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Objective To measure the centripetal force for whirling a mass round a horizontal circle and compare the result with the theoretical value given by F= mw2r .

Extracts from this document...

Introduction

School:

Canossa College

Class:

6B

Name:

Hazel Chow Ho Ying

Class no:

3

Date:

20-10-2010

Mark:

Title

Centripetal force

Objective

To measure the centripetal force for whirling a mass round a horizontal circle and compare the result with the theoretical value given by F= mω2r .

Apparatus

  • rubber bung
  • glass tube
  • screw nuts
  • Wire hook
  • 1.5m of Nylon string
  • Small paper marker
  • metre rule
  • stop-watch

Theory

When a mass m attached to a string is whirled round a horizontal circle of radius r, the centripetal force for maintaining the circular motion is given by

F = mω2r   where ωis the angular velocity of the circular motion.

This force is provided by the tension of the string.

The formula can also be expressed in the terms of the velocity v of the mass, where ω=v/r .

Substituting ω=v/r into the formula for F , F = mv2/r

...read more.

Middle

Time 50 revolutions of the bung and calculate the angular velocity ω.Repeat several times using different lengths L of the string.

Result

Tabulate the results as follows:

        Mass of rubber bung m =   0.03491   kg

        Mass of screw nuts M =   0.13   kg

 Tension in string T = Mg =   0.13   × 9.8 N =   1.274   N

Length of string L/m

0.35

0.50

0.75

0.90

Time for 50 revolutions 50 t/s

30.85

37.04

45.00

49.65

ω = image00.png/rad s–1

10.183

8.482

6.981

6.327

mω2L/N

1.267

1.256

1.276

1.258

        Mean mω2L =   1.264   N

Conclusion

Form the results, we can find that the length of the string L is increasing, the value of angular velocity ω is decreasing. The length of the string is indirectly proportional to the value of angular velocity.

...read more.

Conclusion

ω2L .

They are almost equal.

Possible sources of errors

  1. Friction exists between the glass tube and the string.
  2. The rubber bung is not set into a horizontal circular path.
  3. The rubber bung does not move with constant speed.
  4. The length of the string beyond the upper opening is not constant.

θ increases with ω

Vertical components is T cosθ

Horizontal components is T sinθ

The system has no vertical acceleration

T cosθ = mg

The horizontal component of tension provides the centripetal acceleration

T sinθ = mrω2

Let L be the length of the string

i.e.  r = L sinθ

T sinθ = mrω2

T sinθ = m(L sinθ)ω2

T = mLω2

 mg/cosθ= mLω2

θ increases with ω

When the rubber bung is whirled around with a higher angular velocity ω , the angleθ becomes larger.

Reference

  1. Level practical physics for TAS p. 28 - 30
  2. Physics Beyond 2000 p. 40
  3. http://en.wikipedia.org/wiki/Centripetal_force
  4. http://www.greenandwhite.net/~chbut/centripetal_force.htm

...read more.

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