Question

If the sum of all forces is zero, what are the magnitudes of the unknown forces $x$ and $y$?

• A. $x=10\text{units},y=5\text{units}$
• B. $x=5\text{units},y=10\text{units}$
• C. $x=5\text{units},y=5\text{units}$
• D. $x=10\text{units},y=10\text{units}$

Answer 1

The correct option is B $x=5\text{units},y=10\text{units}$

Angle made by $y$ force with the horizontal is
${180}^{\circ }-({90}^{\circ }+{53}^{\circ })={37}^{\circ }$

Since net force is zero, hence horizontal and vertical components of net force must be zero.
Equate vertical component,
$5\sin {53}^{\circ }+y\sin {37}^{\circ }=10$
$5\times \frac{4}{5}+y\times \frac{3}{5}=10$
$20+3y=50$
$y=10$
Equate horizontal component,
$x+5\cos {53}^{\circ }=y\cos {37}^{\circ }$
$x+5\times \frac{3}{5}=\frac{4\times 10}{5}$
$x=5$