Constant Definition and 1000 Threads

Homework Statement A 48 gram dart is shot vertically upwards from a catapult with a spring constant of 350 N/m. The catapult is initially stretched from the equilibrium point by 21 cm. What is the height above the starting point reached by the dart?Homework Equations KE=PE, rearranging to find...

Hey! :o If the space $W$ is constant (doesn't move with the flow), show that $$\frac{d}{dt}\int_{W}\left (\frac{1}{2}\rho |\overrightarrow{u}|^2+\rho \epsilon\right )dV=-\int_{\partial{W}}\rho \left (\frac{1}{2}|\overrightarrow{u}|^2+i\right )\overrightarrow{u} \cdot \overrightarrow{n}dA$$...

Assuming a flow can be idealised as incompressible, then can you use the constant pressure assumption ? I just want to get my understanding clear. My problem is the following.Consider a fluid element with volume ##V## and a fixed number of molecules. If the flow is incompressible, then the...

Homework Statement The proper length of a spaceship A is 60 m and the proper length of spaceship B is 120 m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed on...

Title should be: Are photon energies constant along null geodesics? [Mentor's note: Title corrected] As I understand it in general relativity the paths of light rays, given by null geodesics, are scale invariant. Is that correct? Now Maxwell's equations in flat Minkowski spacetime are also...

Another silly question... Assuming a surface with no friction in space (you get the idea), I push/kick/give a 1kg block on this horizontal plane a force of 1N. It would start to accelerate in the direction i pushed it with at a rate of 1m/s² forever until another force acted upon it. So far so...

I have some questions about acceleration that I'd like for someone to explain to me. As far as I know, acceleration depends on either change in velocity or change in direction (or both). So if I'm going 1m/s North constantly I'm not accelerating. However, what would be the acceleration if I walk...

Homework Statement What is the magnitude of the electric field due to a 6.0 x 10-9 C charge at a point located 0.025m from the charge? The charge and the point in question are located underwater (κ(water) = 80). Homework Equations I know that E = magnitude of electric field = kq/r2, where k =...

Hi. I was just curious about the current value of the cosmological constant. My astrophysics class lecture notes say on the order of 10^-122, but the Wikipedia article says 10^-35 s^-2. Could someone explain where the 10^-35 s^-2 value comes from? Thanks!

Hi there, I am confusing on the statement that we have classical physics when Planck constant approaching zero. I search the similar topic in Physics Forums and I saw that most of the answers refer to the size effect. It argues that when we measure something in the scale of meter comparing to...

Why cosmological constant term ##\Lambda g_{uv}## in Einstein equation is proportional to ##g_{uv}##. Why it is even proportional to ##g_{uv}## in spacetime of MInkowski?

Homework Statement Consider the wavefunction ##\Psi (x, t) = c\ \psi (x) e^{-iEt/ \hbar}## such that ##\int | \Psi (x, t) |^{2} dx = 1##. I would like to prove to myself that the normalisation factor ##c## is a real number. Homework Equations The Attempt at a Solution ##\int | \Psi (x, t)...

Homework Statement A speeding car has instantenous velocity of 1 m/s when a stopwatch reads 10 seconds. It has constant acceleration of 2 m/s^2. What is the cars speed when it reaches the stopwatch reads 12 seconds. Homework Equations x= (Vinitial)(DeltaT) + 1/2(a09deltaT)^2 I think this is...

Homework Statement An Indy 500 race car's velocity increases from 4m/s to 36m/s over a 4 second time interval. What is its acceleration? 4m/s is the initial velocity, 36 m/s is the final velocity, and time is 4 seconds. Homework Equations final velocity = initial velocity + (acceleration x...

Homework Statement Converting Hubble's constant in SI units of s-1 into kms-1 Mpc-1 (kilometers per second per megaparsec) Number given is 2.31 x 10^-18 s-1. Homework Equations H = v/d (where H is Hubble's constant, v = velocity and d = distance) The Attempt at a Solution I can see how you...

