Effect of arm length on weight

[andelJ94]

I have a practice question that asks what the readout would be on a force sensor at the red dot if the arm of the apparatus were lengthened but F applied at the end of the arm remained the same.

My thinking was the weight would increase due to the longer lever arm, but the answer says it will be the same force.

Am I wrong?

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[theonlytycrane]

It's like a torque problem where the torques on the ends of the beam need to balance. In both cases, the middle point on the beam could be used as the fulcrum and the forces being applied to each end would be the same. The distance of each lever arm would be the thing that is changing.

 

[andelJ94]

It's like a torque problem where the torques on the ends of the beam need to balance. In both cases, the middle point on the beam could be used as the fulcrum and the forces being applied to each end would be the same. The distance of each lever arm would be the thing that is changing.

So I am wrong? The weight would remain the same?

 

[theonlytycrane]

So I am wrong? The weight would remain the same?

Yeah, F applied at the end of the arm will remain the same.

 

[andelJ94]

Yeah, F applied at the end of the arm will remain the same.

I know Fapplied remains the same, that is in the question. But their conclusion, that the measured Fweight remains the same, that is the correct answer? Sorry if I seem obtuse, I am a History/Biology major, not seen physics in a long time.

Thanks!!

 

[theonlytycrane]

Oh- sorry if I wasn't clear. In both scenarios, we can imagine a balance point in the center of the arms. About this balance point, Fapplied and Fweight torque the arm in clockwise and counter-clockwise directions, respectfully. The torques are equal and opposite, though, so the arm stays in place. Torque = r * F where r is the distance from the balance point and F is the force (Fapplied or Fweight in this case).

From scenario 1 to scenario 2, r from the balance point increases but Fweight stays the same because we are told that Fapplied stays the same.