Calculating error in measurements w/ uncertainty

In summary, the conversation discusses error analysis in the context of finding the error in the area and circumference of a circle with a radius of 2.4 cm and uncertainty of 0.1 cm. The suggested method involves using a table for mathematical operations and taking into account the uncertainty values when performing calculations. The conversation also touches on the concept of exact constants and their lack of uncertainty.
  • #1
Wa1337
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Homework Statement


The radius of a circle is measured to be 2.4 cm +/- 0.1 cm.
Find the error in the area of the circle.
Find the error in the circumference.

Homework Equations


Have no idea but I'm taking a guess it could be multiplying fractional uncertainties?

The Attempt at a Solution


I got 18.09 for area and 15.08 for circumference...just need a way to go about calculating error

...really rusty in math and learning physics now, pardon the noob question.
 
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  • #2
A discussion of error analysis can be found here:

http://teacher.pas.rochester.edu/PHY_LABS/AppendixB/AppendixB.html

Near the end of the document is a table showing how to deal with the uncertainty values when performing various mathematical operations.

Keep in mind that constants (like 2 or π) are exact and have zero uncertainty.
 
  • #3
Thanks but I'm still a little confused...would I have to do the 0.1/2.4 twice and add them or what?
 
  • #4
Wa1337 said:
Thanks but I'm still a little confused...would I have to do the 0.1/2.4 twice and add them or what?

For what calculation?

You might want to ponder entry 5 in the table, which deals with numbers with uncertainties raised to a power.
 
  • #5
Well in that scenario delta Z would be the change in 2.4 + .1 and 2.4 -.1 right? What about delta A?
 
  • #6
Wa1337 said:
Well in that scenario delta Z would be the change in 2.4 + .1 and 2.4 -.1 right? What about delta A?

Z is the result. ΔZ is the uncertainty in the result. A is the number with uncertainty ΔA. So in the case of calculating Z = A2, n = 2 and
[tex] \frac{\Delta Z}{Z} = n \frac{\Delta A}{A} [/tex]
giving
[tex] \Delta Z = 2 Z \frac{\Delta A}{A} [/tex]
and since Z = A2, this yields
[tex] \Delta Z = 2 A^2 \frac{\Delta A}{A} [/tex]
You could reach the same result using entry 3 in the table (for Z = A*B) by setting B = A and ΔB = ΔA.
 
  • #7
Ok thanks for clarifying.
 

FAQ: Calculating error in measurements w/ uncertainty

What is the purpose of calculating error in measurements?

The purpose of calculating error in measurements is to quantify the amount of uncertainty or variation in a measurement. This allows scientists to better understand the reliability and accuracy of their data and make appropriate adjustments or interpretations.

What is the difference between precision and accuracy?

Precision refers to the level of consistency or reproducibility in a set of measurements, while accuracy refers to how close a measurement is to the true or accepted value. A measurement can be precise but not accurate, or accurate but not precise.

How is error typically expressed?

Error is typically expressed as a percentage or absolute value. Percentage error is calculated by dividing the absolute error by the true or accepted value and multiplying by 100. Absolute error is simply the difference between the measured value and the true or accepted value.

What are some common sources of error in measurements?

Some common sources of error in measurements include human error, instrument error, environmental factors, and the limitations of the measuring tool or technique. It is important for scientists to identify and minimize these sources of error to obtain more accurate and reliable data.

How can uncertainty be reduced in measurements?

Uncertainty in measurements can be reduced by using more precise and accurate instruments, taking multiple measurements and calculating the average, and controlling for external factors that may affect the measurement. It is also important to follow proper measurement techniques and record all measurements accurately.

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