Briefly explain the determination of a force from its perpendicular components?
Difficulty: Hard
Determination of a Force or a vector from its Perpendicular Components:
Consider FX and Fy as the perpendicular components of a force F. These perpendicular components FX and Fy
are represented by lines OP and PR respectively.
According to head to the tail rule:
OR = OP + PR
Thus, OR will completely represent the force F whose x and y-components
are FX and Fy respectively. That is
F = FX + Fy
The magnitude of resultant force/Magnitude of resultant vector:
The magnitude of the force F can be determined using the right-angled triangle OPR
As
$\left(OR\right)^{2}=\left(OP\right)^{2}+\left(PR\right)^{2}$
$F^{2}=Fx^{2}+Fy^{2}$
Hence
F= $\surd Fx^{2}+Fy ^{2}$ (i)
Direction of the resultant force/Direction of the resultant vector:
The direction of the force F with x-axis is given by
$\tan\theta=\frac{PR}{OP}=\frac{Fy}{Fx}$
$\theta=\tan^{-1}\frac{Fy}{Fx}$
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