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Work procedure and data processing. 1. Deviate the pendulum from equilibrium position by 50 angle and let it off.

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  7. HOLDING PROCEDURES

1. Deviate the pendulum from equilibrium position by 50 angle and let it off.

2. Measure the time of five complete oscillations of the pendulum (t). Enter the results of measurement into table 5.

3. Perform the described actions 50 times.

4. Analyze the obtained values and arrange them in increasing progression starting from the smallest value t min up to the peak value t max.

5. Divide the full range of the measured values into 9 equal intervals D t () and determine boundary values t 0 of each interval (t 01= t min+D t; t 02= t 01+D t etc.). Separate the values t i which are relevant to boundary values by horizontal line in the table 5.

6. Count a number of values D n k which has been included in each interval. Calculate frequency of the measured values occurrence in each interval D n i/ n:

.

Enter all obtained results into table 5.

Table 5

Measurement No. Measured values ti, s Measured values inascending order ti, s Δ t, s Δ nk ν k
           
           
…          
           
Mean value of time tave =, s

7. Draw the histogram of the measured values.

8. Determine tav using the histogram. The mean value of the measured time values corresponds to the middle of the histogram greatest column.

9. Determine the error of the direct measurements of time t.

9.1. Enter the first ten measurements of time t into table 6.

9.2. Determine the deviation of the measured values of time from the mean value of time found in the histogram:

9.3. Determine the root-mean-square error of the series measurements result, that is, the mean value according to the formula:

,

where n = 10.

9.4. Calculate the absolute error of measurements of time:

9.5. Calculate the fractional error of results of measurements:

Enter the obtained results into table 6.

9.6. Write down the final result of series of measurements in a form:

Table 6

Exp. No i Measured values ti, s Mean value tave , s Deviation of the measured values from the mean value , s Root mean square error of the series measurements of time Absolute error of time measurement Δ t, s Fractional error of time measurement e, % Length of pendulum l, m Free fall acceleration gave, m/s2 Fractional error of free fall acceleration measurement , m/s2
                   
     
…    
     

10. Determine the free fall acceleration.

10.1. Measure the length of pendulum l.

10.2. Calculate the free fall acceleration according to the formula (10).

10.3. Calculate the measurements error of free fall acceleration according to the formula (11). Write down the result in a form and enter it into table 6.

questions to be admitted for doing laboratory work and its defence

1. What is probability of a random event?

2. How can you draw the histogram of the measured values?

3. How can you define the distribution functions of the measured values?

4. What meaning does the distribution function of the measured values have?

5. How can you define the distribution functions of errors?

6. Give characteristics of the distribution function of errors.

7. Write down the Gaussian distribution function.

8. What is dispersion? What is its value?

9. What is the connection between dispersion and measurement error?

10. Give characteristics of the confidence probability and confidence interval.

11. Give characteristics of the Student’s coefficient. How is the Student’s coefficient determined?

12. How is the free fall acceleration determined in this work?

13. Deduce an equation for calculation of the absolute error of indirect measurements of gravity acceleration?

 

LABORATORY WORK

Rotational motion dynamics.
Moment of Inertia Determination

 

 

The purpose of the work: to study the basic rotational motion dynamics law; to determine the rotating solid body inertia moment.

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Читайте в этой же книге: Measurement error is the measured result deviation from the true value of the measured quantity. (Errors show accuracy of measured values.) | Measurement types | Estimation rules of direct measurement random error | Indirect measurement error estimation rules | Work procedure and data processing | Work procedure and data processing | Work procedure and data processing | Theoretical information | Tasks for the work carrying out | Data processing |
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