By Göran Grimvall
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Extra resources for Brainteaser physics : hallenging physics puzzlers
The total mass of water is m. The potential energy EA of the water in tank A (relative to the base of the tank) is EA = mgh 2 When the valve is opened, water ﬂows into tank B until the level is the same in A and B. The height of water is h/2 and the mass is m/2, in each tank. ” Eventually it will appear as heat, warming the water. If the valve is opened very rapidly (like in the rapid closing of switches in our capacitor problem), the water levels will oscillate somewhat as they approach the equilibrium.
The laws of Nature, for instance, the conservation of energy and momentum and also the thermodynamic relations derived from basic laws are always true. In a description of an actual physical phenomenon, we make use of a model. That means a simpliﬁcation—certain e¤ects are just ignored, while others are included. For instance, one would not try to include the Earth’s magnetic ﬁeld in a model that describes the damage when two cars collide on a highway. But in some cases a model may leave out aspects that cannot be ignored.
Between A and B, light follows that one, which minimizes the time it takes for the no math required 43 Fig. 11. A light ray takes the path from A to B that minimizes the total travel time. light to travel from A to B (ﬁg. 11). In this example the speed of light is constant. Minimizing the time, therefore, is the same as minimizing the distance traveled. We can take the analogy between the railway and light propagation further. Suppose that the city A has an industry that requires many transports, so that the railway to A should have higher capacity and turns out to be 40 % more expensive than the railway to city B.
Brainteaser physics : hallenging physics puzzlers by Göran Grimvall