Constant Definition and 1000 Threads

I'm looking to see how much the dielectric constant of air will change mostly as a function or air temperature. Is there a formula that outputs air dielectric as a function of temperature or atmospheric pressure?

Assume we have a cylindrical fin which has the effective length of L and its efficiency is given by the equation: $$η=exp(-0.32mL)$$ where $$m=\sqrt{\frac{hP}{kA}}$$ where P is perimeter and A is the cross sectional area of the fin. If the volume of the fin remains constant, which of the...

For constant dark energy, Hubble value will eventually become asymptotic. If dark energy were dynamic and gently decreasing, what will the value of Hubble eventually become - will it asymptote or keep decreasing?

Homework Statement [/B] A particle P1 moves with a constant velocity v along x-axis, starting from origin. Another particle P2 chases particle P1 with constant speed v, starting from the point (0, d). Both motion begin simultaneously. Find - 1. Initial acceleration of P2. 2. Ultimate...

Hi, quick basic question. Alright let's say I have a little drone with rotors that only allow the drone to move up and down (in the y-direction). I need help differentiating between these two situations: 1.) I want the drone to start on the ground, accelerate upwards (to a certain velocity)...

Homework Statement Homework EquationsThe Attempt at a Solution I don't understand part iii, how do you get the relation of A6 by part ii?

So I recently had a conversation with a mathematician friend of mine who studies Einstein's equations, and he asked me this: Why do physicists call it "dark energy"? It isn't like the dark matter problem, where there is almost certainly some massive "stuff" out there gravitationally influencing...

Homework Statement Homework EquationsThe Attempt at a Solution I think I can solve this problem . But I am bit unsure about how current changes in the circuit and the coil when it is shorted . Before the coil is shorted , there will be no induced EMF across the terminals of the coil ...

Homework Statement A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is rotated through an angle of 45o and released from rest and oscillates with a frequency of 2.5 Hz, what is the torsion constant of the wire? A : 1.7 x 10-3...

Homework Statement a)Helium enters a closed system as a flow of compressed gas at a temperature of 14 K and at pressure p (enthalpy conserved). A fraction α emerges as liquid and the rest as gas at 14 K, both at atmospheric pressure p0. Find an expression for α in terms of the enthalpy H(p) of...

Homework Statement Not sure if the link is showing. But it's imgur.com/a/LEvd0 Homework Equations The steps I've taken so far as written in the attempt section below is correct. The solution provided then proceeds with letting ##z = x + iy## and setting ##\ddot z+i \omega \dot z = 0##. Then...

Homework Statement Having a conducting sphere with radius ##R## and charge ##Q##, dielectric is put on it so that a spherical shell with inner radius ##R## and outer radius ##3R## is formed. Calculate: 1. Electric permitivitty ##\epsilon## such that ##E(r), R<r<3R## is constant and there's...

If we have a medium (say, glass) with an index of refraction, n=1.33, the speed of light in it will be c/1.33. However, blue light travels slower in glass than does red light. Since c is constant and the speed of light is changing, doesn't that mean that the index of refraction will vary based...

Homework Statement [/B] The block, initially at rest, slides down the ramp and compresses the spring 0.03 m. Theta = 30 degrees L = 1.25 m M of block = 2 kg Δx = 0.03 m 1) Write the expression for the initial and final energy states 2) Find the spring constant K Homework Equations mgh...

Hey! Short definition: A gradient always shows to the highest value of the scalar field. That's why a gradient field is a vector field. But let's assume a constant scalar field f(\vec r) The gradient of f is perpendicular to this given scalar field f. My Questions: 1. Why does the gradient...

I try to calculate the speed curve of a relativistic rocket driven by a 100% efficient engine with constant thrust, when traveling to a distant star. All equations I can find consider constant acceleration, which of course is not working, since the ships mass decreases when the fuel is used...

Homework Statement Consider a conducting sphere with radius ##R## connected to a voltage source of ##V_0## volts. If the sphere is then covered by a dielectric spherical layer of radius ##9R## calculated the relative permitivitty ##\varepsilon_0## needed so that the field in the empty zone...

