Which Measurement Accuracy Most Impacts the Value of g in Pendulum Calculations?

In summary, the conversation discusses the measurements and accuracy of g, T, l, and a for a pendulum experiment. The formula for finding the probable error is also mentioned. After calculating, it is determined that the accuracy of T needs the most improvement. However, it is also suggested to improve the measurements of T by an order of magnitude to improve the accuracy of l.
  • #1
aruwin
208
0
To get the value of g, the period(T), length of pendulum (l) and radius of pendulum bob (a) were measured.
Well, my question is actually to find which accuracy of one of these measurements need to be improved?
The formulae given to find the probable error are
ε _gT = (partial differentiation of g in respect to T) X ε _T

ε _gl = (partial differentiation of g in respect to l) X ε _l

ε_ga = (partial differentiation of g in respect to a) X ε _a

After calculating, the values were:
ε _gT = 1.1 X 10^-3
ε _gl = 3.5 X 10^-4
ε _ga = 6.9 X 10^-5

Since the ε _gT has the biggest derivative, I think T's accuracy is the one that needs the most improvement. Am I right or wrong?
 
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  • #2
You're right. However, your value of l is also pretty noisy. Improve your measurements of T by an order of magnitude and now it is your l value that will be the primary culprit.
 
  • #3
D H said:
Improve your measurements of T by an order of magnitude .

What do you mean by this?
 

FAQ: Which Measurement Accuracy Most Impacts the Value of g in Pendulum Calculations?

What is the difference between accuracy and differentiation?

Accuracy refers to the closeness of a measurement or calculation to the true or accepted value, while differentiation is the process of finding the rate of change of a function or variable. In other words, accuracy is a measure of correctness, while differentiation is a mathematical operation.

Why is accuracy important in scientific research?

Accuracy is crucial in scientific research because it ensures that the results obtained are reliable and can be replicated by other researchers. Inaccurate results can lead to incorrect conclusions and hinder the progress of scientific knowledge.

How is accuracy measured in scientific experiments?

Accuracy is measured by comparing the results obtained to a known or accepted value. This can be done by calculating the percent error, which is the difference between the measured value and the accepted value divided by the accepted value, multiplied by 100.

What are some factors that can affect accuracy in scientific experiments?

Several factors can affect accuracy in scientific experiments, including human error, equipment limitations, and environmental conditions. It is important for scientists to identify and control these factors as much as possible to ensure accurate results.

How does differentiation help in analyzing data?

Differentiation allows scientists to determine the rate of change of a variable, which can provide valuable insights into the behavior and trends of the data. It also helps in finding the optimum values of a function and can be used to solve real-world problems in various fields of science.

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