Confusion about how to work out the uncertainty in my final calculated value

In summary, the conversation discusses finding the uncertainty in the value of v from the known error in G, where G is equal to a constant divided by v. The suggested method is to take the partial derivative of the function G= constant/v, square it, and divide by G^2. This leads to the calculation of ΔG = [GΔv]/v. The conversation also mentions the potential availability of error functions in the lab manual.
  • #1
Pronitron
9
0

Homework Statement


So basically I have plotted two variables I measured on a graph, which gives a simple linear relationship, and have found the gradient and standard error of the gradient (1.21251 and 0.03275 respectively). Now my problem is that this gradient is equal to a constant divided by the value I'm trying to calculate i.e G=constant/v so when I express the variable v with its uncertainty how do I calculate this uncertainty in v from knowing the error in G?



Homework Equations


(2*pi*f)/c = G


The Attempt at a Solution


I attempted to find the ratio between the standard error of the gradient and the gradient and then multiply by my value for c, i.e 0.02042/0.03275*c, is this the correct method?
 
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  • #2
If I'm reading your questions right.


[Δv/v]2 = [ΔG/G]2

[δG/δv]2/G(v)2 = [ΔG/G]2

bascially you want to take the partial derivative of your function G= constant/v and square it then divide the entire thing by G2

then solve for ΔG which should be ΔG = [GΔv]/v

I can't name the function, if this is for a lab, I'm hoping your school puts the error functions in the manual.
 

1. How do I calculate uncertainty in my final calculated value?

To calculate uncertainty, you must first determine the sources of error in your experiment. This can include measurement errors, equipment limitations, and human error. Once you have identified these sources, you can use statistical methods such as standard deviation or error propagation to calculate the uncertainty in your final value.

2. What is the difference between absolute and relative uncertainty?

Absolute uncertainty is a measure of the actual difference between a measured value and the true value. It is usually expressed in the same units as the measured value. Relative uncertainty, on the other hand, is a percentage or ratio that compares the absolute uncertainty to the measured value. It is often used to compare the accuracy of different measurements.

3. How do I interpret uncertainty in my final value?

Uncertainty represents the range of possible values that your final result could fall within. A higher uncertainty indicates that your measurement or calculation is less precise and has a larger margin of error. It is important to report uncertainty along with your final value to accurately communicate the reliability of your results.

4. Can I reduce uncertainty in my final value?

Yes, there are several ways to reduce uncertainty in your final value. These include using more precise equipment, increasing the number of measurements taken, and minimizing sources of error. It is important to note that uncertainty can never be completely eliminated, but it can be reduced to increase the accuracy of your results.

5. How does uncertainty affect the validity of my results?

Uncertainty does not necessarily affect the validity of your results, as it is a measure of precision rather than accuracy. However, a high uncertainty may indicate that your results are unreliable and require further investigation. It is important to carefully consider the uncertainty in your final value when drawing conclusions from your experiment.

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