Torque and Statics Balance Problem

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SUMMARY

The discussion focuses on a physics problem involving torque and balance, specifically calculating the percentage markup of true weight when the fulcrum of a balance is displaced by 1cm. The initial calculations used a mass of 1g and 2g, resulting in a torque of 7.3575Nm with the fulcrum centered and 7.4556Nm with the fulcrum displaced. The final percentage error calculated was 1.3%. However, participants emphasized the need for a more realistic approach to balance mechanics, suggesting the use of an unknown mass alongside known weights to achieve equilibrium.

PREREQUISITES
  • Understanding of torque calculations using the formula T=rFsinθ
  • Knowledge of gravitational force calculations (F=mg)
  • Familiarity with the concept of lever arms in physics
  • Basic principles of balance and equilibrium in mechanics
NEXT STEPS
  • Study the principles of torque and equilibrium in static systems
  • Learn how to apply the concept of lever arms in real-world scenarios
  • Explore the effects of fulcrum displacement on balance scales
  • Investigate the relationship between mass and torque in various configurations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and statics, as well as educators looking for practical examples of torque and balance concepts.

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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