Standard Deviation Problem in Physics. Help?

In summary, the conversation is about a student's question on finding the minimum value for the uncertainty in the calculation of Rx in a Wheatstone bridge problem. The student is unsure about the correct method to use and is worried about getting the wrong answer. They mention different methods of finding the deviation and ask for confirmation on their approach. Another person suggests using partial derivatives, but the student's physics course does not cover calculus. The student agrees that "Propagation of errors" is the method they are supposed to use, but is confused because there are multiple ways to do it and they often yield different results. They ask for someone to show them a reliable method for finding the deviation.
  • #1
cheechnchong
132
1
Standard Deviation Problem in Physics. Help!?

Homework Statement



In working with Wheatstone bridge one student chose the value for R1 so that the bridge is balanced at L1 = 48.5 cm and L2 = 51.2 cm. If Each measurement has an uncertainty of +/- .05, what would be the minimum value for the uncertainty in the calculation of Rx?

Given Equation: Rx = (L2/L1)*R1

The Attempt at a Solution



I know that R1 can be eliminated when looking at this question. However, my main concern is how to find the deviation using the Division rule? I have been exposed to several methods of finding the deviation. It confuses me a lot!

My guess is that, regardless of the sign (multiplication, division, subtraction, addition), the deviation +/- .10 . it's just a sum of the two .05 uncertainties in measurements.

I just need confirmation. I don't want to end up screwing up this problem...It's kind of a crucial step for the next few problems. Thanks for any help I can get!
 
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  • #2
How does the formula for calculating the deviation in Rx look like?
 
  • #3
Rx = (51.2 +/- 0.050 cm)/(48.5 +/- 0.050 cm)

im ignoring R1 because a random value was chosen for it. anyways, it just comes down to the uncertainties. how to solve it? I am thinking about adding them up, which would be 0.10 cm. what do you think?
 
  • #4
I don't think this is correct. You said that you know of some methods to find the deviation. Do you know a method where you have to take partial derivatives?
 
  • #5
Edgardo said:
I don't think this is correct. You said that you know of some methods to find the deviation. Do you know a method where you have to take partial derivatives?

nope, we never learned that. I'm taking the trig-algebra based physics. we will never learn anything that involves calculus. what is the other way?
 
  • #6
Hmm...I thought it was about "Propagation of errors". Can you show some of the methods to determine the deviation?
 
  • #7
Edgardo said:
Hmm...I thought it was about "Propagation of errors". Can you show some of the methods to determine the deviation?

it is, but I'm confused because there are many ways to do it. the many ways to do it often end up with different answers...i mean WAY different! that's why I am asking this board. it's cool. thanks for the help. i appreciate it!
 
  • #8
Show at least one way how to calculate it and some other that yields a different result as you say.
 

FAQ: Standard Deviation Problem in Physics. Help?

1. What is standard deviation in physics?

Standard deviation in physics is a measure of the amount of variation or dispersion of a set of data from its mean (average) value. It is commonly used to determine the precision and reliability of experimental measurements in physics.

2. How is standard deviation calculated in physics?

The standard deviation in physics is calculated using the formula: σ = √(Σ(x-x̄)2/n), where x represents each individual data point, x̄ is the mean value, and n is the total number of data points.

3. Why is standard deviation important in physics?

Standard deviation is important in physics because it helps to quantify the uncertainty or error in experimental measurements. It also allows for comparison and evaluation of different sets of data, and can indicate the level of precision and reliability of the results.

4. How does standard deviation affect the interpretation of data in physics?

The magnitude of the standard deviation can affect the interpretation of data in physics. A larger standard deviation indicates a higher level of variability in the data, which may suggest that the measurements are less precise or reliable. On the other hand, a smaller standard deviation indicates a lower level of variability and a higher level of precision.

5. Can standard deviation be negative in physics?

No, standard deviation cannot be negative in physics. The formula for standard deviation involves squaring the differences between data points and the mean, which ensures that the result is always positive or zero. A negative value would not make sense in the context of measuring the spread of data.

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