The Resultant Along A Line



It may be desired that the resultant be found, of multiple forces acting along multiple directions. It may also be required that the resultant must lie at a specific angle. If this is the case, and the angle is given, then a relation can be formed by utilizing the known angle. If the angle is known, then one side divided by the other is going to be a numerical value.

For example, here you have AB, AD, and AE. If the tensions in AD and AE are known, then what is the tension in AB if the resultant is to be directed along AC? What then is the resultant force?

Just write something in the form of: ∑Fx / ∑Fy = sin70 / cos70. Where you have one equation and one unkown. The unknown is the force AB. Just express the force in the x and y direction for AB in the form of FAB. The thing is in order to solve for AB you may need to use some trig relations, like sin / cos = tan. See Trigonometric Identities.