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
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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 = 4Fl3
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.
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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.