PhysicsRankPREVIEWTry a problem

THE PRACTICE STUDIO

Go slowly. Ask why. Make it yours.

PRACTICE · MEMBERSAdvanced · Single correct

PRACTICE / Error propagation

When a large zero uncertainty cancels

Two endpoints are read on the same unchanged ruler. Each reading has an independent random standard uncertainty of 0.60 mm. Both also contain the same additive zero offset, whose standard uncertainty is 3.0 mm. There is no scale-factor uncertainty.

What is the combined standard uncertainty of the endpoint separation?

Organize the givens & assumptions
  • Each independent reading uncertainty: 0.60 mm
  • One shared additive zero uncertainty: 3.0 mm

The same offset applies to both coordinates; independent reading errors are uncorrelated with it. The separation is the second corrected coordinate minus the first. All uncertainties are standard uncertainties, not bounds.

  1. A0.60 mm0.60\ \mathrm{mm}
  2. B0.602 mm0.60\sqrt2\ \mathrm{mm}
  3. C3.02 mm3.0\sqrt2\ \mathrm{mm}
  4. D1.20 mm1.20\ \mathrm{mm}

Try it on paper first. Free sample problems in every collection include the complete reasoning: find one in this collection →