One of the highlights of teaching introductory mechanics is always the “karate board” lab, which I start off by punching through a wooden board. That gets the class’s attention, and then we have them hang weights on boards and measure the deflection in response to a known force. This confirms that the board behaves like a spring, and you can analyze the breaking in terms of energy, estimating the energy stored in the board, and the speed a fist must have to punch through the board. As a sort of empirical test, we can drop a half-kilogram mass from the appropriate height to match the calculated speed, and see if it goes through.
As mentioned earlier this week, I have a camera that shoots high-speed video now, so of course I decided to get a shot of the breaking boards:
It’s interesting to see how quickly the break happens– this is shot at 1000 fps, and between one frame and the next, the board goes from solid-but-bent to broken more than halfway through. It’s also interesting that in the second break shown in the video, the break occurs at a point a good deal away from the spot where the mass hits.
And, of course, there’s the obligatory gag reel at the end, from one of the several shots where the board didn’t break, and the mass bounced up to knock over the big demo caliper set that I propped up to provide a reference scale behind the board. Good times, good times…
It’s tough to make out grain direction in that board, but I’m assuming that the grain was running transverse to the line between the supports. And apparently it was very straight, judging by the clean break. But even so, it seems pretty weak, although I guess that might be an illusion of the high speed camera. Do you know what species of wood this was? And how high were you dropping from?
If you want to do the test again, turn the board 90 degrees and you can talk a little bit about strength of materials.
@Tom: If you’re envisioning clamping the board by the sides rather than the ends, I’m not sure that will demonstrate the phenomenon. Clamping at the ends maximizes the torque applied by the weight hitting the center of the board. To do the experiment you have in mind, you would need to find boards with the grain running in different directions, and show that one of the boards breaks while the other produces the sort of result shown in the blooper reel.
Another demonstration would be to turn the board so that the short dimension of the board is horizontal. I expect the board will be harder to break in this orientation, because it bends less for a given force than if it were in the orientation shown in the video. This is the reason why, in wood frame construction, floor joists are installed in this orientation (you can see this for yourself if you live in such a house and you have a partially or fully unfinished basement).
This may have been a case of my eyes deceiving me, but the second board appeared to have a flaw in it at the (off-center) location where it broke. Of course, a board that did have such a flaw would be more likely to break at that location, since it would serve as a nucleus for cracks.
@Eric, the board appears to me to be more or less square, but that may be an illusion caused by the low angle of the camera. In any case, I’m 95% sure from the way these boards are breaking (cleanly rather than splintering) that the grain direction in these tests was parallel to the supports, which you see as in the short direction. (They’re more pivots than clamps, which would change the deformation, and thus the breaking energy, significantly.) Most boards tend to be cut with the grain running along the long direction (since that’s how trees tend to grow), so it shouldn’t be difficult to find an appropriate board in that case.
Regarding turning the board on its side, strain energy and stress are probably the way to think about this problem from a strength of materials standpoint – the board will deflect until either the energy in the bending deflection equals the kinetic energy of the impactor, or until the stress at a point in the material exceeds the strength of the material. Strain energy in pure bending (not that a beam that is tall relative to its length is really in pure bending from this sort of loading) is proportional to 1/h^3, while stress is proportional to 1/h^2, where h is the thickness of the board in the direction of the deflection. (They’re both proportional to 1/b, where b is the width of the board parallel to the supports.) So doubling the thickness means that you will absorb twice as much strain energy for a given stress. Turning a 2 x 4 (which really measures 1.5 x 3.5, which exaggerates the difference) from flat to tall should survive an impact twice as energetic.
I agree that there does appear to be a flaw of some sort in the 2nd board right where it breaks.
The boards are cut so that the grain runs along the short direction. This means that when the boards are held in the apparatus we use to stress them, they bend and break along the grain. The board in the video is placed in the same orientation; the weight is dropped from a height of maybe a meter– we had some trouble getting the boards to break for the camera, though the ones I used in class snapped very easily.
We could get some with the gran the other way, and see how much difference it makes. Might be entertaining.
We’ve actually cut the boards much narrower (in the into-the-screen direction) than we used to, largely because one of my colleagues gets really nervous when the boards hold too much weight. We bend them by piling bricks on a wooden platform suspended from the middle of the board, and the all-time record was about 60 bricks (mass of a bit more than 2kg each). With the narrower boards we’re using now, I don’t think any got past 20 this term.
(I much preferred the stronger boards– piling on large numbers of bricks added a great element of suspense to the lab– but not enough to demand a different size…)
I don’t know if it is an artifact of the video or something real, but I think I see a different grain color at the point where the second board breaks.
In any case, a wave must run along the board (like you see in the third case) until it finds a weak spot and fails or doesn’t and doesn’t.
BTW, what is the percent uncertainty in the breaking load for the boards you are using? How consistent are they?