Resultant of concurrent forces: Direction angle θ of the resultant with the horizontal. Context: Several forces act at a point with components ΣFx (horizontal) and ΣFy (vertical). Choose the correct relation for the inclination θ of the resultant.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
-
Atanθ = ΣF<sub>y</sub> / ΣF<sub>x</sub>
-
Btanθ = ΣF<sub>x</sub> / ΣF<sub>y</sub>
-
Ctanθ = (ΣF<sub>x</sub> + ΣF<sub>y</sub>) / (ΣF<sub>x</sub> − ΣF<sub>y</sub>)
-
Dtanθ = (ΣF<sub>x</sub> · ΣF<sub>y</sub>)
Answer
Correct Answer: tanθ = ΣF<sub>y</sub> / ΣF<sub>x</sub>
Explanation
Given/Definitions
- Resultant vector R has components Rx = ΣFx, Ry = ΣFy.
Derivation tanθ = (opposite)/(adjacent) = Ry / Rx = ΣFy / ΣFx.
Verification/Notes When ΣFx = 0, the resultant is vertical (θ = 90°). Sign conventions determine quadrant but not the basic ratio.
Final Answer tanθ = ΣFy / ΣFx