10/07/2017
The topics for Be Like Bohr, the research event, are as follows:
Section A: Theoretical Research
1. Suppose a person is standing on a disc hinged at the centre. The initial mechanical energy is obviously 0. The person starts moving along the circumference. The disc therefore starts rotating. Now the person has kinetic energy, and so does the disc. Therefore the total energy of the system becomes non zero.
(i) Is this a violation of the law of conservation of mechanical energy? Is this a violation of conservation of energy in general?
(ii) Give a detailed analysis of the whole system’s dynamics.
2. Similar to how the moon orbits the earth, can a grain of sand orbit an astronaut in space? Give a detailed description of all the possibilities and conditions.
3. (i) How would the laws/formulae of science change if the number of spatial dimensions which we can perceive increased? (Currently, we can perceive three spatial dimensions - length, breadth and height. Think of everything from inter-molecular interactions to motion.) Bonus points for pointing out specific new phenomenon which we will be able to observe in such a situation.
3. (ii) Choose any 4D object and try to derive the relation of its centre of mass. If you're able to do that, think about its moment of inertia. (To imagine a 4D object, think like this - like a cube has length, breadth and height, its 4D counterpart (a tesseract) will have another such dimension. Thus, you have 4 axes on which to analyse this body). Generalize the relations to an n-dimensional object.
Section B: Practical Applications
Tip: Be as innovative as you can!
1. Can you apply a concept of physics to help avert traffic jams? Elaborate upon the structure and functioning of the road/car.
(Hint: you can first relate to fields such as thermodynamics and hydrodynamics, and then research in depth.)
2. Suggest a new and innovative method to reduce air pollution. Think of ways to prevent it and of ways to decrease the concentration of current pollutants in the air.
3. Suggest a new and innovative method to generate energy. It should meet the following criteria:
(i) Should be pollution-free
(ii) Should be renewable
Note that a total of 3 topics have to be chosen, including a minimum of one topic from each section. That means either 2 from section A and 1 from B, or vice versa. Send the research documents to [email protected], with the subject as 'Be Like Bohr'. The last date for submission is the 15th of July.
Best of luck!