Calculating error in measurements w/ uncertainty

[Wa1337]

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.

 

[gneill]

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.

 

[Wa1337]

Thanks but I'm still a little confused...would I have to do the 0.1/2.4 twice and add them or what?

 

[gneill]

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.

 

[Wa1337]

Well in that scenario delta Z would be the change in 2.4 + .1 and 2.4 -.1 right? What about delta A?

 

[gneill]

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
\frac{\Delta Z}{Z} = n \frac{\Delta A}{A}
giving
\Delta Z = 2 Z \frac{\Delta A}{A}
and since Z = A², this yields
\Delta Z = 2 A^2 \frac{\Delta A}{A}
You could reach the same result using entry 3 in the table (for Z = A*B) by setting B = A and ΔB = ΔA.

 

[Wa1337]

Ok thanks for clarifying.