The parallel force system in Fig. (a) consists of the three forces shown and the 1250-N·m couple. (1) Determine the resultant, and show it on a sketch of the coordinate system. (2) Determine the resultant if the direction of the 100-N force is reversed.

Question

The parallel force system in Fig. (a) consists of the three forces shown and the [latex]1250-N·m[/latex] couple. (1) Determine the resultant, and show it on a sketch of the coordinate system. (2) Determine the resultant if the direction of the [latex]100-N[/latex] force is reversed.

Accepted Answer

Part 1

The resultant of the force system shown in Fig. (a) will be either a force or a couple. We begin by summing the forces.

[latex]{ iny+}\big\uparrow \:\:\:\:R=ΣF_{z}=100−200+300=200\:N[/latex]

Therefore, the resultant is the force [latex]R=200k\:N[/latex].

We must use a moment equation to find the line of action of [latex]R[/latex]. Using the origin [latex]O[/latex] as the moment center and assuming that [latex]R[/latex] intersects the [latex]xy[/latex]-plane at the point [latex](x,\:y,\:0)[/latex], Eq. (3.10) becomes

[latex]ΣM_{O}=r×R[/latex]

[latex]3i×(−200k)+[(2i + 6j)×300k]−\left(\frac{4}{5} ight)1250i−\left(\frac{3}{5} ight)1250j=(xi + yj)×200k[/latex]

Expanding the cross products and simplifying, we obtain

[latex]800i−750j=200yi−200xj[/latex]

Equating like components yields [latex]x=3.75\:m[/latex] and [latex]y=4\:m[/latex]. The resultant is shown [latex]x[/latex] in Fig. (b).

Part 2

If the direction of the [latex]100-N[/latex] force is reversed, the sum of the forces will be zero, which means that the resultant is not a force. To determine the resultant couple, we must compute the moment about any point. We choose the origin [latex]O[/latex] as the moment center. Because reversing the direction of the [latex]100-N[/latex] force has no effect on the moment about [latex]O[/latex], we conclude that the moment is the same as that found in the solution to Part 1. Therefore, the resultant is the couple-vector [latex]C^R=ΣM_{O}=800i−750j\:N\cdot m[/latex].

Question 3.8: The parallel force system in Fig. (a) consists of the three ...

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