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# Centripetal motion. The objective of this experiment is to verify whether the tension in a centripetal force apparatus is equal to the weight of the mass.

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Introduction

Physics Laboratory Report

Centripetal motion

Aim of experiment:

The objective of this experiment is to verify whether the tension in a centripetal force apparatus is equal to the weight of the mass.

Theory:

(Fig. 1)

Fig. 2 shows an object of mass m moving with constant velocity v in a circular path of radius r.

By keeping the angular speed of the rubber bung constant and considering the equilibrium of all the applied forces in the system, the theoretical value of the centripetal force F is calculated as follows:

F = mv2/r                or     F = mrω2

where v and ω are the linear and angular speeds of the object respectively.

Nevertheless, some correction should be made in this experiment. In this experiment, the following set-up is used.

(Fig.2)

As shown in Fig.3, in reality, the string is not horizontal and moves in a circle of radius r = l sinθ. The weight of the hanger with slotted mass gives the tension (T) in the string.

(Fig.3)

The horizontal component of the tension provides the net centripetal force. Therefore,

T sinθ = mrω2

T sinθ = m(l sinθ)ω2

T = mlω2

Apparatus:

Rubber bung                        x 1

Glass tube (15cm long)        x 1

Nylon thread (1.5m)        x 1

Slotted mass (50g)                x 4

Hanger (150g)                        x 1

Paper clip                        x 1

Meter rule                        x 1

Stop watch                        x 1

Adhesive tape                        x 1

Balance                                x 1

Procedures:

1. The mass of the rubber bung (m)

Middle

Data and data analysis:

Mass of the rubber bung (m) = 0.0211kg ± 0.00005kg

Length of the nylon thread (l) = 0.800m ± 0.0005m

Take g = 9.81ms-2

 Hanger with slotted masses Time taken for complete revolutions / s Angular speed / rad s-1(± 0.05 rad s-1) Tension / N(± 0.10055 N) Mass (M) / kg Weight (W= Mg) / N 30t (± 0.05s) t(± 0.00167s) ω = 2π/t T = mlω2 1st set 2nd set 3rd set Mean 0.15 1.4715 19.35 20.40 19.80 19.85 0.662 9.49 1.52 0.20 1.9620 16.20 18.30 18.00 17.50 0.583 10.8 1.96 0.25 2.4525 16.80 16.35 16.50 16.55 0.552 11.4 2.19 0.30 2.9430 15.90 15.00 14.40 15.10 0.503 12.5 2.63 0.35 3.4335 13.80 13.95 13.80 13.85 0.462 13.6 3.12

With M = 0.15kg,

Absolute difference between W and T = 1.52 – 1.4715 = 0.0485N

Percentage difference between W and T = 0.0485/1.4715 x 100% ≈ 3.30%

With M = 0.20kg,

Absolute difference between W and T = 1.9620 – 1.96 = 0.0020N

Percentage difference between W and T = 0.0020/1.9620 x 100% ≈ 0.102%

With M = 0.25kg,

Absolute difference between W and T = 2.4525 – 2.19 = 0.2625N

Conclusion

Discussion

From the results obtained, it can be easily seen that the differences between the tension of the string and the centripetal force of the circular motion of the rubber bung are 3.30%, 0.102%, 10.7%, 10.6% and 9.13%, with varying mass(M) and hence tension(T) used. It actually does not show much difference between the two values. The errors are indeed caused by the matters stated in ‘Sources of error’. Consequently, it can be concluded that the tension (T) of the string is approximately the same as the weight (W) used.

Furthermore, we cannot circle the rubber bung exactly in a horizontal plane. As shown in Fig.3, if the rubber bung is circled in a horizontal plane, the tension (T) of the string will no longer contribute a vertical force component to balance the weight (W) of the rubber bung. Hence, there will not be any force to balance the weight of the rubber bung. Consequently, the rubber bung must make an angle θ, which is more than or less than 90o, with the vertical, and thus the rubber bung cannot circle in a horizontal plane.

Conclusion

From the experiment, as the tension (T) of the string is approximately the same as the weight (W) used, it can be verified that the tension in a centripetal force apparatus is equal to the weight of the mass.

P.

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