Error analysis, multiplying an error

[bingoboy]

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

 

[harrylin]

Hi welcome to physicsforums.

I suppose that with "degree", you mean degree Celcius. 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

 

[uby]

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.

 

[bingoboy]

yeah thanks harrylin that's exactly what i was trying to figure out, much appreciated

 

[pmacias]

?

I understand the importance of error analysis in any scientific experiment or calculation. In this case, we are dealing with multiplying an error, which can lead to larger errors in our final result.

To answer the question, if ΔT has an error of one degree and it is multiplied by the mass of an object (m), the error in the result (y) will also be proportional to the mass. This means that the error in y will be 2M, as stated in the attempted answer.

However, it is important to note that this error will only be valid if the error in ΔT is consistent for all values of m. If the error in ΔT varies for different values of m, then the error in y will also vary accordingly.

To accurately determine the error in y for a range of values of m and ΔT, it would be best to calculate the error for each individual value and plot it on the graph. This will give a more precise representation of the overall error in the data.

In conclusion, when dealing with multiplying an error, it is important to consider the proportionality of the error and to calculate it for each individual value in order to accurately represent the overall error in the data.