Cantilever Experiment: Is the Relationship Linear?

[alexbib]

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?)?

 

[Tyro]

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 $$z^n \rightarrow 0$$ 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.

 

[NateTG]

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.

 

[alexbib]

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.