Puzzler: If a car was powered by using Mentos and Diet Coke for thrust, how many 2-L bottles would it take to go a kilometer?

What are we even talking about? Well, you are one brief internet search away from hundreds of thousands of related videos, some of which are super cool. The phenomenon of dropping candy Mentos into Diet Coke for an explosive foam geyser has been featured in MythBusters,² many YouTube science channels,3 and even in music videos.⁴ This goes beyond a simple internet meme; we’re talking hard-core science about why Mentos, in particular, work so well at inciting a foam explosion⁵—surface roughness and a little chemistry are the main culprits—and there are even studies on the effects of altitude. At higher altitudes, you get more foam from the same reaction.⁶

The Effect

We know that carbon dioxide is dissolved in the soda at high concentrations. When Mentos are dropped into the soda, the rough surface of the candy acts as many bubble nucleation sites for the carbon dioxide. Furthermore, surfactants in the candy (such as the gum Arabic) reduce the energy necessary to form bubbles, which speeds up bubble formation. The net result is that as the candy falls through the soda, carbon dioxide is released extremely quickly in the form of foam rushing out of the bottle, as seen in Fig. 1. If you add more Mentos, the effect is larger.

The Puzzle

From watching some of the many Mentos and Diet Coke videos available online, I estimate that soda will spray at its farthest about 5 meters horizontally (if ~1 meter off the ground), or as high as 10 meters vertically,7 at room temperature. From the published papers (yes, there are some!) I estimate at least 1.3 kg of mass loss from each 2-L bottle.⁵

As for Mentos propulsion, the logic goes that if the bottles can propel Diet Coke foam several meters in the air and power toy car rockets,^8,9 why couldn’t we use them to propel a real car forward? The question is, how can we figure out what it would take? I’ll start you off with just enough physics to get going but let you puzzle out the answer yourself... (Fig. 2).

Hint 1: It turns out that for most problems I could sketch, the dynamics of a car moving are energetically complicated (duh): we have rolling resistance, air resistance, and even hills to deal with.

Is there some way of estimating the average force or total energy needed to move a car a kilometer?

Hint 2: We need to know the average thrust (which is a force) you can get out of a single 2-L bottle, which is definitely related to the total momentum of the foam spray (Fig. 3).

I now leave you with the puzzler for this issue: About how many bottles of Diet Coke (or Mentos) would it take to move a car a kilometer? What assumptions did you have to make? Email us your answers at sps-programs [at] aip.org.

References:
1. Commons.wikimedia.org/wiki/File:ShimadaK2007Sept09-MentosGeyser_DSC_3294%2B%2B.JPG.
2. “Diet Coke & Mentos,” Myth Busters, www.youtube.com/watch?v=LjbJELjLgZg.
3. Steve Spangler Science, “Mentos Geyser Science Project,” www.stevespanglerscience.com/experiment/00000109.
4. Weezer – “Pork and Beans” music video, www.youtube.com/watch?v=PQHPYelqr0E.
5. Coffey, T. S., Diet Coke and Mentos: What is really behind this physical reaction? Am. J. Phys. 76, 551 (2008); doi.org/10.1119/1.2888546.
6. Kuntzleman, T. S., and Johnson, R., Probing the mechanism of bubble nucleation in and the effect of atmospheric pressure on the candy–cola soda geyser, J. Chem. Educ., 97 (4): 980–985 (Apr. 2020). doi:10.1021/acs.jchemed.9b01177.
7. Science of Mentos–Diet Coke explosions explained, New Sci. (June 2008), www.newscientist.com/article/dn14114-science-of-mentos-diet-coke-explosi....
8. This Is How We Bingham, “Coca Cola and Mentos Experiment,” www.youtube.com/watch?v=2UKW9ObRL8I.
9. Coke and Mentos Rocket Car, Science World, www.scienceworld.ca/resource/coke-and-mentos-rocket-car/.