Based on this scenario, I’m also assuming that the pizza is lying on a flat surface (presumably the box) which we are assuming will survive the g’s. So the question then can be simplified to : Say there is a piece of meat on top of the pizza, how many g’s will it take for the piece of meat to tear through the pizza?
So let’s assume a piece of ham 1cm cube on top of the pizza. The pressure exerted by this cube at 1g (assuming a density same as water) is about 100 Pa. The yield strength is about 6000 Pa, so it will take about 60 g’s to destroy the pizza.
This result shouldn’t be surprising since car crashes typically produce 30g s and pizza is known to survive car crashes.
No, that’s not it either. It’s more like this: I’m standing up straight with both my arms extended straight in front of me, palms facing each other. My left palm is touching the top of the pizza box, my right palm is touching the bottom. I start turning my whole body counterclockwise, pivoting on my left foot. If I turn fast enough, I can drop my left hand since air resistance is enough to keep the box in my hand. I have to turn my right palm slightly towards me to keep the box from flying off. The axis of revolution is my upright body.
Or, more realistically, you take a large centrifuge (such as they use to subject pilots to g-force) and place an upright pizza box - with pizza inside - in the seat.
The question is, what happens as you subject the pizza (and box) to extreme gravitational force? Does it ruin the pizza? When and how does the box break? When does the crust fall in? What happens to the cheese? Do toppings like tomatoes turn to mush?
The only thing I would add is that the pizza should be in a cardboard pizza box. Then you can put that pizza box on a flat surface which will survive the g’s.
I know at some point the box will break, but I’m not sure when or how. One of the things I was wondering is whether the cardboard roof would collapse and then press the liquid out of the cheese. If it collapsed unevenly - say in the center - would that cut through the pizza?
So essentially you are asking, how many pizzas can be stacked on each other without crushing the bottom-most pizza. And the answer calculated above is about 60. 1 g = 1 pizza, 2 g = 2 pizzas and so on.
In the second part of the question, I assume you are asking if the roof will collapse (ignoring air resistance). This is as simple as asking how many empty pizza boxes can be stacked over one another until the bottom most box will collapse. 2 pizza boxes = 2 gs. Note that the sides of the pizza box will collapse first not the top.
I have not looked at calculating the strength of the pizza box but am pretty certain that it is stronger than pizza and 60 empty boxes can be stacked without the bottom one failing.
Depends on what you’re counting as a “failure”. Even with the sides uncollapsed, you could have the lid sagging enough in the middle, enough to reach the top of the cheese. That’s why they have those little plastic tables in the middle of the box, because that can happen even at 1 g.
Let’s say we have a 12" pizza made from… 13 oz of dough, 7 oz of sauce, and 6 oz of mozerella cheese. That’s a 26 oz pizza (1 oz is exactly 28.349523125 g, so 26 oz is 737.08760125 g). There’s some water weight lost when the pizza is baked but I don’t know how to calculate that.
We put this pizza in a 14" x 14" x 1 3/4" corrugated pizza box. Amazon tells me they sell 50 of these at once with a weight of 20 lb, which means each box weighs about 6.4 oz (181.436948 g). There are some quirks about pizza boxes - we’ll assume this box has a single wall although some pizzarias use double-walled boxes to need to insulate the pizza and maintain rigidity. They also have holes to let out the steam, and (in my experience) a piece of wax paper between the bottom of the pizza and the cardboard to prevent the cardboard from absorbing water and deteriorating (negligable weight, maybe an eighth of an ounce?).
So the combined pizza in the box weighs just over two pounds (32.4 oz or 918.52454925 g or 0.91852454925 kg).
I tried doing some research on the mechanical properties of pizza and cardboard, but I’m not confident in my ability to parse the rheology papers I found. I welcome you to check my sources. By my calculations, the yield stress of pizza is about 1,118 Pa. Corrugated fiberboard will yield at 1,000,000 Pa if the force is applied to its face, while a 50.8 mm x 50.8 mm sheet of single wall E-fluted corrugate will yield to 310 N applied to its edge.
yield strength of pizza
Pizza undergoes plastic deformation after 0.5 N of force is applied, more so in the interior than the crust (Bingham et al, 2011). The samples were cut with an original length of 63.5 mm each, 9.53 mm wide, with two cuts on the sides so as to resemble a sort of hourglass. Going by the diagram I'm simplifying it to the sum area of two 9.53 mm x 19.05 mm squares, plus a 9.53 mm x 9.53/2 mm square, plus one 7.935 mm x 9.53/2 mm square: a total area of 363.9693 mm² + 45.41045 mm² + 37.810275 mm² = 447.190025 mm² = 0.000447190025 m². A more precise calculation would require calculating the area of a segment of a circle. Since stress equals force divided by area, that gives me a yield stress of σ = 1,118.0929180105676 Pa.
