Experimental Determination of π PDF

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Summary

Example of the assignment of Experimental Determination of π...

Description

Experimental Determination of π Objective: To gather experimental data and thus calculate the value of π by implementing the formula for the circumference of a circle (πd).

Required Materials:      

4 objects with circular bases 1 m length string Meter stick with cm and mm measurements Tape measure Pencil Recording log

Experimental Procedures: 1. Gather all required lab materials. 2. By using any combination of the measuring tools, find the circumference of one of the circularly-based items. Record this value in a data table. 3. Next, by using any combination of the measuring tools, find the diameter of one of the circularly-based items. Record this value in a data table. 4. Repeat steps 2-3 twice more to get two other values for the circumference and diameter. You should now have 3 values for each.

5. Repeat steps 2-4 for the other three circularly-based objects. Record all values in your data table. 6. After organizing all values in your data table, calculate the average circumference of one of your circles by adding all values together (C1 + C2 + C3) and dividing by three. Record this value. 7. Now, calculate the average circumference of one of your circles by adding all values together (D1 + D2 + D3) and dividing by three. Record this value. 8. Repeat steps 6-7 for the other three circularly-based objects. Record all values in your data table. 9. Finally, take your average circumference and average diameter of your first object and solve for π. (Cav/Dav) Record this value. 10. Repeat step 9 for each of the other three circularly-based objects. Record all values in your data table. 11. Put away all lab materials.

Data Table: Circle 1: 1000 ml pyrex container Circle 2: coffee cup Circle 3: chair stool Circle 4: top to electronic scale

C1 Circle 1

31 cm

C2 31 cm

C3

D1

31.2 cm

9.75 cm

D2

D3

9.8 cm

8.6 cm

Cavg 31.07 cm

D avg 9.52 cm

Pi= Cav/Dav 3.26 cm

Circle 26.9 26.8 25.8 7.9 cm 7.8 cm 2 cm cm cm Circle 132.4 132.3 131.85 41 cm 41 cm 3 Circle 50 cm 48.5 49.8 15.4 15.2 4 cm cm cm cm Therefore… (3.26 + 3.36 + 3.25 + 3.23)/4 = 3.275 3.275 = pi average

8 cm 40 cm 15.35 cm

26.57 cm 132.18 cm 49.43 cm

7.9 cm 40.67 cm 15.3 cm

3.36 cm 3.25 cm 3.23 cm

3.275 = πexp Results: Circle 1

C av 31.07 cm

D av 9.52 cm

Pi = Cav/Dav 3.26 cm

Circle 2 Circle 3 Circle 4

26.57 cm 132.18 cm 49.43 cm

7.9 cm 40.67 cm 15.3 cm

3.36 cm 3.25 cm 3.23 cm

After following procedures to the point and coming up with our data, we were able to come up with a logical conclusive value. By measuring the diameter and circumference and averaging these values, we found that our average value for π was 3.275. While this was very close, this is not the value of 3.14. In order to copy this lab again and get a closer result, we can use more precise instruments. As well, human error could very well have played a part in this, as values will be approximated if measuring by eye. If we were to redo this lab, I believe that a closer inspection of measurements would yield a more accurate result. % Error = |πexp – π| π % Error = |3.275 – 3.14| 3.14 = 0.135/3.14 = 0.0043. 4.3 percent error....