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The Physics Behind the Spill-Proof Cup

The Physics Behind the Spill-Proof Cup

I always find myself knocking over and denting my water bottles, eventually making them so bad they won't even stand up themselves because of the number of dents. I also spill the contents of these water bottles everywhere, even all over important notes and homework. So, I went searching for a solution to this problem. During my search I found a cup that is essentially "unspillable".


This cup is the Mighty Mug Ice Tumblr. Mighty Mug has a few other products in different styles that use the same unspillable idea. Essentially, these cups are not meant to be knocked over easily. I read all sorts of information about this product, and I even watched videos about it. Yet, I still wondered how is this possible? How does it work? Is it really impossible to push them over? If not, what is the force required to topple them?

I decided to research these questions, and it turns out that a good amount of physics actually goes into these cups.

Each cup uses a suction cup on the bottom. Suction cups do not truly suck on to the surface they are on. A suction cup really uses atmospheric pressure to form a rubber seal with the surface of the table. The atmosphere is like a bunch of tiny balls that are constantly at motion.



As these balls move around, they sometimes collide with a surface. When they collide with a surface, they change momentum and exert a force on that area. Thus, the bigger the area, the more collisions and the greater force. The force can be calculated from the pressure and the area.


There are two forces acting below the surface because of the air. One of these forces pushed up, while the other pushes down. With equal pressures, the net force would ultimately be zero. There is a net downward force acting on a suction cup though because there is less air and pressure underneath it than above it. This is why suction cups stick.

Here are the forces that are applied to the cup when pushed near the top:



The forces present are that of gravity and that of the push, as well as that of the table and of the suction cup. The last force present is that of friction, preventing the cup from sliding. To calculate for the maximum pushing force, the net force must be zero, and the total Torque must be zero. Thus, the cup must be in equilibrium.

To find the sum of the vertical forces, the equation would be:


The cup is approximately 400 grams with a height of 15 cm and a diameter of 8 cm. It is assumed that the suction force inside the suction cup is equal to half an atmosphere and the contact area is equal to half that of the bottom of the cup. Thus, we can calculate the magnitude of .




For the total Torque, the suck force location used will be that of the center of mass of a half circle. With this knowledge and using the forces we have, the net Torque equation, and thus the equation for the push force becomes: (x is the distance from the edge of the cup to the location of the suck force)





It takes approximately 49 newtons, or 11 pounds, of force to knock the mug over, which is at least five times the force of a normal tap. So these cups may not truly be "unspillable", but they definitely come pretty close. This cup is pretty impressive and I am definitely going to invest in one to avoid spilled drinks and dented water bottles.

Works Cited:
Allain, Rhett. “Spill-Proof Cups Aren't Magic-They're Physics!” Wired, Conde Nast, 1 Feb. 2017, www.wired.com/2017/02/spill-proof-cups-arent-magic-theyre-physics/.

Staff, WIRED. “The Physics of a Spill-Proof Cup.” Wired, Conde Nast, 9 Apr. 2018, www.wired.com/amp-stories/physics-of-a-spill-proof-cup/.

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