# How do I find the line of action of this resultant force?

by aps0324
Tags: action, force, line, resultant
 P: 9 Three forces are applied to a body. They are : F1 = (4,5) applied at (1,2) F2 = (2,-1) applied at (3,-1) F3 = (-3, 2) applied at (-2,1) i) Find the resultant force Answer : R = (3,6) ii) Find the total moment about the origin (This i know how to do) iii) The line of action of R cuts the Y-axis at (0,d). Find d iv) Find the equation of this line of action How do I solve iii) and iv)
 Sci Advisor HW Helper PF Gold P: 5,959 Did you try calculating the moments about the origin from the the x and y components of the forces separately? Then you can find a set of coordinates through which the resultant passes ($$X = \Sigma{(F_y(x))}/R_y$$, etc.), the slope of which resultant is R_y/R_x.
 P: 9 Three forces are applied to a body. They are : F1 = (4,5) applied at (1,2) F2 = (2,-1) applied at (3,-1) F3 = (-3, 2) applied at (-2,1) i) Find the resultant force Answer : R = (3,6) ii) Find the total moment about the origin Answer: I calculated this and it is -5 Nm iii) The line of action of R cuts the Y-axis at (0,d). Find d [B]Question: Can I assume that R = (3,6) is applied at (0,d) and its moment about the origin is - 5Nm? In order to find what d is? If that assumption is wrong then how do i find d?
HW Helper
P: 5,346

## How do I find the line of action of this resultant force?

 Quote by aps0324 Three forces are applied to a body. They are : F1 = (4,5) applied at (1,2) F2 = (2,-1) applied at (3,-1) F3 = (-3, 2) applied at (-2,1) i) Find the resultant force Answer : R = (3,6) ii) Find the total moment about the origin Answer: I calculated this and it is -5 Nm iii) The line of action of R cuts the Y-axis at (0,d). Find d [B]Question: Can I assume that R = (3,6) is applied at (0,d) and its moment about the origin is - 5Nm? In order to find what d is? If that assumption is wrong then how do i find d?
Can you show your work on determining the moment in part ii)?

Isn't it the cross product of the F X r ?

Doesn't that yield

(4*2 + 5*1) + (2*(-1) + (-1)*3) + ((-3)*1 + 2*(-2)) = ... but ≠ -5
 Mentor P: 39,575 I merged two duplicate threads.
Sci Advisor
HW Helper
PF Gold
P: 5,959
 Quote by aps0324 Can I assume that R = (3,6) is applied at (0,d) and its moment about the origin is - 5Nm? In order to find what d is?
Yeah, as long as you are consistent with your plus and minus signs, that is to say, is d on the positive or negative y axis?

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