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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)