Constant Definition and 1000 Threads

Wikipedia and some of my simpler statistics courses present the gamma distribution with shape ##\alpha## and rate ##\lambda## as $$P(X=x)=x^{\alpha-1}\lambda^\alpha e^{-\lambda x} \Gamma(\alpha)$$ Where ##\Gamma(\alpha)## is a value in terms of alpha to normalize the PDF from the space of x...

Mentor note: Moved from a technical math section, so missing the template. TL;DR Summary: I'm trying to solve the differential equations (D^2 -4D + 3 )y = 2xexp(3x) + 3exp(x)Cos2x On this page , I've solve particular integral by 2 ways, 1st is above the line in which ( see 7th equality from...

Could the numerical value of the Gravitational Constant G have a quantum basis? G=(2pi x h-bar) + h/137

We have that ##\Delta G = -RT\ln K##. This is in my lecture notes. However, it does not specify whether ##K## is ##K_c## or ##K_p##. Fair enough, I assumed that it could be both. However, when writing out the definitions of ##K_p## and ##K_c##, and using the fact that ##P=CRT##, where ##C## is...

We define ##dA=dU+P_0dV-T_0dS \leq 0##. In my notes it says if you fix pressure and entropy, ##dA=dH##. I don't get this, because at constant T and S, I get ##dA=dU+P_0V##. It seems that somehow, ##P_0=P##. Is this correct, or am I missing something? Second question about this: If ##T_0=T##...

I have an issue with (b). What I did was simply integrate ##dS##. It's a perfect gas, so, $$\left(\frac{\partial E}{\partial T}\right)_V=NC_V$$ and $$\left(\frac{\partial E}{\partial V}\right)_T=0$$ Next I used the relation that ##PV=NkT## to get ##\frac{P}{T}=\frac{Nk}{T}##, and after...

x=x0=vt v=v0+at x=x0+v0t+(1/2)at2 That (1/2) there does not make sense to me. It makes sense mathematically, if you integrate the velocity formula you get the (1/2) as a result of the integration rules and if you differentiate its needed to cancel out the 2 and arrive at the velocity...

What does it mean to say that Planck's constant is an energy oscillator composed of imaginary and real numbers? This is an expression I saw in a book.

So I know that since ##x \in R## that means ##2x## can achieve all possible values on the real number line meaning ##f(x)## is a constant function. And I know hwo to calculate the limit beyond that. However my teacher made a point which I dont necessarily agree with he said, if ##f(x)## wasn't...

We know that ##\pi## originates from the L/D relationship of a circumference, where "L" represents the perimeter of a circumference and "D" represents its diameter. The size of a circumference does not matter, as both the perimeter and the diameter of any circumferecence always maintain the same...

If I’m not mistaken, the synchronization of 2 clocks to conduct a measurement of the one-way speed of light is not possible since simultaneity is not possible and 2 clocks even if they are synchronized in a midpoint and slowly moved to opposite ends, depends on c being the same in all...

If the gravitational constant had a different value, say a lower value than the present value, and since the gravitational constant is a part of Planck dimensions, such as Planck mass, Planck length, etc., how would quantum and classical processes be affected? Are there problems which use the...

I understand based on the equation F = ma that if there is no acceleration, the forces on the object all balance out to 0 in all directions. What I don't get is for example, slowly lowering a heavy stone slab at a constant velocity v, and raising it way above my head as high as I can at a...

For this problem, I can confused why they don't include the case where ##b = 0## since ##b < 0##. That is, why don't they include ## λ^2e^{λt} + e^{λt} = 0## when solving the associated homogenous equation? This gives the commentary solution ##u_h = \cos t + \sin t## which is not included in...