Bingham, A. J., Boucher, C. R., & Boyce, J. M. (2011). Textural Variations of Pizza in Commercial Establishments. Worcester Polytechnic Institute. https://digitalcommons.wpi.edu/iqp-all/1818/
yield strength of corrugated material
According to what I've read online, corrugated materials are subjected to two relevant tests, a burst test (Technical Association of the Pulp and Paper Industry, 2017) and an edge crush test (Technical Association of the Pulp and Paper Industry, 2018). The burst test applies force to the face of the board until it bursts, while the edge crush test applies force until the edge of the board until it buckles. I found a paper which rated pizza box burst strength at 900 kPa and edge crush at 155 N, although I'm not sure how to interpret this second number (Hanson et al, 2010). I found a second paper that rated pizza box material with an average burst strength of 1,040 kPa and edge crush resistance of 6.1 kN/m (Stone, 2012, pp. 46-50).
The burst strength ratings are roughly similar, so I'll go with 1,000,000 Pa.
Edge crush resistance is the downward force divided by the length of the sample in that direction. In Stone's paper, the sample measured 50.8 mm x 50.8 mm. This means we have the equation 6.1 kN/m = force kN / 0.0508 m, therefore force = 0.30988 kN = 309.88 N. That is almost exactly twice the force reported by Hanson, which I guess has to do with the height of Hanson's samples being 25.4 mm. So these match, too.
Unfortunately I don't have the surface area of the edge. I know it is 50.8 mm long, but I don't know how thick the board is or how much of it is actually a surface. That means I don't know how to calculate the yield stress in Pascals.
Hanson, J. L., Yesiller, N., Singh, J., Stone, G. M., & Stephens, A. (2010). Beneficial Reuse of Corrugated Board in Slurry Applications. American Society of Civil Engineers Library. https://doi.org/10.1061/41105(378)19
Stone, G. M. (2012). Beneficial Reuse of Corrugated Paper in Civil Engineering Applications [Master's thesis, California Polytechnic State University San Luis Obispo]. https://doi.org/10.15368/theses.2012.12
Technical Association of the Pulp and Paper Industry. (2018). Edgewise compressive strength of corrugated fiberboard using the clamp method (short column test; TAPPI Standard No. T 839 om-18). https://imisrise.tappi.org/TAPPI/Products/01/T/0104T839.aspx
Having established the physical properties of our pizza and pizza box, we now cause it to accelerate in the direction of the pizza’s face. The resulting mechanical stress, from air resistance for example, causes the pizza and box to experience g-force. My question, to you and others who made it to the end of this post, is this: how much g-force can this box of pizza withstand before the pizza is ruined, and how exactly will the pizza be ruined?
He should not have said “pizza”. He should have said “pizza box”. He’s asking how many g’s accelleration before the pizza box collapses under its own weight. At one g, the box is supporting only its own weight. At 2 g’s, it is supporting twice its normal weight. At 60 g’s, the forces are equivalent to a stack of 60 boxes, which then collapse, and ruin the pizza inside the bottom box.
Temperature is an important factor. If you pick up your pizza freshly boxed and hot, the cheese is still molten. Just stomping on the accelerator or breaking hard for a light can shift the cheese (and all its toppings) dramatically. Turns, of course, create sideways movement. If, on the other hand, you are tardy picking up the pizza and it has cooled, you have more leeway.
The weight of anything with a mass (m) on earth where the acceleration due to gravity is (g) equals mg. (SI units).
If you took the mass to another planet, where the acceleration due to gravity was 2g, then the weight there will be m x 2g = 2mg which is the same as having twice the mass on earth (for weight / force calculation purposes). For example on the moon, the weight of the mass = m x g/6 = (1/6) mg.
If your head normally weighs 10 lbs, and you were on a F-16 doing 10g, your head will feel like it weighs 10x10=100 lbs.
If you are looking at rheology papers, it’s likely you are looking at pizza dough (non Newtonian fluid) properties and not the final baked pizza. This maybe the reason you are getting a low yield strength.
You also talk about air resistance. Air resistance is not a function of g but of v2 (velocity squared). I have completely ignored air resistance in the calcs above.