Two forces, F1 and F2, are acting at a point. Find the resultant force if the forces are at right angles.

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caledon | High School Teacher | (Level 3) Senior Educator

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It's impossible to determine the exact nature of the resultant force in this case, because we don't have any information about the magnitude of the original forces.

We also don't know the forces are directed toward the point or away from it. We do know that the resultant force will be some kind of angle relative to the forces generating it, but the direction of that angle relative to the original forces will depend upon their direction. For example, if both forces are directed toward the point, the resultant force vector will point diagonally away from both on the opposite side of the axis. If both are pulling, the resultant will point diagonally toward them on the same side of the axis. If one pulls and the other pushes, the resultant will be flipped across one of the axes.

We know the resultant will be diagonal because we can add vectors together. This is usually represented as if they are stacked on top of one another end-to-end. For example, if we have one force A acting down, and one force B to the left, each with a force of 5, then we can put the base of B on top of the end of A, and calculate the resultant vector as the hypotenuse of a right triangle whose sides are 5 and 5. The exact angle and magnitude of the resultant will depend upon the magnitudes of the original vectors.