Calculating Torque of Parallel Forces on Rod

[nishanth R]

Homework Statement

Two like parallel forces 20N and 30 N act at the ends A and B of a rod 1.5m long. The resultant of the forces will act at a point
1 90 cm from A
2 75 cm from B
3 20 cm from B
4 85 cm from A

Homework Equations

Torque=Force * Perpendicular distance

The Attempt at a Solution

In the solution for the problem, I see that the torque due to the forces are equated
F1(x)=F2(1.5-x)
and then x has been calculated.
I don't understand this approach. What is the point in equating torques? It has not been mentioned that the net torque on the rod is zero. Then how can we assume that the torques due to the forces are equal?

 

[PhanthomJay]

Homework Statement

Two like parallel forces 20N and 30 N act at the ends A and B of a rod 1.5m long. The resultant of the forces will act at a point
1 90 cm from A
2 75 cm from B
3 20 cm from B
4 85 cm from A

Homework Equations

Torque=Force * Perpendicular distance

The Attempt at a Solution

In the solution for the problem, I see that the torque due to the forces are equated
F1(x)=F2(1.5-x)
and then x has been calculated.
I don't understand this approach. What is the point in equating torques? It has not been mentioned that the net torque on the rod is zero. Then how can we assume that the torques due to the forces are equal?

the magnitude and direction of the resultant force is given by the vector sum of the forces. The location of the resultant force must be such that the moment of the resultant force about any point is the same of the sum of the moments of the individual forces about that same point. If you choose the location of the resultant force as the point about which to sum moments, then since the moment ofthe resultant force about that point is 0, then so must be 0 the sum of the individual force moments. The fact that when doing it this way gives 0 moment does not imply the net moment about any point is 0.