If 9 forces, each of value 100 N, are applied at 36°, what is the resultant force?

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caledon eNotes educator| Certified Educator

As written, there are some elements of this question that could bear further clarification; for example, what direction are the forces pointing it? Being at 36 degrees doesn't tell us if all of the forces are in the same direction, as any pair that are opposite would cancel each other out. However, assuming that all the forces are pointing in the same direction, then the force should be 900N. All vectors are additive, and you can visualize this by drawing each vector as an arrow that corresponds in size and angle with its given value, then placing the end of one arrow on the tip of another. In this case, you'd just have a bunch of 100N arrows all lined up back to back, adding up to 900N.

We could also specify that the vertical force and horizontal force exerted by this vector would be different. If we treat the vector like a Pythagorean triangle, then the vertical vector is 900N x sin36, which is 294N, and the horizontal angle is 900N x cos36, which is 728N.