Rolling uphill

The mechanical paradox is a device that seemingly defies the law of gravity: a pair of cones that roll uphill.

Mechanical paradox - physical copy
Museo Galileo, CC BY-SA 4.0, via Wikimedia Commons

This is a neat trick. First, attach two cones together at their bases, so you have something that looks like a spinning top. Then, create two tracks that ascend and diverge at the same time, forming a kind of tilted “V” shape. The double-cone object will roll uphill, coming to rest at the track’s highest point. You can see a demonstration here:

Alas, it is just a trick. This device breaks no physical laws. The object itself, the sideways spinning top, does indeed go up the tracks. But its centre of gravity doesn’t; instead, the object’s centre of gravity falls.

At the lowest point, those two tracks are close to each other. The object touches the tracks close to the thickest parts of the twin cones. This means that the object’s centre of gravity is quite high; the ends of the cones are dangling in mid-air. As the tracks go up they spread out, so their points of contact with the object move from its thick centre to the narrower outside. At the end of the roll, the ends of the cones are no longer in mid-air; they’re resting firmly on the tracks.

To put it another way, the object is falling down a rising track. At the low point of the track, the entire object is above it. At the high point of the track, half of the object is below it. The angles in this video make the true movement obvious:

Examples of this device have been around for a couple of hundred years at least; the example pictured above dates back to the 18th century CE.

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