Statics problem: A ramp is supported by two cables

[Camailee]

Homework Statement

The ramp ABCD is supported by cables at corners C and D. The tensile force in both cables is 420N. Determine the moment about point A produced by the force exerted at point C.

Relevant Equations

Moment at A (MA) = rGA x TCG.
Where rGA = GA/|GA|
TCG = 420N

Problem illustration:

The possible answers are:

I don't understand why it says Mc if it is asking for the moment at A, not C. But maybe I am getting something wrong.

So with the formulas I posted above, I have this:

 

[Delta2]

Your mistake is that you insert $r_{GA}$ in the formula for the moment while you should insert $r_{CA}$. It is the moment about point A, of the force that is applied at point C not at point G.

What you did is calculate the moment about A, of the force that is applied at point G which is not what is asked for. The forces at G and C might be equal in magnitude , but the point of application differs (and the direction reverses).

 

[Camailee]

Your mistake is that you insert $r_{GA}$ in the formula for the moment while you should insert $r_{CA}$. It is the moment about point A, of the force that is applied at point C not at point G.

What you did is calculate the moment about A, of the force that is applied at point G which is not what is asked for. The forces at G and C might be equal in magnitude , but the point of application differs (and the direction reverses).

Thank you for your answer Delta2. Was really helpful!

I understand what you mean. In fact the approach you mentioned is the one I thought first. I did it and the answer I got wasn't included on all the possible answers.

The other approach I posted above, with the $r_{GA}$ was based on an example I found, asking the same thing of the same structure, but with different distance units. Why does $r_{GA}$ is used, instead of $r_{CA}$ ?

Update: As I suspected and mentioned before, the possible answers are wrong because they are referring to the moment $M_C$ and not $M_A$ .

 

[Delta2]

Well sorry , I now see that it is the same thing whether you take the arm to be $r_{CA}$ or $r_{GA}$ because it is $r_{CA}=r_{GA}+r_{CG}$ and when we take the cross product with $T_{CG}$ the term $r_{CG}\times T_{CG}=0$ vanishes. You indeed calculated both to be equal which verifies it.

I don't know why the answer doesn't match one of the options. It might be because they are referring to the moment $M_C$ as you say, i.e moment about point C.