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Physics investigation into the bending of a Cantilever.

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Introduction

Rhiannon Jones


Physics Investigation into the bending of a Cantilever


Safety

  • Although safety in this investigation is not a paramount concern, one should still be careful as rulers can cause eye injuries and damage breakable equipment in the lab.

Introduction

  • This is an investigation into the bending of a cantilever, conducted by changing a variable effecting the deflection of the cantilever when clamped to a table. I have chosen to change the deflecting force, and investigate how a change in this will effect the deflection of the cantilever gradually by adding increasing force to the cantilever. This variable was chosen as it has been shown to be the most reliable and give the most scientifically viable results that can be easily analysed and have sensible conclusions drawn from them, further explanation is also provided in the ‘variables’ section.

Prediction

  • I predict my results will show with an increasing deflecting force the deflection will increase. I predict that proportionality will also occur between the independent and dependant variables, in the way that if the deflecting force doubles, deflection will also. One way in which this can be shown is using the following formula:

    y = 4Fl
    3
         bd3E

    Deflection is shown as y on the left of the equation, and F the deflecting force is on the right with the other variables.
  • On the presumption all other variables are kept constant, F and should be proportional to y and double when it is doubled and so on. Using this formula a quantitative prediction can be made, which will strengthen my original prediction.

    F =
    2                           F = 4                      F = 8

    y = 4 x
    2 x 1                y = 4 x 4 x 1           y = 4 x 8 x 1
         1 x 1 x 1                      1 x 1 x 1                 1 x 1 x 1
      = 8                               = 16                       = 32
         1                                   1                            1
    y = 8                            y = 16                    y = 32

    Doubling F therefore shows y to be proportional as it also doubles proving my prediction to be correct.

  • This prediction was based on scientific knowledge and theories such as Hooke’s law. Hooke’s law states that the length of a spring stretches is directly proportional to the force stretching it and therefore if the length doubles the force must double also. This theory has been applied to the cantilever and therefore the deflection such as a spring is proportional to the deflecting force such as a force that would be stretching the spring. The deflection is also related to scientific knowledge that when materials are bent atoms on the top of a material are in tension and being pulled apart, and atoms on the bottom are being compressed and pushed together. Providing neither tension nor compression is too great the elasticity of the ruler should withhold the deflecting force obey Hooke’s law.
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Middle

3
  = 1/8          = 1/64


This variable can kept the same very simply by using the same ruler, and not altering the depth or width in any way. Keeping d the same will allow the deflection to be purely based on F and therefore fair results will be obtained. If the depth or width were altered this could cause inaccurate results to be obtained and affect the analysis of them, which would hinder the conclusion overall.
Precise measurements of all variables will be made using the most accurate equipment available to me. The deflection will be measured using a meter rule and measured to the nearest tenth of a centimetre, and taken at eyelevel so I can get a correct reading. This will be done by eye, yet should give accurate results that are suitable for the investigation. The meter rule will also be stuck securely to the floor using blue tack to ensure it doesn’t move and provide inaccurate results. Deflection will be measured by seeing the difference from the original height of the cantilever and the height of the cantilever when various weights are added to it. This Difference is the deflection and will be recorded to the nearest tenth of a centimetre.
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Conclusion


I felt the method was reliable as I obtained good results without any anomalous results.
I could improve my method by conducting more repeats of the deflection gained when I increased the deflecting force, this will enable me to gain more accurate averages, and help to identify any anomalous results on the graph. Another improvement I could make to my method is to measure the height of the cantilever more accurately using more precise measuring techniques, or perhaps getting more than one persons judgement. This would help to gain more accurate deflection results.
The results I gained were accurate and did prove my theory and therefore the conclusion I produced was correct, and relevant to the data collected.
To improve this investigation I could use a greater variety of deflecting forces, such as 1.5N and test the elasticity of the cantilever by exceeding 10N. This would give more accurate results and a greater range of results, which would improve my method and investigation.
I could further my investigation by testing another variable, and seeing the affect this has on deflection, and compare this with deflecting force. Although the other variables may be difficult to measure the consistency and accuracy of the equation could be tested by seeing the proportionality of the other variables to deflection.







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