Constant Definition and 1000 Threads

What the question mean by "constant frictional resistance" in terms of formula? I suppose they meant... "resistance force (f)" which is, >> f = m * a. So, here is my try... m = 1.15 ton or 1150 kg vi = 20 m/s vf = 0 d = 800 m v^2 - u^2 = 2ad 0 - 20^2 = 2a* 800 - 400 = 2a* 800 - 400 /...

Let $X$ be a topological space and ##Y## a set. A function ##f: X \to Y## is said to be locally constant if, for every ##x \in X##, there is an open set ##U## containing ##x## so that the restriction ##f|_U: U \to Y## is constant. Prove that if ##X## is connected, a locally constant function on...

I often see this set up in thermodynamic problems and need clarification on how Newton's Laws are involved for the piston: Gas inside a piston cylinder (1) is heated expanding the gas and raising the piston (initially at rest) to a height (2) in a constant pressure quasi-equilibrium process...

Plants prefer C12 to C13 during photosynthesis, so that the C13 to C12 ratio in plants is less than that in the atmosphere (by around 20% for most plants, but less difference in C4 plants like maize). Do plants discriminate against C14 too? If so, won't that cause a considerable uncertainty in...

$$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$ That's what I did. But, book says $$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$ Seems like, $$x_0 + \dfrac{a_0}{2}t^2$$ is constant. How to find constant is equal to what?

I was reading this article at Wikipedia that says particle physics predicts that the cosmological constant is 10^120 larger than per observation: https://en.wikipedia.org/wiki/Anthropic_principle

I'm doing a simple RL Circuit Lab where students use 800- and 1600-turn air core coils to measure the time constant. Experimental results very nicely agree with predicted results. However, when students insert a steel (or iron) core in the coils, experimental results are far different than...

Regarding wave equation we are faced with this form $$\nabla^2 \vec{E}=j\omega \mu \sigma \vec{E}-j\omega \mu\varepsilon \vec{E}=\gamma ^2\vec{E}$$ where $$\gamma ^2=j\omega \mu \sigma -j\omega \mu\varepsilon $$ $$\gamma =\alpha +j\beta $$ where alpha and beta are attenuation and phase...

For a streamlined and bluff bodies, why is it standard to have the projected area be a fixed reference area, but yet the angles of attack (AoA) vary? If one were to vary the AoA then the projected area would technically change. The following link discusses that it is a convention to avoid...

According to the wiki entry on Planck units, https://en.wikipedia.org/wiki/Planck_units, the energy density of the universe, 1.8 × 10−123, is 1/16th the cosmological constant, 2.9 × 10−122. Is there a theoretical reason for this precise relationship?

EDIT: My bad, this is from my professors lecture, but I assume this question is more suitable for the homework section of this forum The problem gives that pV = constant, and thus is assumed to be an isothermal process. However, the given U1 and U3 are not equal to each other. Is it because it...

I understand that it is one of Einstein's postulates, however I don't know of any direct experiments which show that it is true.

This question wasn't particularly hard, so I assume metric compatibility and input Ricci tensor to the left side of Einstein's equation. $$R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=Cg_{\mu\nu}-\frac{1}{2} (4C)g_{\mu\nu}=-Cg_{\mu\nu}$$ Then apply covariant derivative on both side...

https://arxiv.org/abs/2106.04622 Calculating the Higgs Mass in String Theory Steven Abel, Keith R. Dienes [Submitted on 8 Jun 2021] There are at least two properties of the Higgs mass one might hope to explain with such a fundamental calculation: its criticality, and its participation in...

So, the Cp and Cv its very confusing for me. But, i understand what's its happening in this process, so, i use the logic and first i obtain a ecuation for obtain the final temperature ecuaticon: Q=m*C*△T Q=m*C*(T2-T1) T2=(Q+T1)/(m*C) If the process its in constant pressure, i use the Cp valor...

Astronomers1) tell us that a 'cosmological constant' can account for the universe's increasing expansion. Representing the universe by a symbolic expanding ring, Fig.a, at an instantaneous radius r the inward gravitational force varies as the inverse square of this radius, giving Fg ~ 1/r^2...

Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A)...

