Calibration error & zero error

In summary: Adding a zero error to the ruler didn't affect the result,but added to the uncertainty. Adding a % error to the ruler added to both.In summary, the conversation discusses the effect of a zero error and a calibration error on the result and uncertainty of an equation. It is suggested to consider the effect of these errors on the difference terms in the equation. The "uncertainties" represent the limited precision of measurements and can be reduced by repeating the experiment, while the zero and calibration errors affect the accuracy of the result and should be eliminated or compensated for.
  • #1
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Homework Statement


I have an equation with a number of variables, of which the values and their uncertainties are known. Two of these variables are measured with a ruler, h and l. The question is, will a zero error in the ruler affect the answer or the uncertainty in the answer? The same question for a possible calibration error.


Homework Equations


[tex]\mu = \left(\frac{\pi*R^4}{8Q}\right)*\left(\frac{p*g*(h1 - h2) - p*g*(h2 - h3)}{l1 - l2}\right)[/tex]

[tex]R = (400 \pm 4)*10^{-6} m[/tex]
[tex]Q = (100 \pm 0.5)*10^{-9} \frac{m^{3}}{s}[/tex]
[tex]l1 = (163.8 \pm 0.2)*10^{-3} m[/tex]
[tex]l2 = (101 \pm 0.2)*10^{-3} m[/tex]
[tex]h1 = (223 \pm 1)*10^{-3} m[/tex]
[tex]h2 = (83 \pm 1)*10^{-3} m[/tex]
[tex]h3 = (23 \pm 1)*10^{-3} m[/tex]
[tex]g = 10 \mbox{and} p = 1000 [/tex]

The Attempt at a Solution


Evaluating this function I get [tex]\mu = (1.28 \pm 0.07)*10^{-3}[/tex]. The actual zero error isn't given, so I'll assume an error of 1%. Can I simply multiply all the h and l values by 1.01 and then evaluate [tex]\mu[/tex] again to see if it deviates from the above answer? If so, do I multiply the uncertainties in h and l by 1.01 as well, or only their actual values?

As for the calibration error, how is this different from the zero error?
 
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  • #2
As I would read it, I would think they want you to calculate the error with and without the uncertainties in h and l, which I think means that the nominal result wouldn't change but the error may, if it's weight is significant in determining the original % error.

In the case where you have a systematic error like calibration maybe consider what the effect is on the difference terms in the equation.
 
  • #3
I don't understand. If I have a zero error of 1%, can I simply multiply the uncertainties in h and l by 1.01 as well? If I do that and re-evaluatie the equation, I get [tex]\mu = (1.28 \pm 0.06)*10^{-3}[/tex].

In the case where you have a systematic error like calibration maybe consider what the effect is on the difference terms in the equation.[/qupte]

What exactly do you mean by this?
 
  • #4
For a zero error of 2 mm, (e.g using the end of the ruler instead of the zero mark)
true value of h = measured value of h - 2 mm

For a calibration error of 1% (e.g. due to thermal expansion of the ruler)
true value = 1.01*(measured value)
 
  • #5
Thanks. Now if I want to calculate the uncertainties again, do I substract 2 mm from the uncertainties in h and l as well or do those stay the same?
 
  • #6
Shukie said:
Thanks. Now if I want to calculate the uncertainties again, do I substract 2 mm from the uncertainties in h and l as well or do those stay the same?

The "uncertainties" represent the limited "precision" of the measurements.
They are called "random" errors as suggested by the +/-. They can be reduced
(and estimated more reliably) by repeating the experiment several times,
but are inescapable and should always be quoted.
BTW when you are quoting the uncertainty, be careful not to introduce
a "rounding error" by not quoting enough significant figures:
L=101 +/- 0.2 is criminal!


Zero, calibration (and rounding!) errors affect the "accuracy" of the result,
and are called "systematic" errors. They have the same sign, and won't
cancel out with repeating the experiment. They should be eliminated or
compensated for.
 

What is calibration error?

Calibration error is the difference between the measured value of a device and the true value. It is caused by inaccuracies in the manufacturing process or changes in the device's performance over time.

What is zero error?

Zero error is a type of calibration error that occurs when a measuring device does not read zero when there is no input being measured. This can be caused by a variety of factors, such as wear and tear or incorrect calibration.

How do you calculate calibration error?

To calculate calibration error, you need to compare the measured values of a device to the known true values. The difference between the two is the calibration error. It is often expressed as a percentage of the true value.

What are the effects of calibration error on measurements?

Calibration error can cause incorrect measurements, which can lead to errors in data analysis and decision making. It can also result in additional costs for retesting or recalibration of equipment.

How can calibration error and zero error be minimized?

Calibration error and zero error can be minimized by regularly calibrating and maintaining measuring devices, using high-quality equipment, and following proper measurement techniques. It is also important to identify and correct any sources of error in the measurement process.

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