Question

obtain the components of force vector in x and y directions, find the magnitude and direction of F in terms of its components

Answer 1

Being a vector , a force can be represented by its components like any vector. One of the main advantage of resolving forces into their components, is that it is easy to add them, to scalar multiply them, etc.

If |F| is the magnitude and θ is the angle between the positive direction of the x-axis and the force F, then the components Fx and Fy are given by

Fx = |F| cosθ and Fy = |F| sinθ

Hence F may be written in terms of its components as follows

F = (Fx , Fy) = (|F| cosθ , |F| sinθ)

Answer 2

Answer:

F = √( Fx ² + Fy²)

tan∝ = Fy/Fx

Explanation:

∝ being the angle between force vector F and the x - axis , then

Fx = Fcos∝

Fy = Fsin∝

F = √( Fx ² + Fy²)

tan∝ = Fy/Fx