Question

Three forces are applied to a square plate as shown in figure:

Find the direction of the resultant force.

• A. The force is parallel to the diagonal $AC$
• B. The force is along the diagonal $AC$
• C. The force is perpendicular to the diagonal $AC$
• D. The force is at an angle $\theta$ to the diagonal $AC$

Answer 1

Answer: (A), (B)

The force is parallel to the diagonal $AC$
The force is along the diagonal $AC$

$\overrightarrow{F_{res}}=F\hat{i}$ (at point B) $+F\hat{j}$ (at point A) $+F\sqrt{2}(cos45^0\hat{i}-sin45^0\hat{j})$ (at point F)

or,$\overrightarrow{F_{res}}=2F\hat{i}.$
Thus, vector is in $\hat{i}$ direction, or parallel to diagonal AC.