Question:

Is the biscuit tin violating PCOE (principle of conservation of energy) as it rolls upward?

Answer:

Let’s first ask ourselves why we expect a biscuit tin to always roll downslope.

Well, the center of mass (C.M.) of an ordinary biscuit tin is at the center of the tin (see figure below). When the tin rolls downslope, the C.M. goes lower. So the tin loses GPE to gain KE. Everything makes sense.

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The biscuit tin in the video however has a C.M. that is off centre (because of the mass of the magnets). If the C.M. is positioned on the uphill side, the tin rolls upward, but the C.M. actually goes lower. So again, the tin loses GPE to gain KE. There is nothing “anti-gravity” about the tin’s motion.

Delving Deeper

It is even possible for the tin to rest on the slope. This occurs when the C.M. of the tin is vertically above the contact point. The allows the contact force F_C  to balances the weight of the tin, and yet does not exert any moment about the C.M. of the tin.

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