Cantilever Experiment: Is the Relationship Linear?

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Discussion Overview

The discussion revolves around an experiment involving the bending of a ruler when a mass is attached to its end. Participants explore whether the relationship between the vertical displacement at the end of the ruler and the length of the ruler that is free to bend is linear or not. The scope includes experimental observations and interpretations of the data collected.

Discussion Character

  • Exploratory
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant expresses skepticism about the linearity of the relationship observed by their lab partners, suggesting that a perfect linear relationship is unlikely based on their understanding of the physics involved.
  • Another participant notes that tip displacement for a point force on a simple beam typically varies in a cubic manner, but can appear linear under certain conditions, particularly for small displacements.
  • A different viewpoint suggests that the displacement could be linear if the mass of the weight is significantly larger than the mass of the ruler and if the ruler is sufficiently stiff, indicating that the relationship might not be strictly linear in all cases.
  • A later reply mentions that after conducting the experiment independently, they observed a cubic relationship, reinforcing their belief that the initial results reported by their lab partners were implausible.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the relationship between displacement and length of the ruler. While some suggest the possibility of a linear relationship under certain conditions, others assert that the relationship is cubic based on their experimental results. No consensus is reached regarding the validity of the initial data reported by the lab partners.

Contextual Notes

Participants reference the complexity of the relationship between displacement and length, noting that assumptions about stiffness and mass ratios can significantly affect the outcome. The discussion highlights the dependence on experimental conditions and the potential for varying interpretations of the data.

Who May Find This Useful

This discussion may be of interest to students and educators involved in experimental physics, particularly those exploring concepts related to beam bending and material properties.

alexbib
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hi guys, got a lil question:

I had an experiment to do with two partners and one of 'em lost the data. So they had to redo it, but from the data they supposedly collected, I get the impression the faked the results, badly. The experiment was to bend a ruler by attaching a mass at its end. Then, we had to vary the non-fixed length of the ruler and measure vertical displacement at the end. To put it more clearly, we needed data of h0-hf at the end of the rod vs the length of the rod that was free to bend. They got a perfect linear relationship, and I think its is impossible. Is it? I know I already asked the question and the equation can be solved by an integral, but I am still in the process of teaching myself integral calculus... So I got a rocket launcher pointed at my lab partners, should I pull the trigger (ie: is the relationship not supposed to be linear, as I thought?)?
 
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Tip displacement for a point force on a simple beam varies with the longitudinal distance variable in a cubic manner. For very small z, this can be approximately linear (a [tex]z^n \rightarrow 0[/tex] argument for n > 1 and z < 1).

Still, I think your friends are lying. You are talking very small z here for something like that.
 
The displacement might be linear. That would be consistent with a spring. The constant is inversely proportional to the lengh of spring -- cutting a spring in half gives a spring with half the length, and twice the constant.

If the mass of the weight is large compared to the mass of the ruler and the ruler is fairily stiff, then you'll probably see a linear(ish) relationship.

You should blast your lab partners for losing the data anyway.
 
Anyways, I booted my lab partners from my team and redid the experiment on my own. I got a cubic relationship. There is no possible way they could have gotten the results they got. I hate groupworks, you always have to rely on your teammates...Thx for your answers guys.
 

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