If two forces act in opposite directions how do you find the magnitude and direction of their resultant

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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If two forces are acting in the opposite directions (180 degrees apart), the magnitude of resultant force would simply be the difference in the magnitude of the two forces. The direction of the resultant force will be same as the direction of the force with greater magnitude.

For example, a 10 N force is acting in east direction, while a 20 N force is acting in west direction. Using a sign convention of positive being in east direction and negative in west direction ( or something similar on a number line), we can denote the direction of forces with positive and negative signs. The magnitude of the resultant will be 10 + (-20) = -10 N. Using the sign convention, we know that the resultant is acting in the negative or west direction, which is the same as that of force with higher magnitude.

Hope this helps.

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