Question 3 of 3 · Force Systems & Equilibrium · Intermediate · About 22 min

Equivalent force-couple for a machine bracket

A machine bracket is acted upon by a $400\,\mathrm{N}$ force directed $30^\circ$ above the $+x$ axis at $(1.2,0)\,\mathrm{m}$ , a force at , and an applied counterclockwise couple. Determine the equivalent resultant force and moment at the origin .

Coordinate axes with origin O: x to the right, y upward. A thin L-shaped bracket with one arm along the x axis to point P1 at (1.2, 0) m and one arm along the y axis to point P2 at (0, 1.0) m. At P1, a force arrow pointing up and to the right, 30 degrees above the x direction, with the 30 degree angle marked. At P2, a force arrow starting at P2 and pointing down and to the left, along direction (-150, -250). Near O, a counterclockwise curved arrow for the couple. Dimensions of 1.20 m along the x arm and 1.00 m along the y arm. Labels: O; P1; P2; x; y; 400 N; 30°; F2 = (-150 i - 250 j) N; 80 N·m; 1.20 m; 1.00 m — Schematic, not to scale unless dimensions are given.

Given

$\mathbf r_1=(1.2,0)$ m
$\mathbf r_2=(0,1.0)$ m

Find

$R_x,R_y$
Magnitude and direction of $\mathbf R$
Equivalent couple

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Equivalent force-couple for a machine bracket

Given

Find

Assumptions

Worked solution