I expanded ET1=ET2 to get (Total energy at top) 1/2mv^2+mgh = 1/2kx^2 (Total energy at bottom) Rearanged i got k = (mv^2+2mgh)/x^2 so [(73)(20)^2+2(73)(9.8)(52)]/0.465^2 =479137.945N/m

I'm reading "Problem Book In Relativity and Gravitation". In this book there is a problem 7.5 Show that metric tensor is covariant constant. To prove it, authors suggest to use formulae for covariant derivative: Aαβ;γ=Aαβ,γ−AσαΓβγσ−AσβΓαγσ after that they write this formulae for tensor g and...

I'm leaning towards the same, or maybe increase. I actually have no clue.

$$F=kx$$ $$k=\frac F x= \frac {50+50~N} {5+5~ cm}= \frac {100~N} {10~cm}= 10~N/{cm}$$ However, the answer is ##5~N/cm##, because the force on the spring is ##50~N##. I am having trouble understanding why the force isn't ##50~N## + ##50~N##. The diagram looks as though the spring is experiencing...

This is the question. To this point everything is clear. I have problem with following part: The authors claim that each part of the remaining rope is under constant acceleration. So it is in free fall and only gravitional force acts on it. If we release a rope like above, before it hits the...

Please confirm or deny the correctness of my understanding about this definition. For a given set of ##t_i##s, the matrix ##(B(t_i,t_j))^k_{i,j=1}## is a constant ##k\times k## matrix, whose entries are given by ##B(t_i,t_j)## for each ##i## and ##j##. The the 'finite' in the last line of the...

For A the 1.2 kg block is being pulled by gravity hence work is done downwards which will make work positive since it's going with the same direction as the force. 1.2 * 9.8 = 11.76 N pulled downwards Work = F*d 11.76*0.75 = 8.82 J The tension is the other force and since the thing is...

All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll) Help is appreciated Edit. Is vector r describing the curvature that takes place ?

In my physics lab we determined the spring constant of a steel spring. This turned out to be 20 N/m. However, when I search online, I can't see any uses of springs - I know springs can be used everywhere, but nobody seems to specify their spring constant. Anyone know of any applications?

^^

In the first part, I'm asking about acceleration of freefalling objects with different masses. In the second part I'm asking about acceleration of one object with decreasing distance. Please explain where am I getting it wrong. Thank You!

Can the energy of a gravitational wave be related to Plancks constant?

To be honest, thermodynamics is really not my strong suit and I get confused when and how to apply formulas. My thought process is as follows: - there are two ideal gases (ideal gas law applies) - the pressure remains constant (isobaric process), so p1= p2 = p - I imagine there being two...

Scolnic et al have put out a new preprint with an updated value for the Hubble constant as measured from the Tip of the Red Giant Branch: https://arxiv.org/abs/2304.06693

There is some discussion currently and I was hoping to get some opinions here. The question is in regard to a Hook's law problem. The text gives the problem as seen below. The text says the answer is 50lb/in. Several people have tried from several different approaches. Factoring the "y" equation...

im learning thermodynamics and currently in a lesson about thermal processes. one process has constant pressure and before diving into equations or any proof the book provides a figure of a gas cylinder. the cylinder has a movable piston/lid on one side. the book then says "...and the piston end...

In 1916, Karl Schwarzschild was the first person to present a solution to Einstein's field equations. I am using a form of his equation that is presented in Tensors, Relativity and Cosmology by Mirjana Dalarsson and Nils Dalarsson (Chapter 19, p.205). I am approaching what may be the simplest...

I am trying to find Planck's constant using Excel given the data: Frequency [Hz] Photon Energy [J] 7.5E+14 4.90E-19 6.7E+14 4.50E-19 6E+14 4.00E-19 5.5E+14 3.60E-19 5E+14 3.30E-19 4.6E+14 3.00E-19 4.3E+14 2.80E-19 4E+14 2.65E-19 3.75E+14 2.50E-19 I am using Linear...

An insulated container (constant volume, adiabatic) contains an Ideal gas with pressure P1 and temperature T1. We open the container's hatch for a few seconds and let some particles escape from the container, then we close the hatch again. We know container's pressure has reduced by exiting...

