PHYS171_f11_lecture_03

PHYS171_f11_lecture_03 - PHYS171 Principles of Physics I...

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PHYS171 Principles of Physics I Prof. Arthur La Porta Assistant Professor, Department of Physics, Institute of Physical Science and Technology Maryland Biophysics Program alaporta@umd.edu Rm 1111, IPST building (building #085) Chapter 1 Propagation of errors I measure certain quantity x with known uncertainty. I calculate something from the measurements, y=f(x). What is the uncertainty in y ? This applies when there is only one variable. Notation: this is a “partial derivative.” Partial derivative means we take the derivative, assume that any other variables are not allowed to vary. x f x f σ =
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Chapter 1 Propagation of errors A circle has radius 1 meters, with uncertainty 0.1 meters. What is the area and the uncertainty in area? x f x f σ = A circle has radius 10 meters, with uncertainty 0.1 meters. What is the area and the uncertainty in area? Chapter 1 Propagation of errors Often there is more than one variable involved. For example, I measure the length and width of a rug ( w =3m ± 0.2m, h =5m ± 0.3m). What is the uncertainty in the area A = h × w General Formula This assumes uncertainties are “independent” (i.e., due to random measurement error, not mis-calibration of the ruler, for example). In the “partial derivative,” when we take the derivative with respect to x we pretend y is a constant, and visa versa (when we take the derivative with respect to y we pretend x is a constant). 2 2 2 2 2 y x f y f x f + =
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Chapter 1 Uncertainty in Measurement Rules: When adding two numbers, the square of the absolute uncertainty in the result is the sum of the squares of the absolute uncertainties of the terms When multiplying two numbers the square of the relative uncertainty of the result is the sum of the squares of the relative uncertainties of the factors
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PHYS171_f11_lecture_03 - PHYS171 Principles of Physics I...

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