Question

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?

Answer 1

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

forces are given as

`F_1 = 550 N` @125 degree

`F_2 = 600 N` @200 degree

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

here it is given as

`F_(1x) = 550 cos125 = -315 N`

`F_(1y) = 550sin125 = 450.5 N`

`F_(2x) = 600 cos200 = -563.8 N`

`F_(2y) = 550sin200 = -188.11 N`

Now net force in x and y direction is given as

`F_x = -315 -563.8 = - 878.8 N`

`F_y = 450.5 - 188.11 = 262.4 N`

so net force is given as

`F = -878.8 \hat i + 262.4 \hat j`

now the magnitude is given as

`F = √(878.8^2 + 262.4^2)`

`F = 917.13 N`

angle of the force is given as

`\theta = tan^(-1)(F_y)/(F_x)`

`\theta = tan^(-1)(262.4)/(-878.8)`

`\theta = 163.4^0`

so net resultant force is 917.13 N at 163.4 degree