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Practice A2 Investigation: Measuring the torsion of wire

Extracts from this document...

Introduction

Kyle Sawhney 12D

Practice A2 Investigation: Measuring the torsion of wire

Introduction

I decided to investigate how the torsion of wire varies with its length and thickness as it is an interesting, challenging topic which has clearly defined variables. Whilst it is fairly obvious that the torsion of wire would increase as the specimen was made shorter and thicker, the purpose of this investigation was to accurately examine the relationship between the torsion constant of wire, and the variables of length and thickness, using the values of correlation to accurately analyse the effect of these factors and endeavour to explain these conclusions with sound physics knowledge.

Plan

Method

The torsion of wire can be measured in a variety of methods, all of which have their merits and drawbacks. The method I chose to employ for this particular investigation was the Torsion Pendulum technique, as all of the necessary materials were available to me in my school laboratory. One of the alternatives to this method was measuring the vertical displacement of a mass hanging from a spring- this method was inappropriate for my investigation as it is far more complex to measure the variables of thickness and length for a spring than for a single uniform piece of wire. Furthermore, I did not have access to a wide array of springs of differing length and thickness with equal mass.

The method for a Torsion Pendulum is as follows:

  • Use a ruler and micrometer to measure the length and thickness, respectively, of a piece of wire
  • Attach the wire to a retort stand, secure at the point of attachment but hanging freely elsewhere
  • Attach a torsion bar to the bottom of the wire using a screw
  • Use a marker as a point from which the period of oscillation can be measured
  • Pull the torsion bar to any sensible angle, (far enough so the data is accurate but not so far that reaction time becomes a major uncertainty) and release it, allowing it to oscillate freely
  • Time the period of the oscillations over an accurate, logistically feasible length of time
  • Repeat this process at least three times for each measurement
  • Repeat the measurement for wires of same length, different thickness or same thickness, different length

A diagram of this experiment is provided below.

image00.png

The equipment required for this experiment is as follows:

  • Retort stand
  • Selection of wires of different length & thickness
  • Torsion Bar
  • Stopwatch
  • Ruler
  • Micrometer
  • Scales (for measuring mass of torsion bar)
...read more.

Middle

Thickness (m)

Period (s)

6.07E-04

7.62E+00

7.57E+00

7.59E+00

7.59E+00

7.09E-04

5.24E+00

5.21E+00

5.21E+00

5.22E+00

7.96E-04

4.21E+00

4.21E+00

4.24E+00

4.22E+00

1.09E-03

2.44E+00

2.39E+00

2.37E+00

2.40E+00

1.28E-03

1.65E+00

1.66E+00

1.66E+00

1.66E+00

These results clearly show a negative correlation between Period and Thickness, a relationship which supports my earlier prediction that the torsion in the wire would increase with thickness. A decrease in Period conveys an increase in torsion as it means the wire is oscillating faster, and thus has greater torsional stiffness. This assertion is corroborated by the measurement of the torsion constant for this data, given below.

Thickness (m)

Torsion Constant

6.07E-04

3.24E-03

7.09E-04

6.85E-03

7.96E-04

1.05E-02

1.09E-03

3.24E-02

1.28E-03

6.80E-02

Here, one can clearly see there is a positive correlation between thickness and torsion constant. However, this data doesn’t fully convey the relationship until it is presented graphically, accompanied by an analysis of what the graph demonstrates. Below, I have implemented the data into a scatter graph.

The graph clearly demonstrates that there is an exponential relationship between thickness of wire and torsion constant, a conclusion which makes sense in terms of physics, as an infinitely thick material would be infinitely difficult to twist, just as an infinitely thin material would be infinitely easy to twist. I have also included the equation of the line, and the r² value of the correlation,

y = 0.0003e4309.5x

R² = 0.9863.

The equation of the line demonstrates that it is an exponential relationship, whilst the R² value conveys that there is a very strong positive correlation between thickness and torsion constant.

...read more.

Conclusion

The general conclusions one can glean from this investigation are supported by both the data collected throughout the investigation and the underlying physics of this particular topic; the exponential relationship between torsion constant and thickness of wire was postulated in my original prediction, albeit merely a suggestion of a positive correlation rather than an exponential one, the same is also true for the inverse relationship between torsion constant and length. As discussed earlier, the physics behind these conclusions is fairly rudimentary on the surface (the ruler twisting experimentation etc.), but is in fact much more complicated when one investigates further. Were I to repeat this experiment I would take measurements at the extremes of both thickness & length in order to investigate how large the range of the torsion constant can be. I was unfortunately unable to undertake this experimentation during this investigation as it would require specialist equipment to measure the oscillations of both massive and minute lengths & thicknesses of wire. In addition, it would have been useful to have specialist equipment such as a purpose built Torsion Pendulum rather than having to rely on crude solutions such as the pen lid stopping the vertical oscillations.

In conclusion, I believe this investigation has begun to prove that there is an exponential relationship between torsion and thickness of wire, and an inverse relationship between torsion and length of wire. Whilst it is true these claims cannot be given as wholly true as there is a relative scarcity of data- however, given the time and equipment at my disposal I believe it was a successful investigation undertaken with experimental finesse resulting in conclusions free from any impacting uncertainty.

...read more.

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