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I'm working on an answered physics question in the book but I'm having trouble understanding why the problem could be solved by setting net torque equal to 0 and not net force. You are asked to find the magnitude of the tension in the cable (the magnitude of the force from the beam on the cable). With an axis of rotation at the hinge so as to eliminate any forces at that point, the solution is completed by balancing torques: I understand why that works, but I'm not sure why you can't instead balance forces as was done in previous problems. In other words:

(Fh=force of the hinge on the beam; Ft=tension force in the cable; m=mass of the beam; M=mass of the block)

Fhx-Ft=0

-mg-Mg+Fhy=0

these equations produce: Fhcos(theta)=Ft & Fhsin(theta)=g(m+M)

If you divide the equations, you can eliminate Fh and solve for Ft... why is this not appropriate?

I'm working on an answered physics question in the book but I'm having trouble understanding why the problem could be solved by setting net torque equal to 0 and not net force. You are asked to find the magnitude of the tension in the cable (the magnitude of the force from the beam on the cable). With an axis of rotation at the hinge so as to eliminate any forces at that point, the solution is completed by balancing torques: I understand why that works, but I'm not sure why you can't instead balance forces as was done in previous problems. In other words:

(Fh=force of the hinge on the beam; Ft=tension force in the cable; m=mass of the beam; M=mass of the block)

x-horizontal, y-vertical

$Fh_x-F_t=0$

$-mg-Mg+Fh_y=0$

these equations produce: Fhcos(theta)=Ft & Fhsin(theta)=g(m+M)

If you divide the equations, you can eliminate Fh and solve for Ft... why is this not appropriate?

I'm working on an answered physics question in the book but I'm having trouble understanding why the problem could be solved by setting net torque equal to 0 and not net force. You are asked to find the magnitude of the tension in the cable (the magnitude of the force from the beam on the cable). With an axis of rotation at the hinge so as to eliminate any forces at that point, the solution is completed by balancing torques: I understand why that works, but I'm not sure why you can't instead balance forces as was done in previous problems. In other words:

(Fh=force of the hinge on the beam; Ft=tension force in the cable; m=mass of the beam; M=mass of the block) Fhx-Ft=0  -mg-Mg+Fhy=0 these equations produce: Fhcos(theta)=Ft Fhsin(theta)=g(m+M)

If you divide the equations, you can eliminate Fh and solve for Ft... why is this not appropriate?

I'm working on an answered physics question in the book but I'm having trouble understanding why the problem could be solved by setting net torque equal to 0 and not net force. You are asked to find the magnitude of the tension in the cable (the magnitude of the force from the beam on the cable). With an axis of rotation at the hinge so as to eliminate any forces at that point, the solution is completed by balancing torques: I understand why that works, but I'm not sure why you can't instead balance forces as was done in previous problems. In other words:

(Fh=force of the hinge on the beam; Ft=tension force in the cable; m=mass of the beam; M=mass of the block) 

Fhx-Ft=0 

-mg-Mg+Fhy=0 

these equations produce: Fhcos(theta)=Ft & Fhsin(theta)=g(m+M)

If you divide the equations, you can eliminate Fh and solve for Ft... why is this not appropriate?