If the speed of light is constant in any inertial frame then how do we measure a red shift or blue shift or why?

Hi guys and gals. I have a constant current welder. 150 Amps DC/ 230 Amps AC output. There is no provision for measuring output current when the machine is welding. I'm thinking of adding a shunt to either the work lead or the return lead. I don't know what size and rating I need. The input...

Homework Statement A molecule is a harmonic oscillator, and has a fundamental frequency of 1000 cm−1 and a reduced mass of 10.0 amu. From this, determine the magnitude of the force constant, and express it in units of aJ ˚A−2 (atto joules per angstrom). Homework Equations ω=√(k/mr) The...

Homework Statement What should be the spring constant k of a spring designed to bring a 1400 kg car to rest from a speed of 28 m/sec so that the occupants undergo a maximum acceleration of 5g’s? I have the solution manual and can see how they did this, but am curious as to why my attempt did...

Hi! While testing my knowledge of analytical mechanics I stumbled across a fallacy that I am unable to resolve. Could you assist me? When you finish integrating a Lagrangian over the time domain ##[t_1,t_2]##, shouldn't its position ##q(t)## and position dot ##\dot{q(t)}## variables take the...

I am curious about a statement that is usually tacked onto the end of a derivation showing enthalpy with constant pressure being equal to the heat into the system. First Law of Thermodynamics \Delta U = Q - W_{by} Define Enthalpy and look at its change: H=U+PV \\ \Delta H = \Delta U +...

Why magnetic constant is specifically 4*pi*10^-7? I can understand other experimental values, for example it would make sense if it was 3.1415*10^-7. But 4*pi is something we can never confirm experimentally since pi has infinitely many digits. So there has to be theoretical reason for us to...

In my textbook it is written that Electric charge on plates of capacitors (without dielectric ) is Q=CV And when dielectric is inserted in the space between plates of capacitors .charge Q remains the same whereas values of C and V change. i.e Q=C'V' is it correct?

My friend and I were discussing this, and google didn't seem to reveal any result. Much like how Bohr's theory managed to derive the Rydberg constant without much effort, has the gravitational constant been found in terms of other quantities yet? It just seems bizarre that Newton proposed a...

I believe what I am attempting to do is not possible but here goes. I want to design a fixed overall length coil which I can manually adjust the pitch on. Optimally one would be able to grab the coil and by twisting it in place would be able to change it's pitch by changing its diameter but not...

for A+ + X- -> AX with I=3, J=3, K=0 (i is number of components) I don't know the meaning of stoichiometric coefficients vji, and how to calculate it

Homework Statement Suppose that f:R->R satisfies the inequality ##|\sum\limits_{k=1}^n3^k[f(x+ky)-f(x-ky)]|<=1## for every positive integer k, for all real x, y. Prove that f is a constant function. Homework Equations None The Attempt at a Solution I tried taking f(x)=sinx and then using...

Sorry for the simplicity of the question but I encountered a simple math problem whilst autodidacting myself on classical physics. I seen that a surplus of a specific constant variable "b" was extracted from an integral after a bit of manipulation. ∫xdx was turned into b2∫(x/b)d(x/b) Does the...

What does it mean if a scalar field φ is said to be constant on a surface S? Does φ then have a particular mathematical relationship with S?

Homework Statement (a)Sketch how the contributions change with time (b)For no cosmological constant, how long will this universe exist? (c)How far would a photon travel in this metric? (d)Find particular density ##\rho_E## and scale factor (e)How would this universe evolve?[/B] Homework...

Homework Statement Mass car 1200 kg . power car constant 20kw . Resistance car motion 500N. Car passes point X and Y with speeds 10 m/s ,25 m/s. Car takes 30.5 s to travel from X to Y 1. Find acc of car at x 2.considering work/energy find distance XYHomework EquationsThe Attempt at a Solution

Homework Statement A particle moves on the surface of an inverted cone. The Lagrangian is given by Show that there is a solution of the equations of motion where and take constant values and respectively Homework Equations The equations of motion and are (1) (2) So can be...

