Finding Point for Adding Forces Acting on Object

[rew]

I've searched the forum, and found several topics about adding vectors. This one is not as easy... :-)

Suppose I have an object. There are two forces acting upon it. One is acting on a point at -5,0 and the other at +5, 0. The one at -5,0 has magnitude sqrt(17), pointing up (positive y) 4 units and towards the origin 1 unit. The one at +5,0 is pointing -1,4 also sqrt(17) N.

Now I can add the vectors, and I end up with an 0,8 vector of resultant force. However, where does this resultant force act? In this case it will be on the Y-axis, but where?

When the forces are parallel I can find the resulting point: say 1N (0,1) at -1,0 and 3N (0,3) at 3,0 will result in 4N (0,4) in the origin. But how do I find the resulting point if the forces are not parallel ?

Now, back to my original situation. If I add an 0,-8 force in the origin, the total force will be zero. Total moment as well.

However if that force is tilted, say in the -1,-4 direction, do I get a moment around the origin? I think I do. I think I could model this resulting moment by finding a point where the resulting 8N force acts.

Can someone explain how I can find that point?

 

[ZapperZ]

You seem to have a problem with basic vector operations (forces are vectors). So maybe you should look at the mathematics of vectors. Start here:

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

Zz.

 

[rew]

Ehmm no. I can add vectors just fine.

Let me try to paraprase my question.

Suppose I have an object (if you want, the object can be defined as -6<x<6;-1<y<1, a 12x2 rectangle). If I push on it on the left side (force vector (0,4)), it will start to move forward, but also turn clockwise. If I push on it on the right side (again (0,4)), it will also move forward, but start to rotate counterclockwise.

So where a force acts upon an object makes a difference.

So given the two vector forces (1, 4) and (-1, 4) I can add them together: (0, 8) Vector addition.

What we're doing here, is we have multiple forces and "simplify" things by calculating a resulting force.

However, besides a magnitude, a resulting force also has an resulting point where it affects the object.

If the forces (0,4) and (0,4) affect an object at -5,0 and 5,0 the resulting force will be (0,8) affecting the object at the origin ( 0,0 ).

However, when those forces affecting the object at -5,0 and 5,0 are not (0,4) but (1, 4) and (-1, 4) I suspect that the point where the resulting force (again (0,8)) can be thought to affect the object is not at the origin, but somewhere on the positive Y axis.

I want to be able to calculate that point.

 

[K^2]

If each F_i is applied at location r_i, then the total torque on the object is given by Σr_ixF_i. Then your total force, ΣF_i can be applied to any point r, such that rxΣF_i = Σr_ixF_i. You will find that in 2D, there is an entire line of such points. Usually, you take r to be perpendicular to ΣF_i, which gives you a unique effective arm.

x denotes cross product, if it's not clear. In 2D, it is a scalar quantity, and can be found thus.

axb = a_xb_y-a_yb_x

 

[rew]

Thanks! In the practical problem I'm trying to solve, I think this results in "doesn't work". So I'm happy I can now solve the physics involved, but not happy that the physics doesn't solve my problem. :-)
(As you can see from the smiley, for me the theoretical "problem solved" outweighs the practical "have to find another solution")