Solve it without values

Physics

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Step-by-step solution

3 steps

  1. Define the forces and angle.

    Let the magnitudes of the two forces be F1F_1 and F2F_2. Let the angle between these two forces be θ\theta.

  2. Calculate the magnitude of the resultant force.

    According to the parallelogram law of forces, the magnitude of the resultant force RR is given by the formula:

    R=F12+F22+2F1F2cos⁡θR = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta}

  3. Calculate the direction of the resultant force.

    Let α\alpha be the angle that the resultant force RR makes with the force F1F_1. This angle can be found using the formula:

    tan⁡α=F2sin⁡θF1+F2cos⁡θ\tan \alpha = \frac{F_2 \sin \theta}{F_1 + F_2 \cos \theta}

    Therefore, the angle α\alpha is:

    α=arctan⁡(F2sin⁡θF1+F2cos⁡θ)\alpha = \arctan \left( \frac{F_2 \sin \theta}{F_1 + F_2 \cos \theta} \right)
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