The force system shown consists of the couple C and four forces. If the resultant of this system is a 500-lb · in. counterclockwise couple, determine P, Q, and C.

Question

Accepted Answer

This problem contains three unknowns: [latex]P[/latex], [latex]Q[/latex], and [latex]C[/latex]. Because the force system is the general coplanar case, three equations are available to determine the resultant. Since the resultant is a couple, the first two of Eqs. (3.5) become

[latex]R_{x}=ΣF_{x}=0\:\:\:\:\overset{ iny+}{\longrightarrow}\:\:\:\:−\frac{12}{13}Q+\frac{4}{5}P+80=0[/latex] (a)

[latex]R_{y} =ΣF_{y}=0\:\:\:\:{ iny+}\big\uparrow\:\:\:\:−\frac{5}{13}Q+\frac{3}{5}P−20 = 0[/latex] (b)

Solving Eqs. (a) and (b) simultaneously gives

[latex]P=\:200\:lb[/latex] and [latex]Q=260\:lb[/latex]

The third equation is Eq. (3.6), [latex]C^R=ΣM_{O}[/latex]. Because a couple is a free vector, the moment center can be any point. Given that [latex]C^R=500\:lb\cdot in[/latex]., counterclockwise, and choosing point [latex]A[/latex] as the moment center, we have

[latex]C^R=ΣM_{A}\:\:\:\:\underset{+}{\large \curvearrowleft}\:\:\:\:500=−20(3)−C+80(4)+\frac{3}{5}P(6)+\frac{4}{5}P(6)[/latex]

Substituting [latex]P=200\:lb[/latex] and solving yields

[latex]C=1440\:lb\cdot in[/latex].

Because the values for [latex]P[/latex], [latex]Q[/latex], and [latex]C[/latex] are positive, each force acts in the direction shown in the figure.

Question 3.6: The force system shown consists of the couple C and four for...

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