# Tag Info

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In all cases, the two objects move towards one another. In fact they experience exactly the same gravitational force. However, because acceleration equals force over mass $$\mathbf{a} = \frac{\mathbf{F}}{m}$$ that equal forces causes the heavier object to accelerate much less than the lighter one. But technically, the Earth does move towards you very ...

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Because when you push on the chair, you're also pulling on the chair in the opposite direction without realizing it. For example, I just tried pushing the back of the chair I'm sitting in away, but to do so, I had to hold on to the seat of the chair. And if I went flying off of the chair, it would move - but I wouldn't be on it anymore. As others have ...

3

$\frac{dM}{dt} = \frac{\partial{M}}{\partial{t}}+\frac{\partial{M}}{\partial{x}}\frac{d{x}}{d{t}} = \frac{\partial{M}}{\partial{t}}+v\cdot\nabla{M}$ (with no assumption on what is M) . So if $v\cdot\nabla{M} \neq0$ you can have one of $\frac{dM}{dt}$ and $\frac{\partial{M}}{\partial{t}}$ that is zero when the other is not. ...

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Within the Newtonian framework of mechanics conservation laws are tricky to develop and are not obvious at first glance. Lagrangian mechanics generalises the concept of conservation laws by exploiting "symmetries". The connection between symmetries and conservation laws is made by Noether's theorem. An object has a symmetry if it is invariant under a ...

3

You can do so. The energy put in is the integral of $VI$, the product of the voltage and current. It may be hard to calculate $I$ from $V$ because of the back emf and changing circuit resistance. The energy absorbed is the increasing magnetic field energy caused by the expansion of the current loop and the increasing kinetic energy of the wire and ...

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There is a mutual attraction from gravity, and we generally only consider the smaller object here on earth because the earth is so massive, the acceleration of the earth is negligible. This is because $a = F/m$, and with equal $F$ between the two objects, the acceleration will scale as $a\propto 1/m$. For the earth, this leaves $a$ ridiculously small, but ...

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I am only going to leave a brief answer, seeing that the comments are very accurate. The paradox can simply be resolved by considering the elastic nature of all the objects. How so ever instantaneous might the $dt$ or the time of collision seem to the human eye, actually it occurs over a small duration, based on the elasticity of both the objects involved in ...

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This is the relative strength of interactions of elementary particles: strong 1 electromagnetic 1/137 weak 10^-6 gravity 6x10^-39 A free neutron decays through the weak interaction with a lifetime of 14.7 minutes. The gravitational interaction is 10^-33 times weaker than the weak. In the lifetime computations this would be squared .Even if baryon ...

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A physical system in GR is never isolated, in general, as it interacts with the curved metric, i.e., the gravitational background. (However a notion of isolated system can be given in the particular case of an asymptotically flat spacetime as discussed in auxsvr's answer.) Apparently this fact prevents the existence of conserved quantities because the ...

2

Yes. It is much easier to think of this in terms of conservation of momentum: Because light (and electromagnetic radiation in general) has momentum, you will have to gain momentum in the opposite direction to conserve total momentum --- just like if you were to throw the flashlight. It is difficult to think of this in terms of forces because we tend to ...

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Imagine the person pushing you is wearing socks and standing on a slippery floor while they push you. Their feet might slip out from under them and they would get pushed backwards at the same time you are getting pushed forwards. This is Newton's third law - if you push forward on something, you are actually pushing yourself backwards at the same time. We ...

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Does the bigger mass EVER move towards the smaller mass? Yes. $F = KMm/r^2$ $M*a_{M}=F$ $m*a_{m}=F$ As you see the smaller the mass the higher the acceleration and in consequence the higher the traveled distance in a given time t. If the above is true, can we technically move the Earth by us(human population) jumping indefinitely? No. Each ...

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If you sit on the chair and push with same force, it is not an external force. Newton's law of motion: if external force is not acted on a body it will remain same in state. So the chair will not move. Your acted force is an internal force.

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Imaging the balls on a string. You are launching N balls per second, at a velocity $u$. This means the distance between the balls is $u/N$. And $N$ balls per second will pass a certain point in space. Now if the car is moving at a velocity $v$ (same direction as $u$), fewer balls per second can hit it - because subsequent balls on the string have further to ...

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Being "near by" means that there is (unavoidably) an interaction between them. The problem is no longer $$\gamma \to e^+ + e^- \,,$$ but $$\gamma + A \to e^+ + e^- + A\,,$$ (here $A$ represents the spectator nucleus) and there is now a way to share out the energy and momentum. The interaction is generally thought of as mediated by the electromagnetic ...

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yes, the earth will accelerate towards you , however the Earth's acceleration will be so small for all practical purposes that you usually do not consider it. Earth's acceleration is small because the mutual forces between you and the earth are the same, but the masses are different, so this results in different accelerations (remember: $F=ma$). Now if you ...

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This discussion feels familiar; I figure this question is a follow up of some comments to an answer i provided to one of your previous questions. Specifically: thanks for the great answer. Although I have to say i find steady state to be a bit confusing here since this in fluis mechanics normally means $∂_t v=0$ but I venture you mean steady mass state? ...

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For these kinds of system we often define a pair of quantities, one which is characteristic of objects or systems and one which is characteristic of interactions. Examples of these pairs are work (interaction) and energy (system) or impulse (interaction) and momentum (system). There is no commonly applied name for the interaction quantity that pairs with ...

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Let me discuss a simpler version of your rocket-question: one where there is no gravity, so that we don't have to worry about gravitational potential energy. Consider a rocket in free space (vacuum), and consider that the rocket is at rest. Now the rocket fires it's engine for a short time. The engine accelerates the rocket. The rocket now has kinetic ...

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