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There was a lot of hype $10$ to $15$ years ago over the hydrogen economy. It was of course rather odd that anyone could take this seriously. How much free hydrogen gas is available? Answer: virtually none. The problem is that you have to either put electrical energy into water to split it into $H_2$ and $O_2$, or if you chemically condition methane $CH_4$ ...


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It is not true that the same force has to create the same change in kinetic energy. For instance, if two equal forces of opposite directions are applied on a body, the body does not change its energy. Thus each force makes zero work, or zero change in kinetic energy. You could tell that both forces create kinetic energies in different directions and that ...


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Energy is force times distance. You haven't specified a distance, so you can't say how much energy that force delivers. If you allow the force to rotate the sphere, the application point will accelerate faster than it would if the sphere does not rotate. So a constant force will deliver energy to the sphere faster than it would in the non-rotating case. ...


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In simple terms the internal energy can be thought of as the sum of the kinetic energy and the potential energy of the molecules. The kinetic energy of the molecules depends on the temperature - a higher temperature means that the molecules have more kinetic energy. The potential energy of the molecules depends on the bonds (interactions) between them - ...


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But for an ideal gas, internal energy is only a function of temperature and so internal energy remains constant here,no change in average kinetic energy of gas particles takes place, so where does the chaos come from to increase entropy of the system. 'Chaos' is not a very well defined term in context of statistical physics. It is not necessary to use it ...


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You say "rolling without slipping." But what do you think will happen in this situation? Do you think the large disk will "roll without slipping"? Can you do an experiment at home to find out? You can use whatever method gets you to the correct answer. You are given forces (F, weight) so try using forces. Try solving the equations lucas gives you. ...


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Transmit the force $F$ to the center of mass and add its torque. Consider to the relative motion between disc and ground. Then you can recognize the correct direction of friction force (friction force opposes relative motion). Free body diagram of disc is as below. (See this answer to understand better.) Equations of motion are: $$F-F_f=ma$$ $$N=mg$$ $$...


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Your confusion arises from the fact that you are confusing scalars and vectors. Scalars, are like numbers, and they have only magnitude. Vectors on the other hand have direction in addition to magnitude. In your question, you mention the wave vector, which, as its name suggests, is a vector. Typically vectors are written in bold or with an arrow over them; ...


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$f(E)$ is the probability that a quantum state of energy $E$ is occupied. There are two quantum states (for two spin states) at each energy. The probability cannot be doubled, since that could then exceed 1. All that happens for a spin $1/2$ particle is that the number of available quantum states is doubled.


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The values of $E_c$ and $E_v$ in the band diagram depend on the point of reference. So yes they can have negative values if you chose your reference that way. Keep in mind that their difference $E_g$ stays constant nonetheless. Electrons are fermions and therefore governed by Fermi-Dirac statistics. That means that they have to comply with the Pauli ...



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