Physics lab, calculating/combining errors

In summary, the conversation discusses how to calculate T^2 and ΔT^2 for a given value of T, as well as how to calculate d and Δd using v and t values. The conversation also touches on how to calculate a and Δa using given values for d and t. Various equations and hints are provided to guide the calculations.
  • #1
cjweidle
1
0
I just started the semester off in physics lab and I am so rusty. I did three perfectly okay by myself but these last three I can't seem to figure out. Any help on the direction to take with these is appreciated!

c) T = 0.433 ± 0.004 s. Calculate T^2 andΔT^2.

d) Given d = vt, v = 55 mi/hr ± 5% and t = 5.00± 0.03 hrs, calculate d and Δd.
Like here do I put in d= (55 ± 5%)(5.00 ± 0.03)
I know I have to get the percent into an actually number, I can do that. but I don't know if this is the way to go about it and then I really don't know how to get Δd.

e) Given a = 2d/ t2 , d = 82.0 ± 0.2 cm and t = 4.23 ± 0.05 s, calculate a and Δa.
 
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  • #2
Hint:

C) If X = a ± b then ΔX ^ n = X ^ n * ( n * ( ΔX / X ) ) = a ^ n ( n * (b / a ) )

D) Δd = Δ(vt) = vt ( ΔV / V + Δt / t )

E) Δ(2d/t^2) = 2d/t^2 ( Δd/d + Δt^2/t^2)
 

What is the purpose of calculating and combining errors in a physics lab?

The purpose of calculating and combining errors in a physics lab is to determine the overall uncertainty or margin of error in a measurement or calculation. This helps to ensure the accuracy and reliability of the data and results obtained in the lab.

How are errors typically calculated in a physics lab?

Errors are typically calculated by taking the difference between the measured value and the accepted or expected value, and then dividing by the accepted value. This result is then multiplied by 100 to obtain the percentage error.

What is the difference between random and systematic errors in a physics lab?

Random errors are unpredictable variations in measurements that can occur due to factors such as human error or equipment limitations. Systematic errors, on the other hand, are consistent and repeatable inaccuracies in measurements that are caused by faulty equipment or a flawed experimental design.

How do you combine errors of multiple measurements in a physics lab?

To combine errors of multiple measurements, you can use the root sum of squares method. This involves taking the square root of the sum of the squared individual errors. This accounts for both random and systematic errors and provides a more accurate estimation of the overall uncertainty.

Why is it important to report and consider errors in a physics lab?

Reporting and considering errors in a physics lab is crucial for ensuring the validity and reliability of the data and results obtained. It also helps to improve the accuracy of future experiments by identifying and addressing potential sources of error. Additionally, acknowledging errors promotes transparency and honesty in scientific research.

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