Constant Definition and 1000 Threads

The dielectric constant of water is 80, however its refractive index is 1 ·33 invalidating the expression n*n=ε. why?

Hi, I am building a charger for my bicycle front and tail light that uses dynamo to charge them while cycling. However, depending on my speed, current is fed differently to lights and they start to flicker. Therefore, I was wandering if there is a way to make a constant current source which...

Hello everyone! I've been curious about this for a while and couldn't come to a conclusion on my own so I've decided to ask it here. I'm wondering if it's possible for a function, f(x), to have a rule which would allow it and it's derivative to both approach a constant value as x approaches...

Solve for all real number t values. sqrt {2t + 5} - sqrt {8t + 25} + sqrt {2t + 8} = 0 I see there are no constants in this problem. I typically isolate the radical on one side of the equation and the constant (s) on the other side but there are 3 radicals on the left side. This is strange...

I'm confused on why the dry air gas constant varies: Dry Air Gas Constant of 286.9 from The Engineering Toolbox Dry Air Gas Constant of 287.22 from https://www.physicsforums.com/ttp://www.peacesoftware.de/einigewerte/luft_e.html Dry Air Gas Constant of 287.05 from Brisbane Hot Air Ballooning...

Could einstein's theory be completely wrong if we discovered that the speed of light is different in an another galaxy ( speed light isn't constant) and if we proven that there is particles or objects which moves faster than light by 100 or 1000 times?

The Yang-MIlls Lagrangian is given by ##\mathcal{L}_{\text{gauge}} = F_{\mu\nu}^{a}F^{\mu\nu a} + j_{\mu}^{a}A^{\mu a}.## We can rescale ##A_{\mu}^{a} \to \frac{1}{g}A_{\mu}^{a}## and then we have ##\frac{1}{g^{2}}F_{\mu\nu}^{a}F^{\mu\nu a}.## How does the second term change? Does the...

Hi PF! Can someone help me understand how to draw lines of constant pressure in an inviscid flow field, say flow around a cylinder. I am having trouble understanding how to draw these. Any help is greatly appreciated! I ask this question because I am preparing for the Q exam for PhD and one of...

Hello, I'm trying to integrate a signal received on an oscilliscope, but I'm afraid using the function cumtrapz is not giving me the correct value. Here is what I'm seeing when testing out sine functions I could apply an FFt to obtain the components and the phases, and then subtract off the...

Homework Statement A mass/spring system is set in motion. Find the phase constant with the given information. Given: k = 8 N/m (spring constant) m = 0.1 kg (mass attached to string) x0 = -0.12 m (position at t = 0) v0 = 0.9 (velocity at t = 0) Homework Equations x(t) = xmcos(ωt + Φ) v(t) =...

Homework Statement Fe2+and Cr2O72- react as follows: 6Fe2+ + Cr2O7 2− + 14H + >>> 6Fe3+ + 2Cr3+ + 7H2O. The equilibrium constant for the reaction is 1×10^57. Calculate the equilibrium concentrations of the iron and chromium species if 10 mL each of 0.02M K2Cr2O7 in 1.14M HCl and 0.12M FeSO4...

Hi, I'm working on a problem about a spherical balloon as its inflated slowly the radius of the balloon is in cm and the time is in seconds dr/dt = k/r2 Now I know how to rearrange this equation using separable differentiation r=3√3kt+c However I would like to find the value of the...

The beta function for the strong coupling ##g_3## is given by ##\displaystyle{\mu \frac{\partial g_{3}}{\partial\mu}(\mu) = - \frac{23}{3} \frac{g_{3}^{3}(\mu)}{16\pi^{2}},}## with ##\alpha_{3}(\mu = M_{Z}) = 0.118.## We can use separation of variables to solve the beta function equation...

Homework Statement Large cockroaches can run as fast as 1.50 m/s in short bursts. Suppose you turn on the light in a cheap motel and see one scurrying directly away from you at a constant 1.50 m/s. If you start 0.91 m behind the cockroach with an initial speed of 0.82 m/s toward it, what...