Is light's speed constant? The universe is expanding, i think the distant b/w the planets&stars are increasing is that true? is it true then is the time taken to reach sun light to Earth now from past change? if the time is constant then how the speed of light is constant?

Dirac had proposed that Gravitational constant would reduce with time.Why?

I am hoping to recover some of the knowledge of physics I gained in high school that has vanished into the mists of time. Currently, I am being abused on Facebook by a self-proclaimed authority who ridicules my contention that gravitational acceleration is a constant. I get the idea that gravity...

I was wondering why is there a constant that isn't really a constant in mathematics? I am talking about "e", as in exponent e which is the base of the natural logarithm. By definition e = lim (1 + 1/n)^n as n approaches infinity, but doesn't this make e a non-constant since infinity always...

What is the cosmological constant for the Godel metric?

Is there agreement here regarding the relationship between expansion of the universe from its initial conditions, entropy (2nd law), time, (and more tenuously perhaps) "evolution"? I asked a question awhile back that was too specific I think that tried to tie the constant of expansion to the...

I posted this earlier, but I just realized it might have been in the wrong section. Sorry Okay, so consider you have system in which ΔG<0 and ΔS>0. Using Gibbs free energy (ΔG=ΔH-TΔS), you'll know that it will always be negative. As the temperature increases, it will actually become more and...

Homework Statement Distance from planet = 10^14 meters, Radious of the planet = 10^7 meters, mass of the object = 100kg g on the planet's surface = 10 m/s^2, g 10^14 meters away from the planets center = 2.5 m/s^2 Homework Equations Fg=G*m*M/r^2 The Attempt at a Solution I calculated the...

I don't know what to say. sqrt(4) = +/- 2, but constants are fixed. When written sqrt(4), it seems sqrt(4) is a constant, but not in the latter case. Help!

What does the metric look like for constant uniform acceleration, say in the x-direction? ds^2 = g_tt (cdt)^2 + g_xx (dx)^2 g_tt = ? g_xx = ?

It's a combination of centrifugal force and gravity that allows constant acceleration of a rotating object? also is it just coincidence that the most dense objects are near the sun?

Homework Statement Consider a satellite in circular low Mars orbit 300km above the planetary surface. R = 3396km M = 6.419 x 1023kg G = 6.674 x 10-11m3/kg/s2 Find the orbital velocity of the satellite (using the given values, I assume, as there is some inaccuracy in the real-life mass value...

Homework Statement Hello, I'm just curious as to whether I'm going about solving the following problem correctly... Problem Statement: A particle mass m and charge q is in the ground state of a one -dimensional harmonic oscillator, the oscillator frequency is ω_o. An electric field ε_o is...

When modelling the heat transfer through a plate using fouriers equation, what difference would it make if the width and length of the plate were set to a specified value rather than being infinite?

In the book, briefer history of time, hawking says that maxwell's theory of electromagnetism, concluded that speed of light is finite and constant, which made other physicists to give up the idea of absolute time, and think of newer concepts. How did maxwell, through his theories, correctly said...

I've read online that the fine-structure constant (alpha) is at a sort of "goldilocks value" for life generation; if it were 4% lower, stars would not produce carbon or oxygen in their fusion, and if it were greater than 0.1, fusion simply wouldn't occur. These are interesting facts, but can...

I reading book, part about gravity. It is Landau-Lifschiz, "Theory of field". And I trying to understand how to calculate cosmological constant. Re-read part with introduction of cosmological constant several times, still not understood. Let's imagine function of space curvature, without...

Homework Statement (56th Polish Olympiad in Physics, II stage) A photographer has a camera with a lens of focal ##f## with can be set to a value from the interval ##[f_{min}, f_{max}]##. The diameter of the diaphragm is ##d##. The photographer wants to make a photo of a friend so that the...