Constant Definition and 1000 Threads

I am doing an Astronomy GCSE. I have to work out the orbital period for a satellite. I have got quite far with it, but I am really stuck. I have spent hours at it! This is the question:- A space laboratory is in circular orbit around the Earth at a distance of 6000km from the Earth's centre; its...

From what I've seen so far, the basis of the solution space for all the constant coefficient homo linear DE's have been linear combinations of the exponential function e or of some polynomial multiplied by the exponential function. Is this always true that these DE's always result in solutions...

Overall I'd say I'm a somewhat secure person; though definitely a bit weaker than average, I'm not an emotional wreck except for when it comes to one thing: doubt of my capacity/potential, which has lately bothered me a lot. Any time of IQ or intellectual superiority are mentioned I go crazy...

So force equals mass times acceleration. What happens then if we pushed a box horizontally without fiction at constant speed? The box keeps moving but acceleration equals zero? Is there still force? Thank you!

the equation for wave velocity is velocity = wavelength * frequency. now by using the Doppler equation for change in frequency and the Doppler equation for change in wavelength. if you multiply those two equations together you get. frequency' *wavelength' = original frequency * original wavelength.

Homework Statement I'm making a program that draws a graph of the weight of an hourglass. Obviously at first we know the weight, and as the grains begin to fall it decreases by the amount of mass in free fall. However I ran into a problem when the grains begin to hit the bottom. It's impossible...

Hi, I am reading the Einstein original paper on Special Relativity, in this link (English translation), I am having difficulties on this sentence: "We have now to show, that every ray of light moves in the moving system with a velocity c (when measured in the moving system), in case, as we have...

Homework Statement . Show that if and, thenis constant in time.Homework EquationsThe Attempt at a Solution

Homework Statement A block of mass "m" is pulled across a rough table by a string at an angle "θ" above the horizontal at a constant velocity. What is an equation for the magnitude of the kinetic friction force, fk? The answer that I was given was μk(mg-T*cos(θ)) Homework Equations Fk=Fn*uk...

Hi, I have the ODE y'''' - 3y' + 2y = 0 The characteristic equation is then $r^4 - 3r + 2 = 0$ So my 1st question, is there some easier way of finding the roots than long division? I looked at the first and last terms to guess the roots (if real) might come from (r-1) , (r+1), (r+2), (r-2)...

Suppose there are two tanks, tank A and tank B, of equal size and both are very large. Suppose the bottom of tank A is at an elevation that is higher than the top of tank B. Suppose there is a very small tube relative to the size of the tanks that connects the bottom of tank A to the bottom of...

Hey! :o I am looking at the following part: The constant field of the differential field $k((x))$ is $k((x^p))$. Hence if $(1)_p$ has a solution in $k((x))$, multiplication by a suitable constant yields a solution in $k[[x]]$. What exactly is a constant field of a field? (Wondering)

Homework Statement A pendulum, initially at equilibrium, is set into motion by a spring-loaded launcher (compressed a distance of 0.0150 m) which fires horizontally. If the mass of the pendulum bob is 0.340 kg and it rises to a maximum height 0.120 m (relative to equilibrium), what is the...

Homework Statement Hello, In a lab experiment, we wanted to compare the time constant in a simple RC circuit by comparing the value of Resistance * Capacitance that we measure directly and the value of RC that we get from the procedure. The procedure entailed using a wave generator and an...

Homework Statement A cylinder of permeability ##\mu## is placed in an external field ##B_0##. find the strength and direction of magnetic field inside the cylinder for: a) when axis of cylinder is parallel to external field. b) when axis of cylinder makes an angle ##\theta _0## with external...

Hi all, I have a constant torque spring that rotates the drive wheel of a Geneva mechanism. I am facing the following problem. I would like a very slow rotation of the drive wheel whenever the drive wheel is not driving the Geneva wheel of the Geneva mechanism (which is 270 degrees of a...