Morning I am being stupid but cannot work out these problems: 1. Energy supplied to 2.0 moles of an ideal gas is 117J and it changes the temperature by 2.0K (at constant pressure).2. Calculate both molar heat capacities at constant P and V.3. Firstly, I divided 117J by 4 to get the energy...

Good night guys. I've been studying for a test on mechanical vibrations and I came across this problem of a telescopic crane (or whatever its name is). It's necessary to obtain a equivalent constant kp and then it has to be decomposed into its vertical component and the author uses a squared...

I'm trying to figure out or find how fast Earth is moving due to the Hubble constant. I'm runnng into two answers and have difficulty understanding either one. --- One answer is a number of kilometers per second per megaparsec. But that's a distance per time unit per distance unit. I don't...

How can light be a constant for any observer? I understand how it fits into equations and what not, but how can it be a constant. If I throw a baseball forward at 10m/s in a train going 40m/s. I perceive it as 10, an observer on the ground would perceive it as 50. Why doesn't the same apply to...

I'm doing some special relativity exercises. I have to find $$x(t), v(t)$$ of a charged particle left at rest in $t=0$ in an external constant uniform electric field $$\vec{E}=E_{0} \hat{i}$$, then with that velocity I should find the Liénard–Wiechert radiated power. I will show you what I did...

Homework Statement The dielectric cylinder is radius R and thickness d. Origin is at the center of the cylinder, which is oriented along the z-axis. It has polarization P=pz∧I need to calculate the potential V(0,0,h) at h>d/2. Homework Equations σb=P⋅n∧...

Homework Statement Force Extension in (m) 1.0 0.014. 1.5 0.032. 2.0 0.053. 2.5 0.071. 3.0 0.090. 3.5 0.110. 4.0 0.130. 4.5 0.148. 5.0 0.166...

This question has a little bit of physics in it, but it's mostly maths. If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I...

If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I assumed the spring force, which is a function of its elongation x (F =...

I have been reading in various sources that the directly measured value of Ho is high than the global value inferred by precise measurements of the CMB. The local value seems to be around 73 km/s/Mpc where as the global value inferred, assuming a flat Lamda CDM model is about 67 km/s/Mpc...

The continuity equation in fluid mechanics is: Do the condition of "constant-density fluid' and 'imcompressible flow' have the same effect on the continuity equation, in that the first two terms disappear? Or is there a difference between these assumptions?

Hello, could you help me please about how can I calculate dielectric constant form electrical conductivity?

Homework Statement "The fastest measured pitched baseball left the pitcher's hand at the speed of 45 m/s. If the pitcher was in contact with the ball over a distance of 1.50m and produced constant acceleration, (a) what acceleration did he give the ball, and (b) how much time did it take him to...

Will my described method allow me to achieve my objective? If so, could you recommend a rheostat that is rated for at least 20A @120VAC that will work for my application? If not, could you describe an alternate method? Objective: Determine the ampacity of various wires at 120VAC Method: Wire a...

Homework Statement I am solving for the damping constant (b). The amplitude has decreased to 80% of its original height (0.1m) after 10 oscillations. The mass is 2 kg, k is 5000 N/m, w is 50 rads/s, T = pi/25 s. Homework Equations x = 0.1cos(50t) v = -5sin(50t) a = -250cos(50t) The Attempt at...

Homework Statement Suppose that ##T_i## is the contravariant component of a vector field ##\mathbf{T}## that is constant along the trajectory ##\gamma.## Show that intrinsic derivative is ##0.## Homework Equations $$\frac{\delta T_i}{\delta t} = \frac{dT^i}{dt}+V^j\Gamma^i_{jk}T^k$$ The...

Hi. If a planar wire loop is moved through a homogeneous magnetic field (field lines perpendicular to the loop plane) with constant velocity and no rotation, Lorentz force will move some electrons to one side of the loop, creating a potential difference. But how does this work with Faraday's...

I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations. Is it correct to say that this result applies to a sinusoidal wave as an assumption? In my understanding that is (more or less) equivalent to planar waves in vacuum: is it...

Homework Statement Given Ma = Mb =Mc and muk between c and the surface is 0.30 Homework Equations (rope length) = constant Maaa = Mag - T Mbab = Mbg - 2T Mcac = T - (mu)Mcg The Attempt at a Solution The equations I came up on my own and the answer key did as well. The problem is I also need...

