Finding Young’s modulus by bending a beam

[Fraser MacDonald]

I have a question regarding finding the Young’s modulus of a rod by loading a weight to the end and measuring the change in displacement.
The experiment is part of my advanced higher physics project on Young’s modulus however it is the only experiment that I’m doing that the book “Tyler” does not cover, and so I am slightly confused as to how I actually derive the relationship through this method.

I know it isn’t a great set up but it’s all I can do with the equipment I have.

So my question is how do I calculate it via this method?
Thanks

 

[jack action]

You have to use the Euler–Bernoulli beam theory, especially the case of an end-loaded cantilever beam.

 

[Nidum]

Not with the set up shown though . The holding system needs to be much more rigid and the rod needs to be set horizontal .There also needs to be a more accurate deflection measurement method employed .

If you have some freedom to design this experiment properly then I suggest that you use a much longer thin rectangular strip as the test object . Clamp one end of this tightly to the edge of a solid bench and - if nothing better is available - use a metre rule to measure the deflection . The rule being held in a retort stand sitting on the floor . The much larger deflection for given loads and the improved rigidity of the set up should allow you to get better results and a reasonably accurate value for Young's modulus .

 

[Fraser MacDonald]

Once the experiment is set up correctly would the equation to find Young’s modulus be y=(4mgl^3)/(bd^3 δ) and if so, how do I derive this?

 

[jack action]

how do I derive this?

The equation you need is:

Where $E$ is what you are looking for and is the only unknown in your case.

It can be derived from this equation:

Both of these equations can be found in the links from my previous post and since it seems to be part of school work, I will let you do some reading to find out the meaning of the variables and the derivation. If you have questions along the way, show your work and ask a specific question.

 

[Fraser MacDonald]

Is this the correct derivation?

 

[jack action]

The image is too blurry to read it. But if you begun with the initial equation and ended up with the last one, chances are you are correct.