Help with error analysis ly needed

In summary, the student attempted to solve an equation for t and found an error that was much larger than the predicted value.
  • #1
slasakai
16
0
Help with error analysis! urgently needed

Homework Statement


Using the theoretical prediction of t, find the errors of both t and x, . The problem is based on an experiment I did in Labs, In which a small metal ball was fired at 40° (uncertainty 0.5°) to the horizontal, at a height,y= 1.095m (with uncertainty of 0.005m) and fired at another measured quantity of initial speed V=5.23 m/s(uncertainty of 0.01m/s). and t is the time taken to hit the ground and x is the range of the ball.


Homework Equations



y=y0 - (Vsinθ)t - (0.5g)t^2

using quadratic equation to solve for t

t=((Vsinθ+ sqrt((Vsinθ)^2 + (2gy))/g

and later plug in value of t
into equation x=(Vcos40)t for x

also we are instructed to ignore the uncertainty on the constant g

The Attempt at a Solution



putting in values t=0.926 s(3sf) and although I cannot type all of my working here, I used a series of steps calculating the errors on individual functions of the equation for t and slowly combining them, however it keeps resulting in an error of 1.17616421... which obviously cannot be correct as this is larger than the predicted value! I'm clearly making a mistake somewhere, a solution will be greatly appreciated.

Thanks gneill, I see how not including any working would make it difficult to find my mistake. I will try my best to describe the method I used here.

I used the functional approach to calculate all the errors, as I couldn't really understand the calculus method.

here goes:

1. I first calculated the error on sinθ, using α=abs(cosθ) * error on sinθ = 0.3830222216

2. Then the error on Vsinθ, using α=sqrt((errorV/V)^2 + (errorsinθ/sinθ)^2) * Vsinθ = 2.003216532

3. Then the error on (Vsinθ)^2 , α=abs(2*Vsinθ) * (error on Vsinθ) = 13.4687433 [this value is the one where I start to doubt myself]

4. Then I calculate the error on 2gy using α= abs(2g) * (error on value of y) = 0.0981
[wasnt completely sure about taking g to be a constant despite being told to ignore the uncertainty]

5. combining errors of the (Vsinθ)^2 + (2gy) using α= sqrt( errora^2 + errorb^2) = 13.46910059 [an obviously massive value]

6. propogating this error through a power of 0.5, using same functional approach = 1.176164221

7. finally adding the errors of everything under the sqrt sign and the Vsinθ outside it using

α= sqrt( errora^2 + errorb^2) gives such a ridiculous answer = appx 2.3, which is so wrong...

I know this was a bad way to write it out, but if anyone can follow it I would greatly appreciate it
 
Last edited:
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  • #2
Hi slasakai. Welcome to Physics Forums.

There's not much we can do to find your error without seeing the work. But I can tell you that the result for the error in t should be closer to 0.001 seconds than 1 s.

If you're proficient with calculus and taking derivatives, you can find the error for the whole expression at once via:

$$\delta t = \sqrt{\left(\frac{df}{d \theta}\right)^2\delta \theta^2 +
\left(\frac{df}{dv}\right)^2\delta v^2 +
\left(\frac{df}{dy}\right)^2\delta y^2 }$$
where ##f(\theta, v, y)## is the function for the time that you found and the derivatives are taken to be partial derivatives. The ##\delta \theta, \delta v, ## and ##\delta y## are the measurement errors.
 
  • #3
slasakai said:
1. I first calculated the error on sinθ, using α=abs(cosθ) * error on sinθ = 0.3830222216
That looks like the error (in degrees) of theta. That's not the error in sin theta. Need to convert to radians.
 
  • #4
haruspex said:
That looks like the error (in degrees) of theta. That's not the error in sin theta. Need to convert to radians.

thank you so mcuh haruspex, you have literally helped me so much by spotting that error. It was driving me nuts trying to figure out where I'd one wrong
 
  • #5
!



Hello,

Thank you for reaching out for help with your error analysis. It sounds like you have put a lot of effort into trying to find the errors for t and x, but you are still getting a very large error for t. Based on the information you have provided, it is difficult to determine exactly where you may be going wrong. However, I can offer a few suggestions that may help you find your mistake.

First, it is important to double check your calculations and make sure you are using the correct equations for error propagation. It may be helpful to have a peer or teacher review your work to see if they spot any errors.

Second, when calculating the error for (Vsinθ)^2, you should use the formula α=2*Vsinθ*errorVsinθ, as this is the correct way to propagate the error for a squared term. This may be why you are getting such a large error for this step.

Third, when calculating the error for 2gy, it is correct to use the formula α=2g*errory, even though you were instructed to ignore the uncertainty for g. This is because you are still using the value of g in your calculation, so you need to include its uncertainty.

Lastly, it may be helpful to use the calculus method for error propagation, as it can be more accurate and efficient than the functional method. If you are unsure how to use it, your teacher or a tutor may be able to provide some guidance.

I hope these suggestions are helpful and lead you to find your mistake. Good luck with your error analysis!
 

1. What is error analysis and why is it important in scientific research?

Error analysis is the process of identifying and quantifying sources of error in research data. It is important because it allows scientists to evaluate the accuracy and reliability of their results, and make improvements to their methods if necessary.

2. What are the common types of errors in scientific research?

There are three main types of errors: random errors, systematic errors, and blunders. Random errors are unpredictable and can occur due to chance or external factors. Systematic errors are consistent and usually caused by flaws in the experimental design or equipment. Blunders are mistakes made by the researcher, such as incorrect data entry.

3. How do you identify and reduce errors in data analysis?

To identify errors, scientists can use statistical methods to analyze the data and look for patterns or inconsistencies. To reduce errors, it is important to have proper controls in place, carefully calibrate equipment, and repeat experiments multiple times to ensure reproducibility.

4. Can errors be completely eliminated in scientific research?

No, it is impossible to completely eliminate all errors in scientific research. However, by identifying and minimizing potential sources of error, scientists can improve the accuracy and reliability of their results.

5. How do you report error analysis in a scientific paper?

When reporting error analysis in a scientific paper, it is important to clearly describe the methods used to analyze and quantify errors. Results should be presented in a clear and organized manner, and any limitations or uncertainties should be acknowledged. Additionally, it is important to discuss the potential impact of errors on the conclusions of the study.

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