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Centripetal force

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Introduction

Student Name: WONG Wing Yan

Class and class no. : 6G2 (22)

Date of experiment: 11th March, 2009

Experiment 2 - Centripetal force

Objective

In this experiment, we are going the centripetal force for whirling a mass around a horizontal circle; then we compare experimental result with the theoretical value given by the formulaimage00.pngimage00.png.

Apparatus

  • Rubber bung
  • 1.5m of nylon string
  • Glass tube about 15cm long( wrapped by rubber tubing)
  • Labels
  • 50g slotted weight
  • Meter rule
  • Wire hook
  • Stop-watch

Setup


image06.jpg

Theory

When a mass m attached to a string id whirled around a horizontal circle with radius r, according to the Newton’s First Law of Motion, there must be a force acting on it. It is a centripetal force for maintaining the circular motion. To produce centripetal acceleration, a centripetal force is needed. The centripetal force is given by

image10.pngimage10.png

where image17.pngimage17.png is the angular velocity of the circular motion. The force is provided by the tension of the string and it must be directed towards the centre of the circular path.

We can substitute image34.png into the formula for F,
image01.pngimage31.jpg

...read more.

Middle

Time for 50 revolutions 50 t/s

28

32

35

44


Data analysis and Results

Tabulate the results as follows:

Mass of rubber bung m = 0.01369g

Mass of slotted weight M: 0.05kg

Tension in string T = Mg = 0.05x9.8N = 0.49N

Length of string image05.pngimage05.png /m

0.25

0.4

0.5

0.7

Time for 50 revolutions 50 t/s

28

32

35

44

image08.pngimage08.png/rad image09.pngimage09.png

11.22

9.82

8.98

7.14

image11.png

0.4309

0.5281

0.5520

0.4885

Mean image12.pngimage12.png = (0.4309+0.5281+0.5520+0.4885) =0.4999 N

Standard deviation image13.pngimage13.png = 0.0458

Discussion

The percentage error between the theoretical value of the tension 𝑇 and the experimental value image12.pngimage12.pngis

image14.png

The experimental value image12.pngimage12.pngis larger than theoretical value tension 𝑇, since there is some source of error in this experiment.

        Firstly, the position of the paper clip may not be the same, since the label indicate the length of the string, L fluctuates during the experiment, the length of the string beyond the upper opening is not constant. From the formula :

image15.png

when the value of L is increased, the experimental result will be larger than the theoretical result. Oppositely, when the value of image05.png is decreased, the experimental result will be smaller than the theoretical result. Therefore, the results are affected by different value of image05.pngimage05.png.

...read more.

Conclusion

image23.png

image24.png

image25.png

image26.png

For the horizontal circular motion:

image02.png

image27.png

image28.png

From the equation,

image29.png

image30.png

We can know that when the angular velocity image32.pngimage32.pngincreases, image33.pngimage33.pngwill also increase.

Conclusion

        In this experiment, we try to measure the centripetal force by whirling a mass in a horizontal circle for circular motion. We show that image28.pngimage28.png regardless of the angleimage04.pngimage04.png.

We compare the experimental value to theoretical value and find that the experimental one is a bit larger than the theoretical value, which is due to the error of this experiment.

It is also clear to show that image04.pngimage04.png is a constant. And from the formula, image35.pngimage35.pngrimage36.pngimage36.png, we can know the relationship between m and r, which is image37.pngimage37.png.

We can improve the experiment by moving the rubber bung in a constant speed. Also, the rubber bung should be set in a horizontal circular path. We should also keep the length of the string beyond the upper opening constant. The time for more revolutions of the circular motion could be taken for a more precise result.

Reference

  • New Way Physics for Advance Level – Book1(Mechanics) ; Manhattan Press (H.K.) LTD, page 172-173
  • http://en.wikipedia.org/wiki/Centripetal_force

...read more.

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