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

                                                          T sin θ = mω2L sin θ

∴ T = mω2L                

        

        The vertical component of the tension balances the weight of the rubber bung.                                T cos θ = W

                The nylon string is passed though a glass tube to prevent external force acting on the system by the hand.

                        

During the experiment, the paper marker was kept in a constant position below the bottom of the glass tube to help us to keep the angular velocity of the rubber bung constant. (Assume there was no friction between the nylon string and the glass tube)

Apparatus:        Rubber bung, Glass tube, Screw nuts, Wire hook, 1.5m of nylon string, small paper marker, metre rule, stopwatch

Procedures:        1.         The rubber bung and the screw nuts were weighed to find their mass.

2. The experiment set up was constructed as the diagram below.

3. A certain length (L) of the nylon string from the rubber bung to the glass tube was measured.

4. The nylon string was marked at a position below the glass tube by a small paper marker.

5. The glass tube is held vertically and the rubber bung is whirled into a horizontal circle.

6. The angular velocity of the rubber bung ω was increased until the paper marker was at a constant position just below the bottom of the glass tube. As the diagram shown below.

         where θ is the angle made by the nylon string with the vertical

7. The rubber bung was required to whirl 50 complete circles.

The time required for performing 50 complete circles = t

The period of one circular motion (T) = t / 50

The angular velocity of the rubber bung (ω) = 2π / T

Moving the paper marker can adjust the length of L. The corresponding value of ω would be obtained.

8.        Use different value of L and keep the number of screw nuts unchanged then repeat step 3-7.

Readings:

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.

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.

2. 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.

3. 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 was possibly broke.

Some accident may occur at this situation, so we need to very careful when doing this experiment.

3. The edge of the glass tube was very edgy. We should take care to it for prevent it to hurt us.
4. We should take care that the nylon string would cut by the edge of the glass tube. It would let us use more time for complete the experiment.

4. Discussion:

1. As the vertical component of the tension balances the weight of the rubber bung, the angle θ is constant.

2. To ensure the vertical net force acting on the rubber bung is zero, there must exist a vertical force to balance the weight of the rubber bung. Therefore, the angle θ cannot be equal to 90°.

3. Mg cos θ = mg

cos θ = m / M

∴         θ is independent of L and ω

θ is depending on the ratio of the mass of rubber bung to the mass of the screw nuts.

4. Centripetal force         = mω2L sin θ

∵        m & M are constant

∴        m & sin θ are constant

∴        ω2L is constant

L↑ → ω↓

L↓ → ω↑

• If we plot a graph of ω2 against 1/L, a straight line would be obtained.

5. ∵         T sin θ = mω2L sin θ        ∴        ω↑ → T↑

&        T cos θ = mg                        ∴        T↑(M↑) → cos θ↓ → θ↑

                ∴        If kept L & m constant & increase ω, M was required to increase.

6. ∵        Mg = mω2L

∴         If we want to increase the angular velocity ω of the rubber bung:

i.        Increase M

ii.        Decrease m

iii.        Decrease L

5. Sources of error:

1. The nylon string maybe extensible.
2. It is difficult to keep the paper marker at a constant position below the bottom of the glass tube.
3. The rubber bung may not be in exactly circular motion.

   ∴ The centripetal force         ≠ mω2Lsinθ

Tension         ≠ mω2L

4. It is difficult to maintain a constant angular speed of the rubber bung.
5. Friction between the glass tube and nylon string and air resistance will reduce the angular velocity of the rubber bung.
6. 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.
7. L, M and m may not be measured very accurately.
8. The zero error of the metre rule.
9. Random error.
10. The reaction time of press the stopwatch.

6. 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.

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