Finding the Error: ε = dL/L Calculation

In summary, the purpose of finding the error in a calculation is to determine the accuracy and precision of the result. The formula for calculating error is ε = dL/L, where ε represents the percentage error, dL represents the difference between the measured value and the accepted value, and L represents the accepted value. The percentage error can be interpreted as the difference between the measured value and the accepted value expressed as a percentage of the accepted value. There are many factors that can contribute to error in scientific measurements, and it is important for scientists to identify and minimize these sources of error. This can be achieved by using appropriate equipment and methods, carefully controlling experimental conditions, and identifying and accounting for any sources of systematic error.
  • #1
Yegor
147
1
I have the following problem:
The specimen (rod) is hanging vertically. Weight=P. Young's modulus = E. Area = S. What is the ε-?
ε = dL/L

As I know Energy U=V*(E*ε ^2)/2
And the work is A=P*dL(dL of center of mass)
In this case A=p*dL/2
So it must be that ε =P/(E*S)
But the correct answer is ε =P/(2*E*S)
Where is the mistake?
 
Last edited:
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  • #3


The mistake in your calculation is that you are not taking into account the change in length of the rod due to its own weight. When a rod is hanging vertically, the weight of the rod itself causes it to elongate slightly, resulting in a change in length (dL). This change in length needs to be included in the calculation for ε, which is why the correct formula is ε = P/(2*E*S). This takes into account both the weight of the rod and its own elongation.
 

1. What is the purpose of finding the error in a calculation?

The purpose of finding the error in a calculation is to determine the accuracy and precision of the result. It allows scientists to understand the level of uncertainty in their measurements and to make informed decisions about the validity of their data.

2. What is the formula for calculating error in scientific measurements?

The formula for calculating error is ε = dL/L, where ε represents the percentage error, dL represents the difference between the measured value and the accepted value, and L represents the accepted value.

3. How do you interpret the percentage error in a calculation?

The percentage error can be interpreted as the difference between the measured value and the accepted value expressed as a percentage of the accepted value. A smaller percentage error indicates a more accurate measurement, while a larger percentage error indicates a less accurate measurement.

4. What factors can contribute to error in scientific measurements?

There are many factors that can contribute to error in scientific measurements, including human error, equipment limitations, environmental conditions, and systematic errors in the experimental design. It is important for scientists to identify and minimize these sources of error in order to obtain reliable and accurate results.

5. How can scientists reduce error in their calculations?

Scientists can reduce error in their calculations by using appropriate equipment and methods, carefully controlling experimental conditions, and repeating measurements multiple times to check for consistency. It is also important to identify and account for any sources of systematic error in the experimental design.

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