Question

Three forces are applied to an object, as Indicated in the drawing. Force F, has a magnitude of 26.0 newtons (26.0 N) and is directed 30.0* to the left of the ty axis. Force along the +x axis. What must be the magnitude and direction (speaifled by the angle 8 in the drawing) of thethforce F uch that the vector sum of the three forces is 0 N? MacBook Ai

Answer 1

SOLUTION::

magnitude of F_1 = 26 N
angle theta = 30 ^ o
components of F_1 and F_2and F_3
F_ 1x = - 26 cos 30 = -22.5N
F_1y = 26 sin 30 = 13N
F_2x = 17.6 N
F_2y = 17.6 sin 0 = 0
F_3 x= F_3 cos ( 180 +? )
F_3y = F_3 sin ( 180 +? )
The vector sum of three forces is zero
F_1x + F_2x + F_3 x = 0
-22.15 + 13 + F_3x = 0
F_ 3x cos? = -9.15
F_1y + F_2y + F_3 y = 0
13 + F_3y sin ? = 0
F_3y sin ? = -17.6
the magnitude of F_3 = [( -9.15)^2 + ( -17.6)^2 ]^ ( 1 /2 )
= 19.83 N
direction of F_3 = Tan ^ -1 ( -9.15 / -17.6 )
= 47.94 degrees