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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)image01.jpg

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.

image02.png(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.

image03.png(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)
...read more.

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

...read more.

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.

...read more.

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