Propogation of uncertainty in a data set (finger-math at most)

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SUMMARY

The discussion focuses on calculating uncertainty in a physics experiment involving the distance traveled by a vertically falling weight. The absolute uncertainties for time and distance are ±0.010s and ±0.001m, respectively. Participants clarify that relative uncertainty must be calculated for each measured value, as it varies across data points. The consensus is that using a single relative uncertainty for all data points is incorrect; each velocity and acceleration must have its own calculated uncertainty based on the respective measurements.

PREREQUISITES
  • Understanding of basic physics concepts such as velocity, acceleration, and gravitational force.
  • Familiarity with uncertainty propagation methods in experimental physics.
  • Knowledge of how to calculate absolute and relative uncertainties.
  • Experience with graphing data and interpreting linear relationships.
NEXT STEPS
  • Study the principles of uncertainty propagation in experimental data analysis.
  • Learn how to apply the formula for relative uncertainty in various contexts.
  • Explore techniques for graphing velocity versus time and interpreting the slope as acceleration.
  • Investigate the impact of measurement precision on experimental results and data reliability.
USEFUL FOR

Students in physics courses, laboratory technicians, and anyone involved in experimental data analysis who needs to understand how to calculate and propagate uncertainties in measurements.

ZamielTheGrey
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Homework Statement


I have conducted a simple lab, that involves getting the distance traveled by a vertically falling weight at certain time intervals. Velocity is calculated for every time interval (distance traveled per time interval). Then I graph velocity versus time to get acceleration which comes out decently close to g.

Now the part I am confused about is calculating uncertainty for:
a) Velocity
b) Acceleration
c) y-intercept of velocity vs. time graph (acceleration line)

Absolute uncertainty for time is +-0.010s, and +-0.001m (1mm) for distance.

Homework Equations


Relative uncertainty % = Absolute Uncertainty / Measured value
* and / of uncertainties with each other adds their relative uncertainties

The Attempt at a Solution


Since this is of a data set, you have many measured values, and it makes no sense to have a single relative uncertainty in the above equation. It would be different for each data point, correct?

Am I missing something from this concept? Or do I literally have to calculate out a different uncertainty for each velocity? Another possibility could be finding relative uncertainty for the first data point and using that % throughout the problem for all of them but that can't be right...
 
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