The bracket is subjected to three forces and a couple. If you represent this system by a force F, where does its line of action intersect the x axis? Give the answer in m.

Question

Question

Answer 1

Answer #1

Sum of Horizontal forces about x axis zero.

Σ F_x =0

400 -200 = +200 N

Effective horizontal force, F(h): +400 - 200 = + 200 N

Sum of Horizontal forces about x axis zero.

Σ Fy =0

Effective vertical force, F(v): +180 N

Resultant force, F(R) = √(200² + 180²) = 269.07 N

Direction of resultant force, α = tan^-1( 180/200) = 41.98° ≈ 42°

taking moments about down left corner is zero.

Σ M =0

Total Moment produced (with respect to origin), M = 180 * 0.65 + 140 - 400 * 0.6 + 200 * 0.2 = 57 Nm
x intercept = M/ F(v) = 57/180 = 0.3166 m

Answer 2

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