Uphill Cone

Place the double cone at the lower end of the inclined V shaped rails and release. It travels on its own to the upper end. How can any object move up on its own? Even though the double cone seems to be moving up, its centre of mass is actually moving down.

Centre of mass : It is a point where the whole mass of the object can be imagined to be concentrated.

As we see the double cone kept at the lower end of the inclined V shaped rails moves by its own and reaches the higher end, the striking thought that comes to our mind is that this is a clear violation of the law of conservation of energy. This is because the double cone seems to be gaining energy on its own. It is travelling from the lower end to the higher end. The potential energy is increasing. At the same time, it is also gaining kinetic energy since it is moving. This happens without even giving a little push to the double cone. But, as per the law of conservation of energy what we understand is that creation or destruction of energy is impossible. Rather, transformation from one form to another is always allowed.

By looking at the motion of the entire double cone, it is quite natural to think that it is creating energy by itself. At the same time we cannot accept this violation of energy conservation. Under such circumstances, we need to pay attention not to the entire object, but to the centre of mass of the system. It is an imaginary point where the entire mass of the object appears to be concentrated. For a solid cone, the centre of mass lies on the axis of the cone at a distance ¼ times its height from its base. A double cone can be imagined to be made of two solid cones of same dimension by joining their bases. The centre of mass of it lies on the midpoint of the line joining the centre of masses of the individual cones.

If we measure the heights of the centre of mass of the double cone when it is kept at the lower end of the V shaped inclined rails and when it reaches the higher end of the rails, we see that the height of centre of mass decreases as it moves along the rails. In seemingly upward direction. That means, it is actually losing potential energy along journey and it is the loss in potential energy which gets transformed into the kinetic energy of the double cone.

Hence, it is neither violation the energy conservation nor going against gravity.

But, the same double cone doesn’t travel up when left at the lower end of inclined parallel rails. The V shape allows the centre of mass of the double cone to fall downwards as the double cone ascends along the uphill.

Furthermore, any inclination of the rails, an angle between the rails and any angle of the double cone cannot be chosen. There is a certain range of angle of inclination and angle between the rails which works well for some angle of the double cone.