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Extra resources for Analysis of the Stability of Astrophysical Objects and a New Mechanism for Freeing Their Energy
In practice, the resistance of a ladder with three or more steps is the same as that of an inﬁnite ladder. To make that point even more clear, we derive a recursion relation that relates the resistance RN+1 of a ladder with N + 1 steps to that of a ladder with N steps. The ladder with N + 1 steps is constructed by adding one “step unit” to the front end of a ladder with N steps (rather than adding it to the far end of the ladder; see ﬁg. 12). We get RN +1 RRN 2R 2 + 3RRN =R+ +R = R + RN R + RN The resistance converges very rapidly as N increases.
Where the wheels touch the road, their speed relative to the road is zero (otherwise they would slip), while their diametrically opposite parts move forward with the speed 2v relative to the ground. Any caveat? It is not quite true that the speed is zero at the contact point between the wheel and the road. The rubber in the tire deforms and there is a small slip so that, on the average, the rubber at the contact point moves slowly backward. Could there be any other part that moves backward? Some bikes 34 brainteaser physics have an electric generator with a small wheel in contact with the side of the tire.
Therefore, if one ﬁlls the car’s tank to the brim, it will ﬂow over when the gasoline’s temperature increases. A ﬁrst thought might be that the tank itself has a larger volume when it is hot, due to thermal expansion. This is true, but it is a very small effect. Let the tank be made of steel. The linear thermal expansion coefﬁcient a of steel is about 12и10−6 K−1, and the volume thermal expansion coefﬁcient b is three times larger, b = 36и10−6 K−1. 0007 Most liquids have a much larger thermal expansion than steel.
Analysis of the Stability of Astrophysical Objects and a New Mechanism for Freeing Their Energy