Question

Calculate the net torque (magnitude and direction) on the beam in Figure P8.3 about the following axes.

(a) an axis through O, perpendicular to the page

_________N·m

(b) an axis through C, perpendicular to the page

________N·m

Answer 1

(a) The net torque \((\tau)\) about point \(\mathrm{O}\) perpendicular to the page will be

$$ \begin{aligned} \bar{\tau} &=(\mathrm{OC})(F)_{1}\left(\cos 30^{\circ}\right)-(\mathrm{OD})\left(F_{2}\right)\left(\sin 20^{\circ}\right)-(\mathrm{OO})\left(F_{3}\right)\left(\sin 45^{\circ}\right) \\ &=(2.00)(25)\left(\cos 30^{\circ}\right)-(4.00)(10)\left(\sin 20^{\circ}\right)-(0) \\ &=43.3-13.68 \\ &=29.62 \mathrm{~N} . \mathrm{m} \end{aligned} $$

\(=30.0 \mathrm{Nm}\) counter clock wise.

(b) The net torque \((\bar{\tau})\) about point \(\mathrm{C}\) perpendicular to the page will be

$$ \begin{aligned} \bar{\tau} &=-(\mathrm{OC})-\left(F_{3}\right)\left(\sin 45^{\circ}\right)+(0)-(2)(10)\left(\sin 20^{\circ}\right) \\ &=(2.0)(30)\left(\sin 45^{\circ}\right)+(0)-(2)(10)\left(\sin 20^{\circ}\right) \\ &=42.426-6.84 \\ &=35.586 \end{aligned} $$

\(=36.0 \mathrm{~N} \cdot \mathrm{m}\) (counter cock wise)