Solve Force F Moment Problem: Find Mag. & X-Intercept

[asteg123]

The force F has a moment equal to 250N.m with respect to point O -400N.m with respect to point B and has a zero moment with respect to point A.

http://freewebs.com/mcroldan08/prob.jpg

Find the magnitude of F and the x-intercept.


OK, here's what I did,

Using the formula for moment I got the force F*sub*B

M=Fd
-400N.m=F(2.4m)
F=-166.67 N

I think this is the y-component... right??

anyways, I got F*sub*A as zero...

Now, I can't figure out a way to utilize the moment in O and as well as get the intercept and the force...

can anyone help me??

 

[OlderDan]

The line of the force must go through A to have no moment. Where does it have to be in relation to O and B so that the moments about those points have opposite signs?

 

[kyle8921]

Based on the information provided, it seems that the force F has a moment of 250N.m with respect to point O and a moment of -400N.m with respect to point B. This means that the force is creating a clockwise rotation around point O and a counterclockwise rotation around point B. Since the force has a zero moment with respect to point A, this means that it is not creating any rotation around that point.

To solve for the magnitude of the force F and the x-intercept, we can use the principle of moments. This principle states that the sum of the moments of a system of forces about any point is equal to the moment of the resultant force about the same point. In this case, we can choose any point to calculate the moment, but it is most convenient to choose point O.

Using the principle of moments, we can set up the following equation:

250N.m + (-400N.m) + 0 = F*x

Where F is the magnitude of the force and x is the x-intercept. Solving for F, we get:

F = (400N.m - 250N.m)/x = 150N.m/x

To find the x-intercept, we can use the fact that the force has a zero moment with respect to point A. This means that the force must pass through point A in order to have a zero moment. Therefore, the x-intercept is the distance from point O to point A, which is 2.4m.

Substituting 2.4m for x in the equation above, we get:

F = 150N.m/2.4m = 62.5N

Therefore, the magnitude of the force F is 62.5N and the x-intercept is 2.4m.