Error analysis, multiplying an error

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Discussion Overview

The discussion revolves around the concept of error analysis in the context of multiplying a variable with an associated error. Specifically, participants explore how the error in a temperature measurement (ΔT) affects the resulting value when multiplied by mass (m) in an equation.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the error in the product (y) remains the same as the error in ΔT or if it becomes proportional to the mass (M), suggesting a potential error of 2M.
  • Another participant proposes that if ΔT is multiplied by a constant with negligible error, the percentual error remains unchanged.
  • A different participant introduces a general principle that the error in a function's output (y) is the derivative of that function with respect to its input (x) multiplied by the error in x, indicating that for linear functions, the error in y is constant times the error in x.

Areas of Agreement / Disagreement

Participants express varying viewpoints on how to calculate the error in the product of mass and temperature. There is no consensus on the specific relationship between the errors in ΔT and the resulting product.

Contextual Notes

The discussion does not resolve the assumptions regarding the nature of the errors or the specific conditions under which the proposed relationships hold. There is also a lack of clarity on how to apply these principles to multiple values of m and ΔT.

bingoboy
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Equation: M (ΔT)=
The question:
If ΔT has an error of one degree, and i multiply it by the mass of an object (m) is the error in y still one

Attempted answer: or is it proportional to M i.e Δt plus or minus 1 degrees so the error in y is 2M?


P.S i need to be able to know the error for a whole bunch of values because I am putting m delta t as an axis on a graph, would i have to work it out for each value of m ΔT
 
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Hi welcome to physicsforums. :smile:

I suppose that with "degree", you mean degree celsius. If you multiply with a constant (thus the constant has no or negligible error) then the percentual error remains the same.

You can find that answer yourself simply by trying:

5x20=100
5x21=105
 
Last edited:
generally speaking, if you have an error in x then the error in y will be the derivative of the function used on x times the error in x. for a straight line, the derivative is a constant value, thus the error in y is a constant value times the error in x.
 
yeah thanks harrylin that's exactly what i was trying to figure out, much appreciated
 

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