As shown, three forces, F1, F2, and F3, act at the same point on an object. (Par
ID: 1860262 • Letter: A
Question
As shown, three forces, F1, F2, and F3, act at the same point on an object. (Part B figure) The point of application is the origin of a Cartesian coordinate system. F1, which has a magnitude of F1= 19.0 kN, is in the y%u2013z plane and is described by an angle B1= 34.0 degrees . F2 is in the x%u2013z plane and is described by integer lengths of a similar right triangle; its magnitude is F2= 17.5 kN . If the sum of the forces is equal to zero, what is the magnitude of F3?
As shown, three forces, F1, F2, and F3, act at the same point on an object. (Part B figure) The point of application is the origin of a Cartesian coordinate system. F1, which has a magnitude of F1= 19.0 kN, is in the y%u2013z plane and is described by an angle B1= 34.0 degrees . F2 is in the x%u2013z plane and is described by integer lengths of a similar right triangle; its magnitude is F2= 17.5 kN . If the sum of the forces is equal to zero, what is the magnitude of F3?Explanation / Answer
let force F1 act at (x1,y1)
force F2 at (x2,y2)
and force F3 at (x3,y3)
the resultant of the three forces is
F = (Fx^2 + Fy^2)^1/2
where Fx = F1 x cosA + F2 x cosB + F3 x cosC
and Fy = F1 x sinA + F2 x sinB + F3 x sinC
where A,B and C are angles given by
A = tan^-1(y2 - y1/x2 - x1),
B = tan^-1(y3 - y2/x3 - x2)
and C = tan^-1(y3 - y1/x3 - x1)
the angle made by the resultant force is
X = tan^-1(Fy/Fx)
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