I had an argument with my friend regarding constant forces.He said that work done by constant forces are conservative as we can take the force out of the integral and it doesn't depend on the path .But the fact that this information is not given in my textbook as well as by teachers makes me...

Homework Statement Spring Compressed = 20cm = .2m Decompresses and leaves the ground at a velocity of 5m/s Mass = 6.00 kg Homework Equations k = fx The Attempt at a Solution I have no idea where to go from here...

A rocket is in constant velocity. The velocity of the rocket is 150Mm/s (or 0.5 of the speed light, or 150 million meters per second) relative to us (we as observer). We observe two lights, one moving in parallell with the rocket, another is moving in the opposite direction. Below I have made...

After watching this video: The mystery of 0.577 4k1jegU4Wb4 My problem is at position 7 mins 26 secs where he states the following: 1 - Ln = 1 1+ 1/2 - Ln2 = 0.81 1 + 1/2 + 1/3 - Ln3 = 0.73 And so on until we arrive at Eulers Mascheroni Constant Being that he is using 'Ln' have learned this...

Homework Statement decreasing the resistance increases the current if the voltage remains unchanged. Homework Equations V=IR The Attempt at a Solution The solution in the book does not count this as a true statement, but it seems true to me. Is there any reason why the statement would be false?

Homework Statement African baobab trees can have circumferences of up to 43.0 m. Imagine riding a bicycle around a tree this size. If, starting from rest, you travel a distance of 162 m around the tree with a constant angular acceleration of 5.00 × 10–2 rad/s2, what will your final angular...

Homework Statement A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumber system. After the coupling, the motion of the car is defined by the relation ##x = 60e^{-4.8t} sin16t##, where x and t are expressed in millimeters and seconds...

Homework Statement Force of jet= A(r(t))4/3 A: constant determined by the fighter model in the class being considered and the drag force on the plane r(t): the rate of fuel consumption as a function of time Consider 3 possible situations for r(t): 1. when the rate is constant for the...

Griffith's Introduction to Elementary Particles, if I understand it correctly, states that in QED, the fine structure constant contributes less and less to the strength of the EM interaction as we add more and more vertices since the constant is so small (1/137). However, in QCD, since the...

Does the dielectric constant of a material have to be positive?

For instance, in introduction in https://www.sciencedirect.com/science/article/pii/S0550321314001400 we can find that vacuum energy is proportional to ##k_{max}^4## where it is written that "If we believe the general relativity up to the Planck scale ##k_{max}=10^{19}GeV##" And so the...

some questions I have seen tend to word as show that some quantity/tensor/scalar (e.g let this be ##K##) is constant along an affinely parameterised geodesic, others ask show covariantly constant. the definiton of covariantly constant/ parallel transport is: ## V^a\nabla_u K = 0 ##for the...

Hello, this is my first post. I need to solve some problems for my class, and I got stuck with this one. The problem (this is a translation): Your father has just turned 50 (t = 0) and wants to retire in 15 years (t = 15). He thinks he will live 25 years after retirement, until he is 90 years...

Hello all, It seems like a fairly straightforward question but I cannot find any information in the literature. Let's suppose we apply a crack driving force K1=45 MPa.m^0.5 to a notched specimen with an upper shelf fracture toughness K_mat = 50 MPa.m^0.5 at room temperature T0=20 oC. Under a...

Homework Statement Hi. I started studying LR circuits and the first thing that made me do searches in textbooks of mine and in the internet was the time constant which is surprisingly not L times R, but L/R which would mean the time needed to store and release energy is being prolonged with...

Homework Statement A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a projectile an altitude of 730m. The projectile hits the ground 5.00s after release. A plane, diving with constant speed at an angle of 53 degrees with the vertical, releases a...

Homework Statement N2 + 3H2 --> 2NH3 (all gases) Why is such a high pressure needed? Calculate the equilibrium constant at 500k then estimate the percentage conversion at equilibrium at 1 bar total pressure, assuming the stoichiometric ratio of N2:H2 is 1:3. Repeat the process at 50 bar...

Homework Statement A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...