When we talk about systems at constant temperature and pressure, maximum amount of non-PV work can be extracted if process is carried reversibly and in that case it is equal to change in Gibbs energy of the system (decrease in Gibbs energy if system does non - PV work, A.K.A work is extracted...

Hi, On slide 9 of this presentation: http://www.globalcommhost.com/rogers/acs/techsupporthub/en/docs/MWJ_webinar_June20_2017_JC_microstrip_coplanar_stripline_final.pdf it states the signal wavelength can be changed with dielectric constant Dk. As far as I understand the wavelength and the...

The general form of Hubble’s law for a given cosmological time t is given by, v = H(t)D, (1) where v is the recession velocity of an object, D is its proper distance, and H(t) is the Hubble parameter at t. To get the H vs. t plot based on the ΛCDM model, we can use the following steps...

Summary:: Is the magnetic flux density B constant? Is the magnetic flux constant? I am working on a project design for Uni and I am stuck. In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and...

Let me start be making a small sketch of the problem, shown to the right. If the range of the projectile on a still day ##R = v_{0x}T##, then on the windy day the range becomes ##R+2H = v'_{0x}T = (v_{0x}+v_w) T##. Since the maximum height attained by the projectile ##H =...

Assuming the position x = 0 if no air gap, max stroke of plunger is L. Bordery conditions: x(t=0) = L, x(t=T)= 0. Given magnetic force F(x) = kx(t)^-2, here k is constant. If uncontrolled, there is big crash noise afer solenoid actuated, so I wish it pull plunger at constant power. Help me find...

In the following, I set the velocity of light unity. I refer to theories of gravities in higher-dimensional spacetimes. Newton` s constant converts the curvature scalar with dimension ##lenght^{-2}## into the matter Lagrangian with dimension ##energy/length^3##. So its dimension is...

Was the universe always spatially flat due to the presence of the cosmological constant, or has it become flatter in the late-time universe?

So first thing I tried was to separate the variables then differentiate by parts, setting u = E and v = 1/ln(E) (and the other way around) but I couldn't do the integral it gave. Then I tried to reason that because dx was constants then dE/dx is equal to E/x but I was told that's not the case...

Is the Reduced Planck Constant the minimum frequently/movement/spin matter can have to exist? So if a matter were to spin lower than 1.054 571 817... x 10-34 J s, it when cease to exist? Or would matter falling below the Reduced Planck Constant by classified as Dark Matter? I heard that Higgs...

I managed to isolate k to k=4pi^2/T^2 however I don't know If I did it correctly. I am trying to use K to find the mass of a bolt. I am stuck here, not sure If i need to find all three k's and then average them out?

We know linear spring force F = kx(t), k = spring constant, during any moment t of energy release. displacement x(t) = ʃv(t)dt the power p = F*V = kx(t)v(t)= kv(t)* ʃv(t)dt My question: Is there a mathematical function of special v(t) to make power p constant?

Time independent Schroedinger equation in ##\delta## potential ##V(x)=-\lambda \delta(x)##, where ##\lambda >0## is given by -\frac{\hbar^2}{2m}\frac{d^2}{d x^2}\psi(x)-\lambda \delta(x)\psi(x)=E\psi(x). How to find dimension of ##\lambda##? Dimension of ##V(x)## is [V(x)]=ML^2T^{-2}. Because...

My attempt at a solution: Is my logic accurate/correct, and is my answer correct? I consider the forces acting to be: Restoring forces in springs parallel, and Force of the current-carrying conductor in the Magnetic field. I imagine a vertical displacement of y upwards ( direction determined...

Summary:: Doubt in a spring exercise Text of the exercise "a mass of ##m = 0.4 \ \text{kg} ## is attached to a spring and it oscillates horizontally with period ##T = 1.57 \text{s}##; the amplitude of the oscillation is ##d = 0.4 \text{m}##. Determine the spring constant, the total energy of...

I do not understand how in part a, the units for K can be N/m. If Work is in joules which is kg*m^2/s^2 and we are diving by x^2 which is m^2, then m^2 should cancel out and we should be left with kg/s^2. Kg/s^2 makes more sense because in part b when you find the work done you are multiplying...

I thought I'd start by writing the problem in a tensor formalism. I have identified with ##S## the Earth and ##S'## the rocket. Since the acceleration provided is in the rocket's frame of reference, I can write the following four-vector. $$ a'^\mu=(0, a, 0, 0) $$ Since we are interested in the...

