. Dr Actual. Newton's second law tells us that the net force is equal to zero to because the object is moving with constant velocity. Then in that direction, we have to forces F Component X and the 60 Newton Force. So these goes to zero. Therefore, F component X is he goes to 60 new terms. These already of ours to calculate what is the magnitude off the force f. So no to that this is a rectangle triangle. Then it's true that half squared is equals. Two f x squared plus f y squared them half is equals to the spirit off 60 squared plus 80 squared. And this gives us a magnitude off 100 new terms. So this is the magnitude off the force f. Now we have to determine what is the direction off that force. Let us call these on. Go here. Then again using the rectangle triangle. It's true that the tangent off Tita is it goes to have component X divided my f component. Why the reform that tangent off Dita is your course to 60. Divided by 80 we came to me simply fired to three, divided by four. Then Tita is equals to the inverse tangent off three divided by four. And these is approximately 36 0.9 degrees. Then these other angle right here is he close to 90 miners 36.9, which is the question 53.1 degrees, then these east 53.1 degrees. Therefore, indirection is 53.1 degrees self off east or 36.9 degrees east off south.