Calculating Uncertainty: What is the Effect of θ?”

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In summary, the conversation discussed the concept of uncertainty and error in regards to an equation involving the absolute uncertainty in θ. It was determined that option A was incorrect due to the difference between fractional uncertainty and error, and the fact that the percentage uncertainty would be the same for all values of θ.
  • #1
Janiceleong26
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Homework Statement


image.jpg


Homework Equations


Absolute uncertainty in θ = δθ/θ

The Attempt at a Solution


I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?
 
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  • #2
Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?
 
  • #3
haruspex said:
Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?
The actual error in X would be rX? And rθ?
 
  • #4
Janiceleong26 said:
The actual error in X would be rX? And rθ?
Yes. So what is the fractional error in theta?
 
  • #5
haruspex said:
Yes. So what is the fractional error in theta?
r ?
 
  • #6
Janiceleong26 said:
r ?
Right. Can you now see why A is wrong?
 
  • #7
haruspex said:
Right. Can you now see why A is wrong?
No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right? Isn't the effect the same?
 
  • #8
Janiceleong26 said:
No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right?
No, the percentage uncertainty is 100x fractional uncertainty.
 
  • #9
haruspex said:
No, the percentage uncertainty is 100x fractional uncertainty.
What's the difference between fractional uncertainty and fractional error?
 
  • #10
Janiceleong26 said:
What's the difference between fractional uncertainty and fractional error?
Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?
 
  • #11
haruspex said:
Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?
Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?
 
  • #12
Janiceleong26 said:
Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?
Yes.
 
  • #13
haruspex said:
Yes.
Thanks
 

1. What is the purpose of calculating uncertainty in scientific experiments?

Calculating uncertainty allows scientists to determine the reliability and accuracy of their experimental results. It also helps in identifying potential errors and improving the experimental design.

2. How is uncertainty calculated?

Uncertainty is typically calculated by finding the standard deviation of the measured values and using it to determine the range of possible values. This can be done using statistical tools or mathematical formulas such as the propagation of uncertainty.

3. What is the role of θ in calculating uncertainty?

θ, also known as theta, is a symbol used to represent the uncertainty or error in a measurement. It is used in mathematical formulas to calculate the uncertainty of a particular value.

4. How does changing θ affect the calculated uncertainty?

Changing θ can significantly affect the calculated uncertainty. A larger θ value indicates a larger uncertainty, while a smaller θ value indicates a smaller uncertainty. Therefore, it is important to carefully consider and accurately estimate θ in order to obtain reliable results.

5. Can uncertainty be completely eliminated in scientific experiments?

No, uncertainty cannot be completely eliminated in scientific experiments. This is because all measurements have some degree of error and there will always be some level of uncertainty associated with them. However, by carefully controlling variables and accurately estimating θ, uncertainty can be minimized to a certain extent.

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