thecoast47 said:
A Popsicle stick is easier to break of you apply pressure on its flat surface,however if you change the orientation of the popsicle stick so its no longer flat(popsicle stick is no longer lying on its flat surface but is now lying on its "thinner" surface), it becomes much harder to break.
(i hope this made sense)
I've read articles that imply that there is a distribution of tension throughout the Popsicle stick depending on its orientation.
My Questions are:
1.Why is the popsicle stick easier to break on its flat surface?
2.What law of physics explains this?
3.Can all(most) physical objects be interpreted as a chunk of atoms with spring forces acting on each other?(i've read in physics simulation books that most physics can be modeled by springs and I'm wondering if that's the case for real objects as well )
In the simplest model, you can think of the wood as a uniform isotropic material with a definite Young's modulus E and breaking stress σ
U. "Beam theory" provides a model for the stress distribution in a thin beam made out of such a material. The usual simplifying assumption is that the stress distribution is dominated by the local bending moment and that the shear force distribution can be neglected.
In that case, the stress is longitudinal (directed along the length of the beam) and varies from compressive on the concave side to tensile on the convex side. If you imagine you are bending the popsicle stick so that the middle bows upward, i.e. is concave down, then the fibers on the top will be in tension and the fibers on the bottom will be in compression. In this ideal model the beam will fail when the maximum tensile strength σ
U is reached in the fibers on the tensile side.
The stress at a distance z from the "neutral axis" is
\sigma=Mz/I
where M is the bending moment and I is the second moment of area. For a beam of width w and thickness t the second moment is
I=wt^3/12
The maximum stress is seen where z is maximum. For a rectangular beam this will be z
max=t/2. So the maximum stress is
\sigma_{max}=6M/wt^2
Now suppose the popsicle stick has a rectangular section of width a and thickness b with a >> b. In the ordinary orientation (w=a, t=b) the maximum stress is
\sigma_{O}=6M/ab^2
while in the rotated orientation (w=b, t=a) the stress is
\sigma_{R}=6M/ba^2
Hence
\frac{\sigma_{R}}{\sigma_{O}}=b/a<<1
and the rotated orientation experiences much less stress for the same bending moment. Conversely, it takes a much higher bending moment to reach the ultimate stress in the rotated orientation.
In actuality, real wood is anisotropic (the grain establishes a preferred direction) and the breaking stress varies from point to point. Common sense will tell you that the wood splinters when it breaks and that the breaking planes are not at all what an idealized model would predict. But the above should be the basic answer to your questions 1 and 2.
As to question 3, your mileage may vary. Most solids have some linear elastic regime when the strains are small, and the elasticity is due to interatomic forces. I would expect there are substances that have a fairly narrow elastic regime and become non-linear even at low strain levels, but you're welcome to research that yourself. Just remember that a model is just a model.
BBB