Homework Statement Warning: I realize the title is misleading... the function itself isn't what's constant. Mod note: Edited to fix the LaTeX If ##f## is a continuous at 0 such that ##\lim_{x \to 0}\frac{f(x)-f(g(x))}{g(x)}=M##, where ##g(x)\to 0## as ##x\to 0## does this generally mean that...

I searched for, but could not find any name or published value for a constant (with units m-3 K-3) which when multiplied by temperature (in degrees Kelvin) cubed gave the corresponding photon density (in m-3). Does anyone know of such a constant with a published value? I calculated a value, but...

Hello, I've noticed that Planck's constant h and the action of a particle S both share the units of Joule-second. I was wondering if there were a connection between the two, but my Modern Physics textbook (Harris) doesn't say anything about it. Wikipedia's definition of Planck's constant says...

Homework Statement Prove that if f'(x) = g'(x) for all x in an interval (a,b) then f-g is constant on (a,b) then f-g is constant on (a,b) that is f(x) = g(x) + C Homework Equations Let C be a constant Let D be a constant The Attempt at a Solution f(x) = antiderivative(f'(x)) = f(x) + C g(x)=...

1. The problem: Building a (probably very simple) computational model for Ising Spins - particles on a lattice with spin up and spin down, only nearest neighbour interactions. I can't for the life of me figure out the renormalisation constant for the probability of a given particle flipping...

Homework Statement Show that phi_n will find the proper phi_4. IE: show that it gives the correct normalization constant. Richard Liboff...chapter 7 Homework Equations A_n = (2^n * n! * pi^1/2)^-1/2 The Attempt at a Solution I don't know where to start really. I tried some things with <...

When doing constant volume calorimetry, the enthalpy can be calculated as follows: ΔH = ΔU + Δ(PV) ΔH = w + q + Δ(PV) ΔH = PΔV + q + Δ(PV) and at constant volume: ΔH = q + VΔP which I've then see people rewrite using the ideal gas law as follows: ΔH = q + (Δn)RT where Δn is the change in...

Homework Statement A 15.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t)=4.50 cos[(19.5s−1)t−π/8] in centimeters. What is the spring constant of the spring? Homework Equations y...

Homework Statement Solve the following differential equation and compare computer solutions \begin{equation*} 4y''+12y'+9=0 \end{equation*} Homework Equations None The Attempt at a Solution [/B] First of all looking at this equation, even though it is in the section where we learned about...

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you

Homework Statement An electron in a one-dimensional box with walls at x =(o,a) is in the quantum state psi = A o<x<a/2 psi = -A a/2<x<a A) obtain an expression for the normalization constant, A. B) What is the lowest energy of the electron that will be measured in this state...

Hello! The total force F = m*a applied to the bicycle is F = F1 - a*v^2, where F1 is the initial force applied to the bicycle, a is a constant and v is the velocity. That means that the total force applied to the bicycle decrease as velocity increases, like a wind resistance decreases...

Homework Statement It requires 49 J of work to stretch an ideal very light spring from a length of 1.4 m to a length of 2.9 m. What is the value of the spring constant of this spring? Homework Equations u=0.5kΔx2 The Attempt at a Solution u=\frac{1}{2}k\Delta x^2\\ k=\frac{2u}{\Delta x^2}\\...

A question on my lab is find the amount of "stopping force" required to stop the egg, by determining the size of the "crumple zone" A brief description of the lab: Build a container that will keep an egg from breaking as it is dropped from the third floor of the school, your container must...

what speed would you half to obtain going around the Earth to be constantly in line with sun, so it would be day time aways. and how would you go about calculating this. what kinds of equation could you use. Thanks Aiop.

Homework Statement Two cyclists, Anant and Beth, are standing on a straight road a distance d=22.0 m apart. Simultaneously, they begin to move toward each other, Anant with acceleration a_A=0.2 m/s^2 and Beth with acceleration a_b=0.10 m/s^2. Just as they begin to move, a bee, sitting on...

