What are the dimensions of kilo Watt hours? Is is M L2T-2?? If yes, why is that? If no, please teach me about what the right dimensions are and please be kind enough to provide a good explanation. Thank you in advance.
P.S. I am wondering why it doesn't have the dimensions ML2T-3...
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I need help with the following question:
Please have a look at the question and my attempt at the solution.
Alternative cooling systems are considered for a large computing centre requiring 1 MW of cooling...
Homework Statement
The mean field solution for the Ising model is:
$$m = tanh[\beta (mJz + H)]$$
I wanted to carry out a dimensional analysis in order to verify the equation.
Homework Equations
$$m = tanh[\beta (mJz + H)]$$
The Attempt at a Solution
Knowing that:
$$[m] = \frac{A}{L}$$...
Homework Statement
The evolution of the density in a system of attractive spheres can be described by the following dynamic equation.
$$\frac{\partial}{\partial t} \rho (r,t) = D_o [\nabla^2 \rho (r,t) + \beta \nabla \rho (r,t) \int dr' [\nabla V (|r-r'|)] \rho (r',t) g(r,r',t)]$$
a)...
The concept of naturalness as dimensionless ratios of parameters of order unity has recently come under criticism, most obviously because Sabine Hossenfelder wrote a book (Lost In Math) criticizing it.
Very recently however, Peter Shor and Lee Smolin had a discussion about this over at Peter...
Homework Statement
Please look at the screenshot.
Homework Equations
dimensional analysis
The Attempt at a Solution
Since the heat capacity is given as 11.3 kJ/(C*g), and energy is measured in Joules (or kJ), I thought to multiply 11.3 by the change in temp (7.3 C) and also 1.50 g of...
Homework Statement
In PSet 3, Prob. 1(e), you determined the thickness h of a thin film of fluid (of viscosity µ and density ρ) flowing down an incline of angle θ, driven by gravity (acceleration g), via a supplied upstream flow rate Q per unit width (i.e., [Q] = (length)2/time).
(a) Using...
It is mentioned in Reif's book, statistical physics, that trough dimensional analysis it can be shown that: $$\frac{1}{\beta} = kT $$ where ##\beta## equals ##\frac{\partial \ln \Omega}{\partial E}## and k is the Boltzmann constant. I don't quite see how to reach this result, can anyone give me...
Homework Statement
The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional...
Homework Statement
You are applying for a ##\$1000## scholarship and your time is worth ##\$10## an hour. If the chance of success is ##1 -(1/x)## from ##x## hours of writing, when should you stop?
Homework Equations
Let ##p(x)=1 -(1/x)## be the rate of success as a function of time, ##x##...
Homework Statement
Homework Equations
The Attempt at a Solution
Dimension of length using h,G,c
[h] = [F r]
##[G] =[ \frac { Fr^2}{m^2} ]
\\ [\frac { hG}c] = [L] ##
So, the answer is option (b).
Is this correct?
Homework Statement
A block of mass ##m = 1.00 kg## is being dragged through some viscous fluid by
an external force ##F = 10.0 N##. The resistive force can be written as ##R = -bv##,
where ##v## is the speed and ##b = 4.00 kg/s## is a phenomenological constant. You
may ignore gravity (we...
Homework Statement
The object is falling vertically in a strange fluid, the magnitude of the air drag is best described by the following FD = bv+cv2 where v is the speed of the object and b and c are constants.
A. What are the dimensions of b and c
B. If the object has mass m find an algebraic...
Our professor introduced us to dimensional analysis and told us that we can use it to predict how some variables are proportional to others, for example:
I have a ball at a certain height and i want to know the time it requires to touch the grond, i can make a guess that it will depend on the...
Homework Statement
There is a paper in 1973:
T. Kushida, "Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials I. Transition Probability Calculation", J. Phys. Soc. Jpn. 1973, 34, 1318-1326. DOI: http://dx.doi.org/10.1143/JPSJ.34.1318
that explains the...
Hi, this problem is bugging me for several days now. In ”200 Puzzling Physics Problems”, Gnadik, Honyek, Riley there is this Problem 59:
The solution to this is an ingenious resort to dimensional analysis, as follows:
Now, I don't have a problem with this. I wonder however, what if we...
From the equation of motion of inflation, $$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + \frac{dV}{d\phi} = 0$$ Example: ##V= \frac{1}{2}m^2\phi^2##
$$\frac{d^2\phi}{dt^2} + 3H\frac{d\phi}{dt} + m^2\phi = 0$$
If I want to make the DE dimensionless then I let ##~t = \frac{1}{H_o} \tilde t~## and...
I've been making my way through Matthew Schwartz's QFT book "Quantum Field Theory and the Standard Model". In chapter 6 he derives the differential cross-section for a ##2\rightarrow n## interaction. As part of the derivation, he introduces the Lorentz invariant phase space measure (LIPS), and...
Pretend that we do not know gravitational law at all, and want to investigate the gravitational law by dimensional analysis:
Let's suppose the gravitational force are proportional to both masses, distance, hence:
F \propto m_1^am_2^br_{12}^c
But obviously, there is no way to equal the...
Homework Statement
ii)Rayleigh method gives me inverse of expected result.Would really appreciate your help.
Homework Equations
show that ##f(gamma)##=##(\frac {ro*R^5} {E*t^2})##
where ro=density
R=radius
E=energy
The Attempt at a Solution
We will do dimensional analysis on the elements...
Homework Statement
The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by
T = 2π ℓ/g
where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show...
Homework Statement
Equation 1: Find the dimensions of a,b
F = at + bt2
F - force
a - Some unkown value
b - Some unkown value
t - time
In this equation we must find the dimensions of a and b which i did but, in the next similar equation
Equation 2: Find the dimensions of a,b,c
F = at + bt2...
this question is about dimensional analysis involving a number with units and a number with no units, if the question is already answered in another post please redirect me if not here is a simple example, for example, :
say i have 2[in]-1. the 1 is dimensionless and the 2 has units of [in]...
Homework Statement
It is found the terminal velocity ut of a spherical particle in a fluid depends upon the diameter d of particle, the dynamic viscosity μ of fluid and the buoyancy weight W of the particle [given by the difference in density between the particle and the fluid (∆ρ) ×...
In my lectures and notes my professor keeps writing out density as lbs/ft3 and unit weight as lbs/ft3. For a material such as concrete it could have a density of 167 lbs/ft3 but a unit weight of 103 lbs/ft3. I am confused as to how these two values are different even though they have the exact...
Hi All,
My question is twofold and follows:
1) Why the dimension of torque is not Joule, as it is Newton times meter?
2) Why the derivative of the velocity with respect to the distance cannot be measured in Hertz?
Thank you all,
Best Regards,
DaTario
As far as I understand, a natural system of units is one in which the numerical values of ##c## and ##\hbar## are unity. However, they still have dimensions, indeed ##[c]=LT^{-1}## and ##[\hbar]=ML^{2}T^{-1}##. How is it the case then, that certain quantities, such as the action ##S##, can be...
Homework Statement
A capillary filled with water is placed in a container filled with a chemical of concentration C_{0} , measured in number of molecules per unit volume. The chemical diffuses into the capillary of water according to the following relation (where x is distance along...