Question

part a determine the moment of the force about point o. assume f = 780 lb (figure 1) express your answer to three significant figures and include the appropriate units. mo = value units

Explanation:

Step1: Resolve the force into perpendicular - component to the line from O.

The perpendicular distance \(d\) from point \(O\) to the line of action of the force \(F\) needs to be calculated. First, find the horizontal and vertical distances from the geometry of the problem. The length of the member from \(O\) to the point of application of the force is \(L = 5 + 0.5=5.5\) ft.
The perpendicular - component of the force \(F\) with respect to the line from \(O\) is \(F_{\perp}=F\sin(20^{\circ})\).

Step2: Calculate the moment about point O.

The moment \(M_O\) about point \(O\) is given by the formula \(M_O = F_{\perp}\times d\). Here, \(d = 5.5\) ft and \(F = 780\) lb. So \(M_O=F\times\sin(20^{\circ})\times5.5\).
Substitute \(F = 780\) lb into the formula: \(M_O=780\times\sin(20^{\circ})\times5.5\).
\[M_O = 780\times0.342\times5.5\]
\[M_O=780\times1.881\]
\[M_O = 1467.18\approx1470\] lb - ft.

Answer:

\(M_O = 1470\) lb - ft