TITLE: Position of resultant of two like parallel forces
QUESTION [0 upvotes]: I am solving Statics and stuck in middle of a trivial understanding.
Let us say we have two like parallel forces acting on a rigid body. Force $P$ has point of application as A and Force $Q$ has point of application B. Something like this:

How do i prove that the resultant $R$ lies such that
$$P \cdot AC = Q \cdot BC$$

REPLY [1 votes]: You can only say that PxAC=QxBC if you are told that there is no net torque (no rotation) of the rigid body about the point C.  Of that is the case then the resultant of the two forces P and Q at at point C is simply a vertical force of $R=P+Q$ with no rotation about the point C.

Let us say that there is no torque. How do i prove then P . AC = Q .
BC ?

If there is no net torque about the point C then the sum of the torques about C has to be zero. Letting clockwise torques being positive, that means the net positive torque about C (the force P times its moment arm AC) has to equal the net negative torque about C (the force Q times its moment arm of BC).
Hope this helps.
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