Resultant of concurrent forces: Direction angle θ of the resultant with the horizontal. Context: Several forces act at a point with components ΣF<sub>x</sub> (horizontal) and ΣF<sub>y</sub> (vertical). Choose the correct relation for the inclination θ of the resultant.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
Answer
Correct Answer: tanθ = ΣFy / ΣFx
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