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A few years after asking this question I stumbled upon this super interesting video tweet, which is relevant for this question: link to tweet video. The video shows two ways of emptying a certain water bottle. In one case, the bottle is simply flipped upside down. In the other case, the bottle is also flipped upside down and quickly moved in a circular ...


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You write 1. The trolley exerts a forward force on the towbar 2. As the towbar pulls the second trolley along, the second trolley exerts a backwards force on the towbar and that's correct, but the second force is slightly smaller than the first one. The towbar's acceleration "consumes" a little bit of the first force for its acceleration. The ...


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The two horizontal forces acting on the towbar will only cancel out if the towbar has zero mass - in a mechanics problem, it would be described as a "light" towbar. Suppose the towbar has mas $m$ and each trolley has mass $M$. The horizontal force on the left hand trolley is $F - T_1$ where $F$ is the driving force and $T_1$ is the tension on the ...


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The forces on the towbar are only exactly equal and opposite if we assume the towbar has no mass. If $m = 0$, then from $F = ma$ we can have $a \ne 0$ and $F = 0$. For a real towbar the mass is not zero, and the forces at each end are not equal and opposite, except when the towbar is not accelerating. Another way to think about this, which avoids the ...


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There are two effects that lead to the presence of the small jagged peaks and valleys in the binding energy per nucleon. (The main shape of the curve is given by the semi-empirical mass formula, derived from the liquid drop model of the nucleus. The model has a positive binding energy proportional to the number of adjacent nucleon-nucleon pairs, a Coulomb ...


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It has to be with the pairing term. Nature likes even-even pairs of nucleons. I mean, an even number of protons and an even number of protons. The reason is ultimately related to spin couplings. So, odd-even pairs are more or less over the curve. Even-even isotopes, like $C^6$, or $O^18$, are especially stable. On the other hand, odd-odd pairs are especially ...


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Yes. This is exactly what Einstein did in his 1905 paper on special relativity. He considered how coordinates are defined operationally and from this he derived results mathematically. Admittedly, Einstein used the empirical assumption of the constancy of the speed of light, but the logical (mathematical) argument does not depend on the physical properties ...


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