Centripetal Force Experiment. Measure the centripetal force and compare it with the theorectical value Fc=mrω2

3. Method

Refer to the figure in the worksheet.

1. Electronic balance was used to measure the mass of bung, metal weights and hanger.
2. Meter ruler was used to measure the length of string.
3. Stop watch was used to record the time for 20 revolutions.
4. It was not easy to keep L unchanged when whirling the bung, so we had to practise for a while before taking the data.

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4. Data Analysis

Mass of rubber bung (m) is 0.0192 ± 5×10-5 kg.

Table 1

5. Errors and Accuracy

After calculations, the fractional errors are summarized as follow:

= ±2.60×10-3

Table 2

6. Discussion

Assumptions

1. Acceleration due to gravity (g) is taken as 9.81 ms-2. Actually it varies in different position on Earth.
2. The string is massless.
3. The bung is whirled in absolutely horizontal circle.
4. During wirling, ω and L were kept constant.

Random and Systematic Errors

Random errors include measuring length of string, time for 20 revolutions (due to reaction time, miscount) and mass of bung/weights (due to wind).

Systematic errors include measuring mass of bung/weights (due to inacurracy of balance).

Limitation of Appartus

1. There is friction between glass tube and the string.
2. The string is extensible.
3. Air resistance cannot be avoided

Suggestions for Improvements

1. Use smoother string or lubricate the string with oil.
2. Increase mass of weights used to reduce the effect of friction.
3. Increase number of revolutions (say 30 revolutions.)

Precautions

1. The rubber bung was tied securely and is whirled safely without hitting any person or object.
2. Swith off the fan for more accurate measurment of mass.

Comparison of Experimental with Expected Result

Refer to Table 1, for M=0.1, 0.16 and 0.18, tension (mω2L) is smaller than Mg. For M=0.12 and 0.14, tension is larger than Mg.

Apart from errors, the main source of such difference is friction between glass tube and string.

Friction can act on the string either upward (when ω slightly decrease) or downward (when ω slightly increase).

For M=0.1, 0.16 and 0.18, friction act upward.

For M=0.12 and 0.14, friction act downward.

7. Conclusion

Taking the errors into account, Fc=mrω2 is verified.

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