FBD of a loaded Dumptruck platform that is Tilting

[Mech_LS24]

Homework Statement

Draw a FBD from the loaded platform of the truck. D has a mass of 25 kN and it's center is at point G. D rest on a pin in A and is connected with a hydraulic cylinder pinned in point B. Give the meaning of the forces.

Relevant Equations

Momentsum= 0;

Hi,

From the picture the following statement is asked:
"Draw a FBD from the loaded platform of the truck. D has a mass of 25 kN and it's center is at point G. D rest on a pin in A and is connected with a hydraulic cylinder pinned in point B. Give the meaning of the forces."

I made a FBD and I am curious doing it correctly, due to the missing answer at the book...
As well I added a momentsum about point A to find force Fbc, did I have done it both correct?

Thanks in advance!

 

[jack action]

The FBD is OK, but you will have to separate forces G and F_BC into two components to be useful.

The moment equation is all wrong. Only the perpendicular component of a force with respect to the lever arm is relevant to the moment applied.

 

[Mech_LS24]

Thanks,

Is this what you mean?:

 

[Delta2]

I think you have a slight mistake in your moment equation, that sin60 should be sin50. That angle you mark as 60 degrees (with vertex B) is in fact equal to the sum of the opposite interior angles of that triangle. That is equal to 20+30=50.
And be careful at the algebra, the solution of that equation is NOT 2.97KN (even if we take the equation to be correct).
I solved the corrected moment equation and find $F_{BC}\approx 18.81kN$

 

[Mech_LS24]

Thanks for pointing me on that angle. A good lesson for me, I re-draw a sketch on scale and see the difference now (see below).

And I found my mistake in my moment equation. My calculator was in radians .