# Tag Info

91

What you cannot see by drawing the picture is the velocity of the individual points of the string. Even if the string is flat at the moment of "cancellation", the string is still moving in that instant. It doesn't stop moving just because it looked flat for one instant. Your "extra" or "hidden" energy here is plain old kinetic energy. Mathematically, the ...

90

The problem is what Konstantin Tsiolkovsky discovered 100 years ago: as speed increases, the mass required (in fuel) increases exponentially. This relation, specifically, is $$\Delta v=v_e\ln\left(\frac{m_i}{m_f}\right)$$ where $v_e$ is the exhaust velocity, $m_i$ the initial mass and $m_f$ the final mass. The above can be rearranged to get $$m_f=m_ie^{-\... 89 Cory, here's a different way of thinking about gravity assists that may help: First is my short answer for readers in a hurry: What is really going on is a giant game of pool, with fast-moving planets acting as massive cue balls that impart some of their energy when they whack into tiny spacecraft. Since you can't bounce a spacecraft directly off the ... 67 Can photons push the source which is emitting them? Yes. If yes, will a more intense flashlight accelerate me more? Yes Does the wavelength of the light matter? No Is this practical for space propulsion? Probably not Doesn't it defy the law of momentum conservation? No In fact that last question is the key one, because photons do ... 64 The work you need to do (to insert the log) against the pressure of the fluid at that depth is equal to the work done by the fluid to get the log up to the height you desire. If you consider a log of volume V and a tank of depth h, the pressure at that depth would be \rho gh, where \rho is the density of the fluid, and g the acceleration due to ... 58 One word: inertia. When you're riding a bike on a level gradient you just need to give it a push to get going, then you can coast for quite a while before friction and air resistance slow you down. The human body doesn't have wheels that can store kinetic energy, so while running you have to give a good kick to get going, and then another kick to keep going ... 58 When light is propagating in glass or other medium, it isn't really true, pure light. It is what (you'll learn about this later) we call a quantum superposition of excited matter states and pure photons, and the latter always move at the speed of light c. You can think, for a rough mind picture, of light propagating through a medium as somewhat like a ... 54 At the physics 101 level, you pretty much just have to accept this as an experimental fact. At the upper division or early grad school level, you'll be introduced to Noether's Theorem, and we can talk about the invariance of physical law under displacements in time. Really this just replaces one experimental fact (energy is conserved) with another (the ... 50 [5/3 - Extended the answer, made some corrections, and responded to John Duffield's comment] This is actually the paradox that led Einstein to General Relativity. Consider a special case: An electron and positron are at the Earth's surface. Bring them together and they annihilate, creating gamma rays (which is very energetic light). The gamma rays travel up ... 48 ACuriousMind's excellent description was missing a picture. Here it is: This clearly shows that for the wave moving to the right, the front is moving up and the rear is moving down. For the opposite wave traveling to the left, the front (now on the left) is moving down and the rear is moving up. Summing them, you get a straight line with significant ... 39 Not if the laws of physics (particularly the laws of gravity) are as we understand them. In general relativity, there are a set of equations, called the Einstein field equations, that relate the curvature of space (roughly speaking, how much gravity there is) to how energy and momentum are distributed in space and time. To be consistent, these equations ... 37 For the photons that make up light to exist they have to be travelling at the speed of light. This means that to store them you have to put them in a container where they can move around at the speed of light until you want to let them out. You could build the container out of mirrors, but no mirror we can build is 100% reflective, or indeed can be 100% ... 37 Energy is in fact conserved, even in gravitational slingshots. After the slingshot, the velocity of the spacecraft may indeed change, which means its kinetic energy will also change. If this happens, the energy increase (or decrease) will be made up by a commensurate decrease (or increase) in the kinetic energy of the planet. In plain English: The planet ... 34 Just for completeness, I'll explain how to obtain the time taken for an arbitrary curve. If h is the initial height of the child and y the height once he has started falling. By energy conservation:$$mgh=mgy+\frac{1}{2}mv^2\implies v=\sqrt{2g(h-y)}\tag{1}  We know know the speed at any time. Let us denote the horizontal position as $x$. The ...

