Atwood's Machine Lab Help (proportional error)

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SUMMARY

The discussion focuses on calculating proportional error in multiple variables for a lab involving Atwood's Machine. The user seeks clarity on the formula for proportional error, specifically for independent measurements represented as ##x\pm\sigma_x## and ##y\pm\sigma_y##. The proportional errors are defined as $$p_x=\frac{\sigma_x}{x}$$ and $$p_y=\frac{\sigma_y}{y}$$, with the combined proportional error for the product $$z=xy$$ expressed as $$p^2_z=p_x^2+p_y^2$$. The user emphasizes the need for a step-by-step approach to mastering these calculations.

PREREQUISITES
  • Understanding of basic error analysis concepts
  • Familiarity with independent measurements in experimental physics
  • Knowledge of mathematical notation for uncertainties
  • Experience with Atwood's Machine experiments
NEXT STEPS
  • Study the principles of error propagation in physics experiments
  • Learn how to apply the formula for combined uncertainties in product calculations
  • Explore practical examples of proportional error calculations
  • Review Atwood's Machine lab procedures and data analysis techniques
USEFUL FOR

This discussion is beneficial for physics students, lab partners working on Atwood's Machine experiments, and anyone involved in experimental error analysis and measurement techniques.

atir.besho
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I have attached the lab

right now I am stuck on proportional error in multiple variables

I want to take the lab step by step so i can learn how to do calculate all the variables from now on.

I have lab partners during the lab but I am completely clueless when I am working on it on my own.

Can someone just explain the formula needed to get the proportional error please?
I know I need 1 gram as uncertainty.
 

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For independent measurements ##x\pm\sigma_x## and ##y\pm\sigma_y##, the proportional errors are given by:$$p_x=\frac{\sigma_x}{x}, p_y=\frac{\sigma_y}{y}\\
z=xy\implies p^2_z=p_x^2+p_y^2$$
 

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