- #1

Magemano

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I'm trying to get a deeper understand about this, and I hope you guys can shed some light on the issue. I'm not an enginner, so this may sound a little dumb. Anyway, here it goes.

Suposse I drop a piece of chalk. As it hits the floor, it will likely break into pieces, and I'd like to understand how some factors, such as, the chalk's length and the height from which it was dropped, can affect the number of pieces it'll break into.

According to this, when the piece of chalk hits the floor, it will land slightly off center. Therefore, the piece will be under a shear stress, caused by gravity and the reaction force applied at the region of chalk that touches the floor first.

As I understand (correct me if I'm wrong) the shear stress the piece of chalk will experience is:

[itex]τ = \frac{F}{A}[/itex]

Where F is the force (the gravity force) and A is the cross section area of the chalk. If τ is equal or bigger than the Shear strength of the chalk, then it will fail.

But this doesn't depend directly on the chalk's length, and doesn't help me to determine into how many pieces it's likely to break. Another relation to consider, is the one presented on Giancoli's Physics for Science and Enginnering:

ΔL = [itex]\frac{F Lo}{G A}[/itex]

Where ΔL represents how much the chalk is "stretched" by the shear stress. The explanation contained on the link above states that: if ΔL is big engough, the chalk will fail.

So, I'd like to know a few things:

-How can I relate the ΔL to the shear strength? I mean, how much must the chalk be stretched until it fails?

-Is there a way to predict where the chalk will break, and into how many pieces based on this? (I'd like something as simple as possible, there's no problem for me to consider the simplest possible scenario).

-Where can I find the shear strength for a piece of chalk?

Any help is welcome. If you guys can point me something to help me, I'd be very glad.

Thanks in advance.