Three forces are applied to an object, as shown in the figure. Force F1 has a ma

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?  

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

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