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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 ...

16

Work is calculated as force times distance. $$W = Fd$$ The purpose of a simple machine like a screw jack is to lessen the force required. However, the work needed is still the same, so the distance over which you exert the force has to increase. Halving the force requires doubling the distance. In this problem, you want to lift 2000 lbs a distance of 1 ...

14

In step 1 you lower the mass and this generates energy. Let's say you store this energy is a spring, and for the sake of argument let's say the energy stored is 1J. The energy has to come from somewhere, and of course it comes from the rotational energy of the torus so the rotational energy of the torus is now 99J. In step 2 you slow the torus, perhaps by ...

10

A classical explanation to supplement Rod's excellent quantum mechanical one: If you make a Huygens construction of wave propagation (I assume you know how to do that) then every point on the wave front is treated as the source of a new wave of the same frequency and phase. How that wave propagates depends on the medium it encounters. So the Huygens ...

5

Energy conservation stems from Noether's theorem applied to time (i.e., time-invariance leads to energy conservation, similarly to how spatial-invariance leads to momentum conservation). Since the universe is expanding (and accelerating at that), the state of the universe today is different than it was yesterday and will be tomorrow, hence energy ...

5

Actually, if the mass comes to rest relative to the torus after landing, the energy of the system goes down. Let $I$ be the moment of inertia of the torus, $r$ be the radius of the mass from the axis of rotation before it is dropped, $R$ be its radius after it lands, $\omega_1$ be the angular velocity before the mass is dropped, and $\omega_2$ be the ...

5

From the geometry, you can state that in order to move the screw by 1 unit of distance, you have to move the end of the handle by $10\times 20\times 2\pi$ units of distance. Let's call the unit of distance $[L]$ - in this case, an inch might be a good unit but we don't have to be explicit about that. Conservation of energy says that work done on the system ...

4

Rather than beating your student over the head with facts, try to approach the problem the way scientists did in the first place, by following the scientific method. Your student should come up with a hypothesis, and use known theory to make a prediction (calculate the momentum transfer in some idealized model), and then build a model to test the prediction. ...

3

When one says that "kinetic energy is conserved in an elastic collision" that means that the total kinetic energy of the system of particles involved in the collision doesn't change. It does not mean that the kinetic energy of each particle is unchanged. For a two particle system, the kinetic energy of each will change, but the sum won't. Also, your ...

3

Step 1: the rotational energy $E=1/2 \omega L$ does increase because $\omega$ increases (bacuse I decreases) and L is a constant ( $L=\omega I$). This is wrong again in step 3: The rotational energy of the torus does not change So the potential energies of the lifted objects is not the same in both situations, because they will also convert rotational ...

3

The torque on electricity generators is continuously adjusted to keep them running at a constant speed (e.g. 60Hz in the US and 50Hz in the UK). When you turn on some electrical item the current it consumes places a greater load on some electricity generator somewhere and this reduces the speed. To counter this, at the generating station more torque is ...

2

You're making a mistake in assuming that there is any left. Heat and sound account for all of it. There is one exception, though. If it crashes into something, and that breaks or bends the object, then the potential energy of the molecules is higher. That's why cars end up smashed after a collision. The molecules of the metal or plastic or whatever have ...

2

The height $h$ is probably the vertical displacement pointing downwards. Therefore: $$h = \left(-\mathbf{\hat j}\right)\cdot\mathbf s = -|\mathbf{\hat j}||\mathbf s|\cos\alpha = -s\cos\alpha$$ Now we can derive: $$\frac{dh}{ds} = -\frac{d}{ds}\left(s\cos\alpha\right) = -\cos\alpha \quad\Longrightarrow\quad \frac{dh}{ds} = -\cos\alpha$$ Therefore, ...

2

The simple answer is that in an elastic collision (for objects >> in mass than typical molecules) energy moves from kinetic to potential then back to kinetic as long as the "elastic limits" of the materials are not exceeded. In other words, as long as they act like springs. In non-elastic collision the energy goes mostly from kinetic of the colliding masses ...

2

What is the difference that leads to conservation of kinetic energy in elastic collision ? The difference is only in the properties of the material of a body. If it is elastic (happy ball) it can deform itself (thus absorbing KE) and then recover the original shape, giving back roughly the same amount of KE, which is considered as temporarily stored ...

2

Step 1 The mass is dropped ... The rotational energy of the torus does not change. Going to stop you right there. Although total energy is indeed conserved, rotational energy does not need to be conserved. Remember that the potential energy of dropped objects is generally converted to heat when they go thud on the ground. Angular momentum is however ...

2

Power generation and supply management is not easy and it is to their credit that most of the time power companies supply people with AC at the same voltage no matter what the demand for power is. So when we turn on appliances we do not see the voltage drop as a result. Or more realistically when everyone gets home from work and starts cooking/ boiling ...

2

The difference is only in the properties of the material of a body. You can see in this video If it is elastic (happy ball) it can deform itself (thus absorbing KE) and then recover the original shape, giving back roughly the same amount of KE, which is considered as temporarily stored in the lattices If it is not elastic the body will stay ...

2

However, isn't any closed loop on a PV diagram reversible? The arrows can simply be drawn in the reverse way to create a refrigerator. If any closed loop is reversible then why does the specific Carnot engine (a specific loop) have the highest efficiency? This was exactly the question I asked myself ten years ago :-) The problem is that often students ...

1

The other answers are great. I decided to plot it, however, because it's nice visualizing these things. Since your biggest doubt is about kinetic energy, be sure to pay attention to the last graph. SYSTEM. Motorcycle going to the left, truck going to the right, bound by an elastic rope ten meters long ($k=100\frac{\mathrm N}{\mathrm m}$). Masses and speeds ...

1

Frankly, no one really knows! In the day of Ampere, Faraday, and Maxwell they thought that the so-called ether passed the energy from one "ether particle" to its neighbor-much like a fire brigade passing a bucket of water along a line from hand to hand. Nowadays, there is no real certitude about precisely how the energy propagates through space. We can ...

1

Exerting force does not necessarily lead to energy changes.

1

This is literally what I get when I Google "non-conservative force". From the very first link (to Wikipedia), here's a more detailed explanation: A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Equivalently, if a particle travels in a closed loop, the ...

1

Moving the mass inside the rotating object takes energy - when it is "lowered" against the artificial gravity it does work against the force resisting this motion so the final kinetic energy of the system with "lowered" mass is not the same as before. The equation: $$E=\frac12I\omega^2=\frac{L^2}{2I}$$ is the clearest way to see why this is so - when ...

1

Assuming that hands remain completely static, and the object do not breaks, then all of its energy can be considered to be converted into heat and sound (as you have already described).

1

What we like to call the energy, i.e., the total matter/energy content of space-time, might not be conserved. However, there is a lot of reason to suspect that fundamentally the universe is some big quantum system, and that space-time and particles and fields are emergent from this underlying idea. In that case, we expect there to be a Hamiltonian $H$ and ...

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