Uncertainty in Derived Experimental Results
For a differentiable result f(x_1,...,x_n), first-order worst-case uncertainty is bounded by Delta f approximately sum |partial f/partial x_i| Delta x_i, which reduces to standard sum and power rules in common cases.
Why this shows up in the exam
Laboratory constant determination · Sensor-derived quantities · Multi-step calculations
Learn the idea
An uncertainty calculation should follow the actual equation used to obtain the reported experimental quantity. The measured inputs are the roots of an uncertainty tree; trace how each enters the final formula before combining its contribution.
🧠 Memory hook: Propagate through the formula actually used, not a memorised nearby one.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta f approximately sum |partial f/partial x_i| Delta x_i — first-order worst-case propagation
- Delta f/f approximately sum |a_i| Delta x_i/x_i — monomial special case
How to approach it
- 1Write the final result directly in measured variables
- 2Choose differential or standard rules
- 3Keep guard digits until the final report
Common slip-ups that cost marks
- •Propagating through an intermediate rounded value
- •Including exact constants as uncertain
- •Using percentage addition for an additive formula
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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