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Published: 17 September 2021

• mechanics
• simulation

The Double Cone is a sometime-puzzling and always fun demonstration of equilibrium and inclined surfaces, and a good way to challenge your students to think hard about an apparently paradoxical result. We have both large (demonstration B1-06) and small (demonstration B1-07) versions in our collection, for use in any size of classroom.

The device consists of a solid wooden double cone, resembling two cones placed base to base. They rest on a sloping track. When released in the middle of the track, the cones appear to roll uphill! And in one sense they do, but in a more fundamental sense they do not.

The track consists of two rails in a triangular shape, joined at the base and widely separated at the upper end. The key to the demonstration is the carefully planned difference between the angle of the slopes of the cones, the slop of the ramp, and the angle of the separation of the rails. As the double cone rolls “up” the ramp, the center of mass is actually getting lower

Check out this animation at +plus magazine https://plus.maths.org/content/defying-gravity-uphill-roller to see an excellent diagram of how this works, and why.

You can read more about the physics behind this in several physics journal articles:

N. Balta, New versions of the rolling double cone, TPT 40, 156-157 (2002).

https://aapt.scitation.org/doi/10.1119/1.1466550

S. Ghandi & C, Efthimiou, The ascending double cone: a closer look at a familiar demonstration, EJP 26, 681 (2005)

https://iopscience.iop.org/article/10.1088/0143-0807/26/5/002, also https://arxiv.org/abs/physics/0501135

J. Havill, Defying Gravity: The uphill roller, +plus magazine (2006)

https://plus.maths.org/content/defying-gravity-uphill-roller