Determine the resultant of the three concurrent forces shown in Fig. (a).

Question

Accepted Answer

Because the three forces are concurrent at point A, they may be added immediately to obtain the resultant force R. The rectangular components of each of the three forces are shown in Fig. (b). Using Eqs. (2.3) [latex]R_{x}=\Sigma F_{x}[/latex] [latex]R_{y}=\Sigma F_{y}[/latex] to determine the components of the resultant, we have

[latex]R_{x}=\Sigma F_{x}\overset{+ }{\longrightarrow}R_{x}=30-5=25N[/latex]

and

[latex]R_{y}=\Sigma F_{y}+\uparrow R_{y}=40+8.66-60=-11.34N[/latex]

The signs in these equations indicate that [latex]R_{x}[/latex] acts to the right and [latex]R_{y}[/latex] acts downward. The resultant force R is shown in Fig. (c). Note that the magnitude of the resultant is 27.5N and that it acts through point A (the original point of concurrency) at the [latex]24.4^{\circ }[/latex]angle shown.The foregoing solution could also have been accomplished using vector notation. The forces would first be written in vector form as follows,

[latex]F_{1}=30i+40j N[/latex]

[latex]F_{2}=-5i+8.66j N[/latex]

[latex]F_{3}=-60j N[/latex]

and the resultant force R would then be determined from the vector equation

[latex]R=\Sigma F=F_{1}+F_{2}+F_{3}[/latex]

[latex]R=(30i+40j)+(-5i+8.66j)+(-60j)[/latex]

[latex]R=25i-11.34j N[/latex]

Whether you use scalar or vector notation is a matter of personal preference.

Question 2.1: Determine the resultant of the three concurrent forces shown...

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