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A longer popular text why energy conservation becomes trivial (or violated) in general relativity is e.g. here: http://motls.blogspot.com/2010/08/why-and-how-energy-is-not-conserved-in.html To summarize four of the points: In GR, spacetime is dynamical, so in general, it is not time-translational-invariant. Because it's not, one can't apply Noether's ...

32

The extra force in a lever comes from the distribution of energy over a smaller distance of action. We can look at it very generally from the perspective of conservation of energy, or the lossless transmission of work through a machine. When we move something against a resistance, with a fixed force, we are putting in energy and doing work. This work is ...

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Do black holes violate the first law of thermodynamics? No. See Wikipedia re the first law of thermodynamics: "The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from ...

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We know through experimental observation. That is the beginning and end of the subject of physics, at least the part of it the tells it apart from, say mathematics. Conservation of momentum is simply an inductively reasoned hypothesis to summarize certain patterns in experimental data. You are alluding to the conservation of momentum's being "explained" ...

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TL;DR: This answer arrives at roughly the same conclusion as Kyle Kanos', i.e. in addition to payload considerations, the difficulty lies in stuffing a small rocket with a mass of fuel exceeding to the mass of the rocket itself. This answer, however, is more rigorous in how the $\Delta v$ budget is treated. Developing a relationship between rocket and ...

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Can we create an amount of energy at a point in space and destroy an equal amount of energy at another point in space, with both the processes occurring simultaneously? This will not violate energy conservation, as the total energy in the universe is constant. So is it possible? If you learn about Einstein's Special Relativity, you'll discover that the ...

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We treated this a while back at University... First of all, I assume you mean global cancellation, since otherwise the energy that is missing at the cancelled point simply is what is added to points of constructive interference: Conservation of Energy is only global. The thing is, if multiple waves globally cancel out, there are actually only two ...

27

Yes, kinetic energy is a relative quantity. As you might guess, this means that when you're using energy conservation, you have to stay within a single frame of reference; all that energy conservation tells you is that the amount of energy as measured in any one frame stays the same over time. You can't meaningfully compare the amount of energy measured in ...

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The topic of "Energy Conservation" really depends on the particular "theory", paradigm, that you're considering — and it can vary quite a lot. A good hammer to use to hit this nail is Nöther's Theorem: see, e.g., how it's applied in Classical Mechanics. The same principle can be applied to all other theories in Physics, from Thermodynamics and Statistical ...

25

Waves always travel. Even standing waves can always be interpreted as two traveling waves that are moving in opposite directions (more on that below). Keeping the idea that waves must travel in mind, here's what happens whenever you figure out a way to build a region in which the energy of such a moving wave cancels out fully: If you look closely, you will ...

25

Your examples are a bit misleading. For example you say: We can store cold (ice),heat (i.e. hot water bag) But we can only store heat temporarily, just as we can only store light temporarily. Your ice pack will eventually heat up and your hot water bottle will eventually cool down, just as light stored between two mirrors will eventually escape. ...

25

The shape of the slide definitely determines how long it takes to go down it. Consider if the slide was completely vertical. Now, a certain famous [recently deceased :( ] comedian had the astute observational powers to point out that this would, in fact, be a drop, not a slide. Nevertheless, you would quickly reach the bottom. Now imagine if the slide was ...

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Just to complement the other excellent answers, here's an animation showing what two wave pulses with opposite amplitude passing through each other actually look like: You can clearly see that, at the instant when the string is momentarily flat, it's not stationary but rather moving quite rapidly, and thus will not stay flat for long. (Obviously, the ...

24

The short answer to your question is that the statements that "virtual particles need not conserve energy" and "intermediate components of Feynman diagrams need not be on the mass shell" are equivalent statements, but from two different historical perspectives. The concept of a virtual particle was introduced into physics in the mid-1920s while the ...

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Why does the author say that we would need to know the shape of the slide to find the time taken for the child to reach bottom of the slide? As you've discovered, the speed going down a frictionless slide only depends on the vertical distance. This speed is not the vertical component of velocity. It is the magnitude of the velocity. The vertical component ...

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Contrary to what is stated in many textbooks, energy-momentum conservation alone cannot explain the behavior of Newton’s cradle. For N balls we have two equations and N final velocities to calculate. Hence, conservations laws can do the job only for N=2. This means that if we want to give an explanation of the cradle behavior based on conservation laws, we ...

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