The body shown in Fig. is pivoted at point `O`. Three forces act on it `F_(a) = 10N` at point `A, 8.0 m` from `O, F_(b) = 16 N` at` B, 4.0m` from O, and `F_(c) = 19 N` at `C, 3.0 m` from `O`. What is the net torque about `O`.

Explanation

As is clear from Fig.

`overset rarr(tau) = overset rarr(tau_(a)) + overset rarr(tau_(b)) + overset rarr(tau_(c))`
`= r_(a) F_(a) sin phi_(a) - r_(b)F_(b) sin phi_(b) + r_(c) F_(c) sin phi_(c)`
`=(8.0) 10 sin 135^(@) - (4.0) 16 sin 90^(@)`
`+ 3.0 xx 19 sin 160^(@)`
`= 80 xx (1)/(sqrt(2)) - 64 xx 1 + 57 xx 0.342`
`| overset rarr(tau)| = 56.6 - 64.0 + 19.5 =12.1 N-m`