Find the magnitude and direction of a force, if its x-component is 12 N and y-component is 5 N. (13 N making 22.6⁰ with x-axis)
Difficulty: Medium
Solution:
$F_{x}$ = 12 N
$F_{y}$= 5 N
- Magnitude of the force = F = ?
- Direction of the force = θ = ?
F = $√F_{x}^{2} + F_{y}^{2}$
F = $√(12)^{2} + (5)^{2}$
F = √144+25
F = 13 N
θ = $tan^{-1} =\frac{F_{y}}{F_{x}}$
θ = $tan^{-1} =\frac{12}{5}$
θ = $tan^{-1}$ (2.4)
θ = 22.6⁰ with x-axis
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