1. The problem statement, all variables and given/known Spring constant of trampoline and cradle Homework Equations k=F/x The Attempt at a Solution I think a trampoline should have a low spring constant so that the extension is bigger. Is this correct? For cradle, in my opinion, it should have...

I was going through Periodic Motion chapter of my book and came across an equation while defining the relation between Time Period of on oscillating particle and force constant. k/m=w2 which was applied in, T = 2xpie/angular velocity can anyone please help me define this equation. I can't seem...

Third question about wave optics in two days, hope it's not too much. When we look at the intensity of light on the screen in a double-slit interference experiment (assuming negligible diffraction), we find something like this : When we look at the intensity of light on screen in a...

Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.

Hello! (Wave)We consider the initial - boundary value problem $$u_t(t,x)=a(t,x) u_{xx}(t,x)-c(t,x) u(t,x) \forall t \in [0,T_f], x \in [a,b] \\ u(0,x)=u_0(x) \forall x \in [a,b] \\ u(t,a)=0=u(t,b) \forall t \in [0,T_f]\\ a,c \in C^1, a(t,x)>0, c(t,x) \geq 0$$ $$\tau=\frac{T_f}{N_t}, t_n=n...

Hi I want to create a thought experiment involving waves of any kind. I am going to create a thought experiment I am on a boat that is at rest in the ocean. I am standing on the boat measuring the size of the waves and the frequency. So I measure the wave along the side of my boat to have a...

Homework Statement Show that the internal energy at constant entropy and volume decrease for a spontaneous process Homework Equations F = U-TS The Attempt at a Solution Use Clausius: dS-dQ/dT > 0 Assume constant volume: TdS > dU assume constant entropy this becomes 0>dU Since dU is...

Homework Statement We have a heavy chain with length of L and weight of m placed on a table. we take an end of it and move it with constant velocity of v upwards. so each moment it gets heavier. If the force needed for this uniform speed is called F, and length of chain which is higher than the...

I am an electrical guy, i can't understand the concept of constant flow system...and how temperature is controlled in room by Air conditioner...thanks

Acceleration due to gravity is used as a constant throughout the massive body,but it varies due to height and depth & also varies from equator to pole,so it affect the rotational speed of planet from equator to pole.So, why would it takes as a constant.

1. The problem statement, all variables and given/known Homework Equations P=Fv K.E = 1/2 mv2 The Attempt at a Solution This is the examiner report: Why infinite acceleration? Is it because the mass is too small?

Hi all, A question about the vacuum energy density and spectrum. The only spectrum that is frame invariant involves the cube of the frequency. Is it also possible to have a constant offset term (which would also be frame invariant), to 'adjust' the energy density so it doesn't turn out to be...

Homework Statement It is said that the potential in the neutral regions of a PN junction diode is CONSTANT. Homework Equations V=Q/4ΠΣr The Attempt at a Solution It is said in all textbooks to ASSUME that the electric field in the neutral regions as zero. Two aspects confuse me. 1. What...

Homework Statement The mass of a car that acts on one wheel is 100 kg. The elasticity (spring) constant in the suspension system of that wheel is k = 10^4N/m. Design the strut (find the friction/resistance constant c) such that any vertical motion of the wheel (set up for example by going over...

In the EFE, what does adding Λgμν mean and why is it not included in the Einstein tensor?

Assuming that we have a chemical plant which produces methanol through the following equations: CH4 + H2O <--> CO + 3H2 CO + 2H2 <--> CH3OH CO2 + 3H2 <--> CH3OH + H2O I know that with specific pressure, temperature and flow rates, I can produce reactions with specific equilibrium constants. Are...

Okay, so please help settle a dispute. A toy car is moving at a constant speed of 1 m/s. The car is powered by a battery. Now, when the car is going at a constant speed, there is obviously no net force on the car. The dispute comes when trying to draw a FBD. Is there friction (traction)...

Example 3 shows the derivation of one of the kinematics equations. I am quite familiar with it. At the part where it says dx/dt = gt + constant, how does one determine if constant = x_0 or v_0? Thank you.