- #1

jonjacson

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## Homework Statement

I´ll use an image to show the problem that you can see as attached file. I need to calculate a force-couple system applied to the point C in red, equal to the force f0 applied to the point E.

## Homework Equations

M=fd

## The Attempt at a Solution

Well in these kind of problems you just need to add two equal and oppossite forces f1 and f2 at the point C.

Now f1 is the equivalent force, and f0-f2 is the couple.

f1 is simply a 250 N applied at -45º to the point C.

My doubt is about the couple, it´s a bit confusing to me to guess what is the moment arm of the forces.

If the bar BD weren´t in the system it would be easy:

M=f2*0 (because it´s a force applied to the point and the moment arm is 0) + f0*0.72 (0.4+0.2+0.12).

But now I think that BD it´s like the basis of a seesaw. B is the point were the system would be turning around so if I project the forces f0 and f2 to the line CA, the components lying down on the line CA don´t have moment arm, only the orthogonal ones do.

So, the angle u must be 45, that means that v is 75 degrees.

f2 orthogonal = 250*sin(75)=241.48 N

The moment arm of this force is 0.4 meters, the distance CB.

f0 orthogonal = f2 orthogonal

The moment arm of this force now is the distance BA plus the radius of the disc 0.12, finally:

M total of the couple as function of f2 and f0= 250*sin(75)*0.4 + 250* sin(75)*0.32=173.86 Nm

The problem is that the book gives the answers and it´s 174.9 Nm, I know 1 Nm it´s a small difference but maybe I didn´t use a correct reasoning, so I´d like to check if the moment arms are right or not.

And it´s not too clear to me why the problem suggests you to start calculating the force couple system at the point A, I can´t see any benefit in doing that.

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