Magnitude of Force Formula |
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| \( | \overrightarrow{F} | \;=\; \sqrt{ F_x^2 + F_y^2 + F_z^2 } \) |
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| Symbol | English | Metric |
| \( | \overrightarrow{F} | \) = Magnitude of Force | \(lbf\) | \(N\) |
| \( F_x \) = x Component of the Force Vector | \(lbf\) | \(N\) |
| \( F_y \) = y Component of the Force Vector | \(lbf\) | \(N\) |
| \( F_z \) = z Component of the Force Vector | \(lbf\) | \(N\) |
Magnitude of force abbreviated as \( F_m \), also called strength of force or size of force, is a scalar quantity that represents how large or intense a push or pull acting on an object is. Unlike the vector quantity force, which has both magnitude and direction, the magnitude of force focuses only on the numerical value, without regard to the direction in which the force is applied. For example, if two people push on opposite sides of a box with forces of 50 N to the right and 30 N to the left, the magnitude of each individual force remains 50 N and 30 N respectively, even though the net force magnitude would be only 20 N in the direction of the stronger push. The magnitude of force is used in physics because it determines the degree to which an object will accelerate, deform, or change its motion according to Newton’s second law, where the greater the magnitude of the unbalanced force, the greater the resulting acceleration.
