Dos personas ejercen una fuerza sobre un mueble , la primera persona empuja con una fuerza de 550N con una direccion de125° mientras que su compa?ero ejerce una fuerza de 600N con una direccion de 200° ?cual es la fuerza resulltante?

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aristocles aristocles · Answer 1 · 2018-11-10T03:14:21+01:00

here two forces are acting at different angles and we need to find its resultant

forces are given as

[tex]F_1 = 550 N[/tex] @125 degree

[tex]F_2 = 600 N[/tex] @200 degree

now in order to find its resultant we will find its components

here it is given as

[tex]F_{1x} = 550 cos125 = -315 N[/tex]

[tex]F_{1y} = 550sin125 = 450.5 N[/tex]

[tex]F_{2x} = 600 cos200 = -563.8 N[/tex]

[tex]F_{2y} = 550sin200 = -188.11 N[/tex]

Now net force in x and y direction is given as

[tex]F_x = -315 -563.8 = - 878.8 N[/tex]

[tex]F_y = 450.5 - 188.11 = 262.4 N[/tex]

so net force is given as

[tex]F = -878.8 \hat i + 262.4 \hat j[/tex]

now the magnitude is given as

[tex]F = \sqrt{878.8^2 + 262.4^2}[/tex]

[tex]F = 917.13 N[/tex]

angle of the force is given as

[tex]\theta = tan^{-1}\frac{F_y}{F_x}[/tex]

[tex]\theta = tan^{-1}\frac{262.4}{-878.8}[/tex]

[tex]\theta = 163.4^0[/tex]

so net resultant force is 917.13 N at 163.4 degree