Question

A weightless rod CD, 1.0m long is acted upon by horizontal forces of 2N, 4N, 8N is shown in the figure. What force will be necessary to produce equilibrium?

Answer 1

Since there is no figure shown, hope these basic principles will help to solve the real problem. 8N acts on the left edge down, and on the right 2N - up and 4N - down.

Moment of force equals force times distance (from the point where the force is applied to the axis of rotation):

$M=F\cdot d$

Forces that try to move a rod upward are positive, downward - negative. For equilibrium, a sum of moments on the left must be equal to the one on the right:

$-8N\cdot \frac{l}{2}+ x\cdot \frac{l}{2} =2N\cdot \frac{l}{2} - 4N\cdot \frac{l}{2}$

From this we get that x is the force acting upward on the left edge and is equal to 6N.