How does length affect the bending of a horizontal beam?

[Apothem]

Homework Statement

We were shown this image ^
We were later told that it is suggested that the depression (y), is directly proportional to the length of the beam cubed (L³). We were asked to give reasons why this is so.
EDIT: The 1kg mass is placed at L/2

Homework Equations

y is directly proportional to L³

The Attempt at a Solution

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I am rather confused, I think moments may be involved and we were told to consider the force acting on the metre rule. I know it isn't much of an attempt, but any guidance in the right direction will be extremely grateful.

Thanks.

 

[haruspex]

The thing to be proved is not a "relevant equation". The idea is to post standard equations that you might need to solve the problem. In the present context, should be something about bending moments.

 

[ME_student]

Did you figure it out?

 

[Matternot]

Try working through this revision guide on it: http://www.doitpoms.ac.uk/tlplib/beam_bending/bend_moments.php

The important results are:

The equation for the moment(s) prodced e.g Fx
The equation for the bending moment for the rod being EI/R where I is the 2nd moment of area of the rod: http://en.wikipedia.org/wiki/Second_moment_of_area
1/R is the radius of curvature of the rod. This can be essentially considered as d²y/dx²

From this, you should be able to work it out.

Hope I can help :)