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Three forces act on an object. Two of the forces are at an angle of $ 100^\circ $ to each other and have magnitudes 25 N and 12 N. The third is perpendicular to the plane of these two forces and has magnitude 4 N. Calculate the magnitude of the force that would exactly counterbalance these three forces.

26.09 $\mathrm{N}$

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Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

talk about this question? Have we given our three forces act on an object? And 22 of the forces are at an angle of 100 degrees to each other. And have a magnitude of 25 20 newtons, respectively. The third force is perpendicular to the plane. All these two forces and has a magnitude of four Newton's wind. To calculate the magnitude of the force that will exactly counterbalance, that were exactly counterbalance these three forces. So we're gonna draw simple figure that represents the situation. Let these be the true vectors which are separated by an angle of 100 degrees and they are lying in the same plane. So this is a 25 newton. This is 12 newtons and we have a third force which is perpendicular to the plane. So, if this is an xy plane, that the other forces can be represented by a cross symbol, Which means that it is going into the plains. Or does that 90° with respect to these two planes? And that has a magnitude of four Newton's. Uh So you got to find the net Force of these vectors, these forces. So, first, let's talk about these two forces. So they are separated by an angle of 400°. So we're going to say that if let's call it F one. So F one is going to be equal to uh F one is going to be equal to that's going to be equal to the square root of 25 square plus 12 square plus two times 25 times 12 times cause of 100 degrees. So this is the formula for the reactor edition, uh for the factor edition. And let me grab my calculator. So that's going to be equal to plus uh the 12 cause 100 degrees. So that's coming as 25.25.78 Newtons. And if this is 25.78 Newtons, we have another force which is perpendicular to word, which is this for Newton's so we can represent it like this. So this is for Newton's it's not in uh in a downward direction, but if it is seen from this side seen from this side, it looks downward. So this is four new tenant. This is 25.78. So the F net is definitely gonna be square root of four square plus 25.78 square. So let me do that. That's going to come out as 26.09. So 26.09, Newton is the net force and the same forces required to counterbalance these forces. Thank you