Objective

To measure the centripetal force for whirling a mass round a horizontal circle and compare the result with the theoretical value given by F = m(2r . Apparatus

12 slotted weights with hanger (0.02kg each)

1 rubber bung with nylon string about 1.5m

1 glass tube about 20cm long

1 triple beam balance

1 meter rule

1 stop watch

Several small paper markers

Theory

When a mass m attached to a string is whirled round a horizontal circle of radius r, the centripetal force for maintaining the circular motion is given by F = m(2r , where ω is the angular velocity of the circular motion. The centripetal force is provided by the tension of the string.

The string will always make an angle( to the horizontal instead of lying on the plane of the horizontal circle described by the mass m. Thus, the centripetal force is given by the horizontal component of the tension. It is shown that the tension T = m(2L regardless of the angle(. Procedure

1. Measure the mass m of the rubber bung by the triple beam balance.

2. Attach the rubber bung with nylon string thread through the glass tube and a number of weights. First start with M = 0.12kg.

3. Measure the length of L from the rubber bung to the glass tube (i.e. 0.8m). Adjust the position of a small paper marker 1cm below the glass tube. The set up is shown below.

4. Hold the glass tube vertically and whirl the rubber bung around above your head in a horizontal circle. Increase the speed of the rubber bung gradually and allow it to move out (i.e. let L increases) until the marker is about 1 cm below the lower end of the glass tube.

5. Keep the angular speed constant so that the marker is always about 1 cm below the glass tube throughout. Ask your partner to time 20 revolutions of the bung using a stop watch. Start the stop watch at 0 and stop it at 20. Take one more confirmatory reading and obtain the mean time for 20 revolutions.

6. Calculate the angular velocity ( and hence find m(2L.

7. Repeat the experiment using different masses M (i.e. 0.16kg, 0.20kg, 0.24kg). Precaution

1. Make sure that the surrounding is cleared before the experiment.

2. You should wear safety goggles.

3. The glass tube should be held above your head.

4. The angular speed of the motion should be kept constant so that the marker was always about 1 cm below the glass tube throughout.

Result

Mass of the rubber bung m = 0.0543 kg

|M / kg |Mg / N |Time for revolutions 20t / s |Angular speed |m(2L / N | | | | |[pic][pic] / rad s-1 | | | | |1 st trial |2 nd trial |Mean | | | |0.12 |1.2 |22.3 |22.1 |22.2 |5.66 |1.39 | |0.16 |1.6 |21.8 |21.7 |21.8 |5.78 |1.45 | |0.20 |2.0 |19.0 |19.1 |19.1 |6.60 |1.89 | |0.24 |2.4 |17.4 |17.1 |17.3 |7.28 |2.31 |

Discussion

1. The string is not exactly horizontal when the rubber bung is whirling, but the angle( made between the string and the horizontal is very small, so the tension T is calculated as m(2L regardless of the angle(, the values of m(2L are similar to the values of m(2r .

The centripetal force is given by the tension in thread, because T = Mg, so the centripetal force is also equal to the weight of the slotted weights (i.e. F = Mg). From the result above, the values of the centripetal force are similar to the values given by F = m(2L (i.e. Mg= m(2L).

2. The sources of errors...

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