Resultant Force in Non-Perpendicular Forces and Law of Cosines

Apuntes

In physics, the composition of forces involves determining the resultant force when multiple forces are acting on a body. The resultant force, denoted as $FR$, can be calculated using the Pythagorean theorem when the forces are perpendicular to each other. The formula is: This equation is used when two forces, $F1$ and $F2$, are acting at right angles. When the forces are not perpendicular, the formula to calculate the resultant force includes the angle $\alpha$ between the two forces: This formula accounts for the angle between the forces, providing a more general solution for the resultant force. In geometry, the law of cosines is used to find the length of a side in a triangle when the lengths of the other two sides and the included angle are known. The formula is: $$C^2 = C^2 + C^2 - 2 \cdot C \cdot C \cdot \cos B$$ This equation is used to calculate the length of a side in a triangle, where $C$ represents the sides of the triangle and $B$ is the angle between them. The law of cosines is particularly useful in solving triangles that are not right-angled.