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Centripetal Force

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Introduction

AL PHYSICS

Experiment B

CENTRIPETAL FORCE

Form:                                                                          Date:  3-12-2009

Name:

Objective:        To measure the centripetal force for whirling a mass round a horizontal circle and compare the result with the theoretical valueimage00.pngimage00.png.

Apparatus:        1 rubber bung, 1 glass tube about 15 cm, 1 set of slotted weights, 1 wire hook, 1.5m of nylon thread, triple-beam balance, small paper clip, metre rule, stop-watch.

Theory:        When a mass m attached to a string is whirling round a horizontal circle of radius r, the centripetal force for maintaining the circular motion is given by image08.pngimage08.png where ω is the angular velocity of the circular motion. This force is provided by the tension of the string.

The formula can also be expressed in terms of the velocity v of the mass where image17.pngimage17.png.

Hence, image24.pngimage24.png.

Part A – Whirling of rubber bung in horizontal circle

Procedure:

  1. One end of the nylon string is attached to a rubber bung. The free end of the string is passed through a glass tube and then attached to some weights.
  1. With the glass tube held by the hand, the bung is whirled and set into circular motion in a horizontal plane. The rotating portion of the string was nearly horizontal.
...read more.

Middle

:
  1. It is impossible to make the rotating string exactly horizontal. Why?

It is impossible to make the rotating string exactly horizontal. The string dips at an angle to the vertical line instead since the weight of the rubber bung has to be balanced by the vertical component of the tension.

  1. If M is the mass of the hanging weights, what is the tension T in the string? Assume no friction inthe glass tube.

image03.png

  1. If β is the angle between the rotating string and the horizontal and m is the mass of the rubber bung, how is β related to M and m?

image04.png

image05.png

image06.png

As image07.pngimage07.png increases when β increases, β is directly proportional to m but it is inversely proportional to M. That is, when either m increases or M decreases, β increases, vice versa.

  1. What is the magnitude of the centripetal force acting on the rubber bung to keep it in circularmotion then?

image09.png

  1. Hence explain why a choice of image10.pngimage10.png is made in this experiment.

From question 3, image06.pngimage06.png. Thus, a larger value of image11.pngimage11.png (i.e. 5) is chosen in order to make image07.pngimage07.png as small as possible. As image07.pngimage07.png decreases when β decreases, in that way, β can be kept small.

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Conclusion

2L regardless of the angle θ.

image18.png

image19.png

image20.png

image21.png

Discussion:

  1. What is the relation between tension T and the theoretical value of mω2L?

From question 8, image21.pngimage21.png. Thus, T increases with image22.pngimage22.png, vice versa.

  1. Discuss the possible sources of errors in this experiment. Which error is most significant?

First, friction exists between the glass tube and the string. Thus the tension T may vary throughout the experiment. Moreover, the rubber bung is not set into horizontal circular path. There will always be a component of gravity no matter how fast we swing the bung. Thus the true centripetal force is merely a horizontal component of the tension in the string.

Besides, the rubber bung does not move with constant speed. Thus, the may affect the accuracy of the time required for the 50 revolutions. Also, the length of the string beyond the upper opening is not constant and this will affect the calculation of image23.pngimage23.png

The above-mentioned errors are mainly caused by human. It is difficult for us to keep the velocity of the bung constant while making the path of the bung as close to horizontal as possible. Thus, human error is the most significant error.

...read more.

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