Homework Statement Determine the "Damping Constant and Time Function" v(t)= 8ε^-106t Homework Equations ∝=Damping Constant = 1/∝=Time Contstant = 1/DC The Attempt at a Solution -848ε^-106t = DC then 1/DC = *1.087x10^-49 It does not look right...Is the e in my calculator the same...

Homework Statement A man was driving a car at 78 km/h, he saw a deer at the distance of 101m, how much time is needed so that the car slows down after it drove 99m and stops. Homework Equations Δx = 1/2 (vi + vf) * t The Attempt at a Solution I'm thinking about finding the Δx

Hi guys, 42 year old engine hobbyist here, not a student. I've had great luck figuring out my questions in this portion of the forum in the past and look forward to your input. Keep in mind that I'm not formally educated, so if it's possible to dumb something down a bit I'd appreciate it.1...

Based on my thinking if gravity was a constant wouldn't it be equally hard to walk up a hill versus walking on a flat surface or even going down? Too me it seems like the steeper the angle the more gravity and smaller angles would be less gravity. So it is pushing you against an angle.

Homework Statement Homework EquationsThe Attempt at a Solution EPE is (0.5)kx^2 Let Y have spring constant of K then X has spring constant of 2K So EPE of Y is (0.50kx^2 which is E So EPE of X must be (0.5)2kx^2 which is kx^2 which is 2E? But correct answer is E/2??

Hello everyone, I was reading this application note and I am having trouble understanding how a parallel RC circuit with ESR bring driven by a current source has a transfer function of 1-pole. When I do my math I get a pole and a zero. I have attached an image of the claim that there's 1-pole...

Assume that (x-4) is a factor of 2x^2-4x-z. What is the value of z? How would you set it up to use the foil method?

Homework Statement for the opamp circuit give in the figure, find Vo(t) for t > 0 the figure is attached. Homework Equations I know that tau = R * C that is the time constant of a capacitor discharging is equal to the product of the resistor that it discharges through and its capacitance.The...

Hello, When we assume the universe is expanding at a constant rate, we could say the age of the universe is 1/Ho. but I always feel unsure about that because 1/Ho is the distance over the velocity. However, the velocity changes over time, that is, when something is closer to us, the move slower...

Boltzmann's constant appears in many distributions of statistical physics, and I have been left confused whether it is always the same constant with certainty. For example, suppose we define the Boltzmann's constant so that it is the constant that works with certainty for gases, i.e. it gives...

Homework Statement When a mother lifts he child with her foot (as shown in figure) what force should the upper muscle exert to lift her child at a constant speed? Homework Equations W = F x D f = mg I think these might be the right equations to use, correct me if I'm wrong. The Attempt...

I am having trouble understanding why blood flow rate is constant between the aorta and the sum of capillaries/sum of the arterioles. I keep thinking that in the arterioles or capillaries there is a decrease in velocity and somehow this decrease in velocity will decrease the total amount of...

How is the constant used to measure resistance? I can't find a clear answer anywhere. The constant is h/e^2 but that doesn't really help in seeing how it is linked to resistance other than the units being the same in base units.

I am really confused here. I have studied that if the kinetic energy of a moving body is not changing then the net work being done on the object is equal to zero. But when we are talking about a body moving upwards at constant velocity there is no change in its kinetic energy but there is still...

Homework Statement Homework Equations These are the equations he provided. The Attempt at a Solution I actually have no idea how to do them. So any help would be much appreciated.

I am coding a game in which I desire a projectile to undergo realistic curving when rotating while moving through the air. Let's consider the instance of a projectile that is initially moving forward while spinning clockwise along an axis placed vertically in it is center of mass. The object...

Homework Statement Find the magnetic dipole moment of a spinning sphere of voltage ##V## and radius ##R## with angular frequency ##\omega##. Homework EquationsThe Attempt at a Solution To find the dipole moment, we need to do ##I \int d \vec{a}##, which would be ##I 4 \pi R^2 \hat{r}##, but I...