Roshnica
contestada

Find the resultant force when
F1 = 50 N and F2 = 20 N
(F1 is vertical and F2 is horizontal. It looks like it's a graph and there's a diagonal line going between them and the line is labeled "Resultant".

Respuesta :

The resultant is the vector sum of the sum of each component.  The components are perpendicular, like an x-y graph.  Since you only have two components altogether, your resultant is the sum of 50N along y, and 20N along x.  It's given simply by

[tex]F_{res}=20 a_x + 50a_y [/tex]

where [tex]a_x[/tex] is the unit vector along x and [tex]a_y[/tex] is the unit vector along y.  The magnitude of [tex]F_{res}[/tex] is given by the Pythagorean theorem as

[tex]|F_{res}|= \sqrt{20^2+50^2}=53.85N [/tex]

Its angle above the x-axis is given by the arctangent of the y-component divided by the x-component:

[tex]\theta = tan^{-1}( \frac{50}{20})=68.2 \deg [/tex]