Question

a force f has the components fx and fy,the magnitude f of the force component in the x direction is given by?

Answer 1

Answer:

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:

The magnitude of the x component of the force is given by

$f_{x}= \sqrt{f^{2}-f_{y}^{2}}$

Explanation:

Force is a vector quantity.

$f=f_{x} i + f_{y} j$ , where $i, j$ are direction along x co-ordinate & y

co-ordinate

In terms of magnitude,

$f^{2} = f_{x} ^{2} + f_{y} ^{2}$

The magnitude of force component along x direction will be

$f_{x} ^{2} =f^{2} -f_{y}^{2}$

Taking the square root of the above equation

$f_{x}= \sqrt{f^{2}-f_{y}^{2}}$

Thus, the magnitude of x component of force is $f_{x}= \sqrt{f^{2}-f_{y}^{2}}$