Brainteaser physics : hallenging physics puzzlers by Göran Grimvall

By Göran Grimvall

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This problem may bring to mind an interesting observation regarding the odometer reading in cars. Odometers measure the number of rotations of a wheel. The outer tire radius is about 30 cm (1 ft). A worn tire has a radius that is decreased by almost 2 %, and the odometer reading increases by the same amount. Perhaps you regularly drive a long distance with the same car and the same tire pressure. The difference between the distance recorded by the odometer when the tires are new, and some years later when the tires are worn, should be observable.

It is now obvious, according to the schematic illustration (fig. 15) that the extra gravitational force from an underwater mountain gives rise to a small hump on the ocean surface. How physicists think. The mathematically minded physicist would say that the shape f(r ) of the ocean surface represents an equipotential surface for the gravitational potential. The gravitational force on a water element near the surface is directed along the gradient −∇f(r ). Here −∇f(r ) is a vector, which forms a normal to the surface described by f(r ).

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. Our problem with the two capacitors is an illustration of that. ten hits 23 Fig. 14. When the valve connecting the full and the empty tank is opened and equilibrium is reached, the total potential energy of the water is halved. Where does the other half of the energy go? The understanding of a physical phenomenon is often deepened if one can think of a similar phenomenon that is well known or is easier to analyze.

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