How Should You Analyze Data from a Cantilever Beam Experiment?

[DarkBlitz]

1. Hey! i have done a physics lab on cantilevers, and what i did

1. Hey! i have done a physics lab on cantilevers, and what i did was i varied the length of the leaver while keeping the force applied constant and measured the displacement down of the leaver. However, i am not sure what to graph and what formula i should be using as we have not done cantilevers in school (this is a design lab and we can investigate anything).



2. i calculated the spring constant (k) for each of the different lengths by using f=-kx but I'm not sure if that is the right formula to use. i have graphed (length of leaver)^2 VS. Displacement but i am not sure what the gradient is equal too. And i tried graphing the Length of leaver VS. K that i calculated but i get an exponential and have no clue what the gradient is equal too.


It would be very helpful you someone could please point me in the right direction!

 

[Dickfore]

Try listening to your heart. The side it is placed on is called left. Right is the opposite one.

 

[PhanthomJay]

The displacement does not vary with the length squared. It varies with the length cubed. I assume you are applying a load at the end of the cantilever each time, and measuring the displacement at that end each time you change the length while keeping the load the same? You should see a pattern developing.

 

[DarkBlitz]

ah thanks guys, ill have another go at it now
its a one sided cantilever by the way, fixed at one end. We haven't done any work on cantilevers yet in class, the teacher just gave us our first complete lab for over the summer and cantilevers was the topic.

Edit: i just graphed it and its more linear then the graph i had before thanks!
and i looked for a formula with l^3 in relation to cantilevers and i found this one

k=F/delta=(ewt^3)/(4l^3)

oh wait, so delta (displacement) is proportional to (L^3) ahhh then rearranging 4f/ewt^3=delta/l^3

but shouldn't w be different for all the readings because the length was varied, therefore changing the k value for each reading?

im guessing that i should calculate the E for the different lengths of cantilever? and because i didn't measure the width of the ruler i guess i will have to use standardized measurements and state it in my conclusion and evaluations then :/

im just thinking out loud kinda here :P
so what i can do with these results is calculate the value for e any length of a cantilever made from that specific ruler? is that correct?

 

[pongo38]

Jay's assertion about displacement being proportional to L cubed is for a perfect cantilever, but your cantilever had support, material, and geometric imperfections that might cause this ideal relationship to vary. Plotting Displacement against L^3 will show you the reality, and you should think about and report on what the variations might be. Your formula is correct, but engineers usually refer to the elastic constant E (not e) as Young's modulus. A further thought is that by rearranging your expression as displacement d = C*L^3 where C is a constant, and then if you plot log d v C*log L, the gradient will have a meaningful value for you.

 

[DarkBlitz]

Ok thanks for the help, i tried what you said, and i got the constant to be 24.311, and the gradient of the log d vs c*log l graph to be 0.1158 :S is that gradient equal to 3log(4f/Ewt^3)? but its not eqaul :S i am really confused :/ the constant i have must be wrong then :/ ill try and find out

 

[DarkBlitz]

is C the constant of integration? or is it just some other constant? cose i looked it up on google and there was calculus and inertia moments, and I've only just started calculus and we haven't done any work on cantilevers in class so i am confused about the moments of inertia :S

 

[DarkBlitz]

GAH! just realsied tat w is width not angular velocity... so i should be able to calculate the E of the material...

thanks for all the help guys!

 

[pongo38]

You get C from the formula you gave F/delta=(ewt^3)/(4l^3) rearranged so that delta= C*l^3