Torque and Statics Balance Problem

AI Thread Summary
The discussion revolves around a physics problem involving torque and the displacement of a fulcrum on a balance scale. A user calculated the torque for two different positions of the fulcrum, initially centered and then displaced by 1cm, resulting in a percentage error of 1.3%. Another participant pointed out that the approach was unrealistic, emphasizing that a balance operates by equating torques with known and unknown masses. The conversation highlights the importance of correctly applying the principles of balance and torque in solving such problems. The focus remains on accurately determining the unknown mass when using a balance scale.
lemonlimesoap
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Homework Statement



Two pans of a balance are 50cm apart. If the fulcrum is displaced by 1cm what percentage is the true weight marked up?

Homework Equations



T=rFsinθ
F=mg

The Attempt at a Solution


I solved for torque of the fulcrum in a hypothetical situation where a mass of 1g is on one end and a mass of 2g on the other

First with the fulcrum in the center making the lever arms 25cm
T=T1+T2

T=7.3575Nm

then with the displaced fulcrum by 1cm. Making the lever arms 24cm and 26cm

T=7.4556Nm

finally i just did percent error

(7.4556Nm-7.3575Nm)/7.3575Nm *100= 1.3%

I'm pretty sure this is wrong since I was just winging it.
 
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hi lemonlimesoap! :wink:
lemonlimesoap said:
Two pans of a balance are 50cm apart. If the fulcrum is displaced by 1cm what percentage is the true weight marked up?
…
I solved for torque of the fulcrum in a hypothetical situation where a mass of 1g is on one end and a mass of 2g on the other

nooo :redface: …

you're not being realistic about the way a balance works …

a balance works by being balanced …

you put an unknown mass in one pan, and known masses in the other pan until the torques are equal …

so start again, with 1g in one pan, and m in the other pan …

what is m ? :smile:​
 

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