Three forces are applied to an object, as shown in the figure. Force F1 has a ma
ID: 2273590 • Letter: T
Question
Three forces are applied to an object, as shown in the figure. Force F1 has a magnitude of 21.4 Newtons and is directed 30 degrees to the left of the y axis. Force F2 has a magnitude of 15.9 Newtons and point along the x axis. What must be the a) magnitude and b) direction (specified by the angle (theta) ). The thirs force F3 such that the vector sum of the three forces is zero Newtons?
Explanation / Answer
the force F1 = 21.4 N at angle A = 120o
the force F2 = 15.9 N at angle B = 0o
let F3 be the third force at angle C
the resultant of the three forces is
F = (Fx^2 + Fy^2)^1/2
but here,F = 0
or Fx = Fy
or F1x + F2x + F3x = F1y + F2y + F3y
or F1 x cosA + F2 x cosB + F3 x cosC = F1 x sinA + F2 x sinB + F3 x sinC --------- (1)
let the angle made by the resultant force be D
we know that
tan(D) = Fy/Fx
let D = 60o
or Fy = 1.732 x Fx --------(2)
solving equations (1) and (2) for F3 and angle C