In https://physicsworld.com/a/physicists-measure-smallest-gravitational-field-yet/ the gravitational constant was measured by the smallest object until now, this is a small golden ball, with a radius of one mm. The intention is to measure some quantum gravitational effects in the future. But, I...

I am trying to determine the Fermi Coupling Constant which is measured to be ##1.1663787 *10^{-5}\text{Ge}V^{-2}##. The formula for Fermi is ##\frac{G_F}{(\hbar c)^3}=\sqrt{\frac{\hbar}{\tau_\mu}\cdot\frac{192\pi^3}{(m_\mu c^2)^5}},## where ##m_\mu## is the mass of a muon which is ##\approx...

Hi, PF, I think I've found a typo in my textbook. It says: "In the case of a multiplication by a constant, we've got $$(Cf)'(x)=\displaystyle\lim_{h \to{0}}{\dfrac{Cf(x+h)-Cf(x)}{h}}=\displaystyle\lim_{h \to{0}}{\dfrac{f(x+h)-f(x)}{h}}=Cf'(x)$$" My opinion: it should be...

I know Phi appears often when modelling exponential growth and, probably because of that, also in Biology/Ecology. But does it appear spontaneously in the mathematical description of some fundamental physics phenomenon at all? (As does Pi, the ubiquitous irrational number) Hope I'm posting on...

[Note: this thread was spun off from another metrology discussion] OMG! How does that work, starting with h? I'm trying to think of formulae with h in - as you do. I read about the 2019 definition but, unlike the definitions of length and time, starting from scratch with the mass definition and...

Is there any way that I can find concentrations and then find the rate constant, k? And, using them, make an Arrhenius graph to find activation energy (including the catalyst)? Any help would be much appreciated. Change in pressure was found using a Vernier Gas Pressure Sensor. The starting...

I was pondering my practice of talking about circular motion in the horizontal direction and the vertical direction. But I'd often would see in books, notes, and the internet that we assume constant velocity for the vertical case. However, when one thinks about the forces at different points in...

John is walking at a constant speed in front of a motion sensor. After 1 s, she is 2.5m from the sensor, 2 s later, she is 4 m from the sensor. a) Find an equation of in the form d=mt+b b) Determine the slope and d intercept and explain what they mean c) How far will John be from the sensor 5s...

As we all know, integration by parts can be defined as follows: $$\int u dv = uv - \int v du$$ And the usual strategy for solving problems of these types is to intelligently define ##u## and ##dv## such that the RHS integral can easily be evaluated. However, something that is never addressed is...

Edit: Picture of the Circuit (Simple RL circuit) The value of L is not given. Attempt to Solve for T by Rearranging Equation 1: I rearranged the equation to solve for T, using Ohm's Law so solve for I = V/R at each time. https://www.desmos.com/calculator/qlb2n6w4bg This graph is...

I keep seeing that it's assumed that photons interfere with each other, and there are other points of proof for this like destructive interference, etc., but I've never seen an experiment in which a constant beam is used but both slits are analyzed or the energy required for measurement is...

I have been trying for a long time to build a costant current source which I know is impossible to keep the current exactly the same but as much as possible. This is what I have done so far: The operation is very simple . If VCC is increased the VAC is increased a little bit. When VA is...

The question is regarding an electrically excited synchronous generator. Consider that this generator is not connected to the grid and thus not locked with the grid frequency. This generator is spinning at variable speed and gets constant and similar excitation current meaning that the...

A body on a circular orbit in the field of a central force (satellites in gravity field of Earth; a charge in a magnetic field) is subjected to a force which is always perpendicular to its initial velocity v, hence in a time period dt it acquires an additional velocity dv, which is also...

Hi all, I'm a little confused about something. Force-extension graphs and stress-strain graphs are always both straight lines up until the limit of proportionality, implying both the spring constant and the Young modulus are constant up until then. For a force-extension graph, Hooke's Law...

Helicopter lift weight of 500kg ,weight is connect with load cell to meassure tension. Neglect aerodynamic drag.. If helicopter accelarate up ,tension is rope is greater than 500kg. If helicpter accelarate down ,tension is rope is less than 500kg. If helicopter fly up with constant speed...