Find Net Couple with P=0 | Magnitude & Direction of Axis

[utkarshakash]

Homework Statement

If P=0, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis.

The Attempt at a Solution

Position vector of B(r_b)=0.3i
Similarly, r_d=0.16j+0.17k

∠GCF=atan(16/30)=28.07°
∠DEF=atan(DF/FE)=45°
Then I tried to resolve the forces into its individual components. For 34N force applied at B, in vector form,

$34 \cos 28.07 \hat{i}-34 \sin 28.07 \hat{j}-34 \cos 45 \hat{k}$
For the other force at B, I can write -18k.
At D, $-34 \cos 28.07 \hat{i}+34 \sin 28.07 \hat{j}+34 \cos 45 \hat{k}$

Now I take moments of all the above forces about the origin which gives me
1.13i + 7.51j

the magnitude of which is given by $\sqrt{1.13^2+7.51^2} = 7.59$

which is incorrect according to answer key.

 

[SteamKing]

Are you sure angle DEF is 45 degrees? It doesn't look it from the figure.

 

[ehild]

You calculated the components of the 34 N force incorrectly. The 34 N forces are parallel to the vector connecting D and E or F and B. Find the direction of those vectors from the coordinates of the points. Multiply the magnitude of the force with the unit vector in the appropriate direction. ehild