Homework Statement Homework Equations Time constant = 1/ξwn The Attempt at a Solution Time constant = 1/ξwn Damping factor = ξwn So T = 1/ξwn If ξwn is reduced by factor of 2, then Time constant must be increased by factor of 2. So Answer is: B Book answer is A How? p.s. I know I'm posting...

Homework Statement Homework Equations Express denominator as 1 + sT1 The Attempt at a Solution In denominator s+2 can be written as : 2(1 + 0.5s) s + 3 can be written as: 3(1 + 0.3s) So I have two time constants. Should I multiply them to get final time constant? There is another formula...

Hi! I've found some excercices and expanation of Work always consider a constant velocity, this is a net Force equal to cero. Like spring or gravity excercices related against a force applied. Does this relation with constant velocity has some usefull explanation why? Should I always assume...

Why are the fundamental physical constants called "constants" when they change over time? I've read that the constants were adjusted in 1986. How can there even be something that is constant, when we can't even see the entire universe?

Homework Statement I need to calculate a spring constant using measurements from a Hooke's Law Apparatus, a spring, and some weights. The weights are hung vertically from the spring and the distance is measured from the equilibrium point of the spring. If I'm solving for k, then k=F/x. I do...

Hi. π is a constant. The purpose of π is to use it to find circumference of a circle or area of a circle. Correct? Can you please elaborate? Can you point out any other two constants and its purpose? Thanks.

I am trying to find a paper which explains the derivation of the Cosmological Constant. I looked several books and sources and it only says " The cosmological constant ##Λ## appears in the Friedmann equation as an extra term" or etc. Sometimes It directly puts it in the Friedmann Equation which...

Homework Statement [/B] An X-ray tube gives electrons constant acceleration over a distance of 14 cm . If their final speed is 1.0×107 m/s , what are the electrons' acceleration? Express your answer to two significant figures and include the appropriate units. Homework Equations My prof. has...

Hi, I'm reading about the wave packet solution to the dirac equation but in the book I'm reading it states that \int \frac {d^3p} {(2\pi)^3 2E} [a u e^{-ipx} + b^\dagger \bar{v} e^{ipx} The normalisation constant confuses me. I guess the 2pi^3 is reasonalbe. However, the 1/2E seems a bit...

Homework Statement 14.27 The 2.5-kg weight is released from rest in position A, where the two springs of stiffness k each are undeformed. Determine the largest k for which the weight would reach position B Homework EquationsThe Attempt at a Solution Hi. Can you check if I am going at...

Homework Statement Show that the normalized wave function for a particle in a three-dimensional box with sides of length a, b, and c is: Ψ(x,y,z) = √(8/abc) * sin(nxπx/a)* sin(nyπy/b)* sin(nzπz/c). Homework Equations Condition for the normalization: ∫0adx ∫0bdy ∫0cdz Ψ*(x,y,z)Ψ(x,y,z) = 1...

Homework Statement Homework EquationsThe Attempt at a Solution ## n_1 = \sqrt{ \epsilon _1} ## ...(1) , ## n_2 = 1 ## ...(2) ## \frac { \sin {\theta_i}}{ \sin {\theta_l} } = \frac { n_1}{n_2} = n_1 ## ...(3) ## \cos{\theta_1} = \frac { n_2}{n_1} = \frac1{ n_1} ## ...(4)...

An antelope moving with constant acceleration covers the distance between two points $\textbf{70.0m}$ apart in $\textbf{7.00s}$ Its speed as it passes the second point is $\textbf{15.00 m/s}$. What is its speed at the first point? The answer to this is 5 m/s ok this should be real simple but...

Homework Statement Homework Equations I know for RL circuit T = L/R For RC circuit it is RC But how to go ahead for RLC circuit.The Attempt at a Solution I calculated for RL as 1/4 = 0.25 And RC as 1 Then I added both time constant and got 1.25 Book answer is 0.5. How to solve this? In...

Homework Statement A particle is restrained to move in 1D between two rigid walls localized in ##x=0## and ##x=a##. For ##t=0##, it’s described by: $$\psi(x,0) = \left[\cos^{2}\left(\frac{\pi}{a}x\right)-\cos\left(\frac{\pi}{a}x\right)\right]\sin\left(\frac{\pi}{a}x\right)+B $$ , determine...