Physics

Physics

Problem

Two forces act simultaneously at a point: F1=6 i^−2 j^ N\mathbf{F}_{1}=6\,\hat i - 2\,\hat j\,\text{N} and F2=−4 i^+8 j^ N\mathbf{F}_{2}=-4\,\hat i + 8\,\hat j\,\text{N}. a. (a) Obtain the magnitude and direction of the resultant force Fres=F1+F2\mathbf{F}_{\text{res}}=\mathbf{F}_{1}+\mathbf{F}_{2}. Give the direction as an angle measured from the positive x–axis. b. (b) A third force F3\mathbf{F}_{3} is applied so that the point remains in translational equilibrium. Determine the magnitude and direction of F3\mathbf{F}_{3}.
Intuitive explanation

When multiple forces act on the same point, they combine as vectors—you simply add their components independently. The key is to treat the ı^\hat\imath and ȷ^\hat\jmath directions separately, then find the magnitude and direction of the net force. This is the foundation of understanding how forces superpose in physics.

Intuitive explanation

When multiple forces act on the same point, they combine as vectors—you simply add their components independently. The key is to treat the ı^\hat\imath and ȷ^\hat\jmath directions separately, then find the magnitude and direction of the net force. This is the foundation of understanding how forces superpose in physics.

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