How a single force is resolved along the perpendicular axis acting an angle theta with horizontal?
Answers
Answer 1
Answer:
A single force, which is acting at angle θ from a horizontal axis, can be resolved into components which act along the perpendicular axis.
Consider the perpendicular axis x and y, where x represents the horizontal axis and y represents vertical axis.
The Force is resolved into 2 parts, one acts along x-axis and is represent by X. The other acts along y-axis and is represented by Y.
From the diagram we can see that the Force and its components X and Y makes up a right angles triangle, where θ is the angle from the x-axis
Find X:We know that:
cosθ = Base/Hypotenuse
cosθ = X/F
X = Fcosθ
Find Y:
We know that:
sinθ = Perpendicular/Hypotenuse
sinθ = Y/F
Y = Fsinθ
Relation of Force and its Components:
Force F can be represent by:
F = Fcosθ (along x-axis) + Fsinθ (along y-axis)
As they form a right angled triangle, we can use Pythagoras Theorem to show the relation between Force and its components.
Hypotenuse² = Base² + Perpendicular²
F² = X² + Y²
F² = (Fcosθ)² + (Fsinθ)²
[tex]F = \sqrt{(F\cos\theta)^2+(Fsin\theta)^2}[/tex]
Where θ can be found by using any of the trignometric functions.
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