The 7/8" Kinetic Recovery Rope like this yankum rope is the most common size used for Jeeps, Broncos, and other SUVs. I apologize for English units but that's how ropes are sold and marketed. I've talked to the biggest rope suppliers and they have no idea how to compute the rope's spring...

For this problem, Did they get ## x## approaches one is equivalent to ##t## approaches zero because ##t ∝ (x)^{1/3} + 1##? Many thanks!

If the speed of light in the vacuum of empty space is the same for all observers, how can there be a Doppler effect on light? Doesn't the shift of color/frequency indicate a change in speed? Sorry if I posted with the wrong prefix, I'm just a curious senior (as in old guy) :oldconfused:

I am sorry but I can't seem to find the actual estimated value of the cosmological constant that is predicted by quantum field theory. Can anyone help me and tell me the approximation of that value and/or the value of the approximate observed cosmological constant that physicists today think...

The answer given for part (c) in the back is that temperature doesn't change as the gas in cylinder A expands to fill cylinder B. The thermodynamic system here is composed of the two cylinders A and B joined by some pipe. But, I cannot find a satisfactory explanation for temperature...

Power P = F x v,where F is force and v is velocity, if power remains constant then i think force can not remain constant as it will change the velocity v, but the solution I found is, F = ma, v = at, so, P = F x v = ma x at = ma2 t, after that calculus comes to show that displacement is...

Hi, First of all, sorry if this is not the right place to post my question I was not sure where exactly to post this kind of question. I'm wondering how can I find the value of a constant experimentally. For instance, I have a equation ##l = AB^{4/3}##, with a set of data for ##I## and ##B##...

I got to the quadratic equation of the motion where: 4gt^(2) - g(delta t)t - g(delta t) = 0 and tried to solve for t. In this case, we would take the positive discriminate since we are dealing with the passing of time. t = ((sqrt(17) g(delta t)) + g (delta t)) / (8g) However, this is the...

Given the definition of whole numbers as integers, https://www.google.com/search?q=what+is+a+whole+number&rlz=1C1VDKB_en-GB&oq=what+is+a+whole+number&aqs=chrome..69i57j0i512l9.11619j0j15&sourceid=chrome&ie=UTF-8 Is it known why atom vibrations are only at whole numbers ( ref plank’s constant)...

Kinetic energy before collision =1/2 mv² + 1/2 mv² = mv² (since energy is a scalar quantity, the direction does not matter). Kindly tell why am I not getting the required answer i.e: 1/2 mv². Am I doing the calculation wrong?

I once read (though I don’t remember where) that in the same way that you talk about a dimensionless ratio between Y and X in ordinary space, you can conceive of c as a dimensionless ratio between T and X in spacetime. Do you know where I can find a reliable treatment of that idea? As...

I mean, what's "general relativity but without the cosmological constant term" (##G_{\mu \nu}=\kappa T_{\mu \nu}##) called?

I am not understanding the 2nd part of the question where it is asked about how many revolutions will the blade make when it reaches full speed. Please help

I take a wire of metal X which has a diameter d. Let the total length of it be L and I roll it around a cylinder with diameter D to create a spring. Is it possible to predict the spring constant of this system (and relate it to the elastic constants of the metal)? Has anybody seen/heard/know a...

A diatomic molecule ##D_{2}## in ##30K##, in ##t=0##, is in the state ##| \psi (0) \rangle = \frac{1}{\sqrt{26}}(3 | 1,1 \rangle + 4| 7,3 \rangle + | 7,1 \rangle )##, where the kets denote states ##| l,m \rangle##. Use ##\frac{\hbar}{Ic4\pi}=30.4cm^{-1}##. Obtain ##| \psi (t) \rangle ## I...

SO2(g)+1/2O2(g)⇌SO3(g);ΔHo=-98.32KJ/mole,ΔSo=-95J/(mole-K). find Kp at 298 Kelvin? In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol. Then Keq will be calculated using equation = Δ G = -RT ln Keq...

I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.