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Classroom
In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.
The Magnetohydrodynamic Generator A Physics Olympiad Problem (2001)
The XXXII International Physics Olympiad was held in Antalaya, Turkey from June 28 - July 6, 2001. It marked India's fourth foray into this exciting event where sixty-five nations participated. As the delegation leader of the Indian team at Antalaya, one of us (VAS) was privileged to be in the thick of action. Our performance was a resounding success. With three gold and two silver medals we were placed second after the People's Republic of China (four gold medals and one silver medal) and at par with Russia and USA. This article describes an interesting problem on the magnetohydronamic generator that was posed as part of the five hour theoretical examination
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Oscillatory reactions form the backbone for any kind of ‘self-organizing system’. For the sustenance and persistence of oscillatory reactions, there should be at least one ‘autocatalytic step’ – i.e.,
A + X ---> 2X
With the advent of ultra-short pulse lasers, the traditional notions of a ‘transition state’ have been challenged and it has been possible to visualize the structure of the ‘transient activated complex’. In this context my queries are –
1. In the above type of reaction, does the rate increase due to increase in concentration of X, or does it actually catalyze the reaction? Is autocatalysis really a misnomer?
2. How does one visualize the structure of the transition state for such an autocatalytic reaction?
Response
Oscillatory reactions have attracted both experimental and theoretical attention due to the recognition of the fact that so many life processes are periodic – from heart’s beat to the leopard’s spots. Let us consider the famous Lotka–Volterra mechanism (see Box 1), which has three simple steps.
The following type of problem is discussed in many textbooks of dynamics. Suppose, a train starts from rest with a uniform acceleration, attains a certain speed and thereafter retards with a uniform retardation finally to stop at the next station. In most of the problems the train is considered to have moved with that speed for some time before taking up the retardation. How does one determine the minimum time of travel? Given the applied force per unit mass, the resistive force per unit mass due to braking, the distance between the stations and also the friction between the rails and the wheels, our aim here is to determine the minimum time of journey by the train.
Area of a Spherical Cap
Consider a circle drawn in the usual manner using a compass, with the radius set at L. The area of the circle is, of course, pi x L^2. Now, keeping the gap between the legs intact, place the point of the compass on a sphere and trace out a circle on the sphere (see Figure 1). What will be the area of the spherical cap thus formed? Surprisingly, the same formula applies! -- the area is pi x L^2, as earlier.
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