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# Experiment test for F = m2L by whirling a rubber bung (centripetal force)

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Introduction

Physics Laboratory Report

Title:Experiment test for F = mω2L by whirling a rubber bung (centripetal force)

Aim:                1.        To help us to study uniform circular motion, and

1. Prove that centripetal force required for keeping circular motion

= mω2r

where        m =        mass of the object performing circular motion

ω =        average angular velocity of the object

r =        radius of the circular orbit

Principle:        When the rubber bung was being whirled in a circle, it was performing circular motion. When a body performs circular motion, it requires a net force towards the center to give the centripetal acceleration that causes the change of direction of the body.

This net force towards the center is called centripetal force. The centripetal force acting on the rubber bung was provided by the tension of the nylon string. The nylon string was attached to a number of screw nuts of known mass.

Forces acting on the rubber bung: (negligible air resistance)

1. Tension of the nylon string
2. Weight of the rubber bung

∵        Tension was constant though the nylon string (Assume there was no friction between the nylon string and the glass tube)

∴        Tension of string = weight of the screw nuts

The tension in the nylon string can be vary by change the number of screw nuts in the system.

Middle

Mass of rubber bung m         = 0.03 kg

Mass of screw nuts M         = 0.104 kg

Tension in string T         = Mg

= 0.104 × 9.8 N

= 1.0192 N

Results of using different lengths (L) of nylon string in the experiment.

 Length of string L (m) 0.4 0.5 0.6 Time for 50 revolutions (s) 37.22 39.52 40.23 Angular velocityω = 2π / T (radian s-1) 8.4406 7.9494 7.8091 mω2L (N) 0.8549 0.9479 1.0977

Errors & Accuracy:

Mean mω2L         = (0.8549 + 0.9479 + 1.0977) / 3

= 0.9668 N

Percentage of accuracy         =｜T – mean value of mω2L｜/ T × 100%

=｜1.0192 – 0.9668｜/ 1.0192 × 100%

= 0.0524 / 1.0192 × 100%

= 5.14%

1. Conclusion:

The value of tension calculates from my experiment result and the value of tension in the nylon string are very close together. It is a reasonable value. It implied that the frictional force and human error were not too large.

1. Assumption:
1. The frictional force was neglected.
2. The mass of the nylon string was neglected.
3. The nylon string was assumed to be inextensible.
4. The orbit was assumed to be exactly horizontal circular motion.
5. The angular velocity of the rubber bung was assumed to be constant.
1. Precautions:
1. This experiment requires 2 students to do. Otherwise, if we use one hand to hold the glass tube and whirl the rubber bung, the other hand use the stopwatch. It was very difficult to hold the glass tube stably, count the number of revolution accurately and press the stopwatch immediately after the rubber bung complete 50 circles.
2. During the experiment, the nylon string

Conclusion

the angular velocity of the rubber bung.The rubber bung was whirled at a very high angular velocity. It was very difficult to count the number of revolution. Therefore, the rubber bung may not be whirled for exactly 50 revolutions.L, M and m may not be measured very accurately.The zero error of the metre rule.Random error.The reaction time of press the stopwatch.
1. Possible Improvement:
1. Use a nylon string that the force constant is much larger.
2. Whirl the rubber bung at a constant angular velocity so that the centripetal force requires for do the circular motion is constant.
3. Do the experiment carefully and ask a partner to see whether the rubber bung is doing a circular motion.
4. Provide a constant force to the system to overcome the frictional force and catch the glass tube stably.
5. Use a glass rod that has a smooth edge and a rubber bung that has a streamline shape.
6. Use a larger L to do the experiment.

∵ L↑ → ω↓

## If the angular velocity was decreased, it would be much easier to see the rubber bung and easier to count the number of revolution.

1. Measure those values many times and take the mean of all results.
2. Use a new metre rule.
3. Do the experiment many times to reduce the random error.
4. Raise the number of revolution from 50 to 100 to reduce the percentage error of using the stopwatch.

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

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