Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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Does 'variance' have a physical meaning?

Let's say we have some probability density function $f(x)$, we can find the mean by solving $\mu = \int_{-\infty}^{\infty}xf(x)dx$. In a similar way, we can find the center of mass of an infinite wire ...
2
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2answers
63 views

Volume integral of electric field (hemisphere solid)

Let $S$ be a hemisphere of radius $R$, and let $\sigma$ be the constant charge density at each point $(x',y',z')$ in $S$. The electric field generated by the hemisphere is a vector function: ...
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65 views

Charge distribution in a conducting sphere

This is a math problem that appeared in a physics one: "Evaluate the density of electrical charge in the surface of a hollow sphere such that the electric field is constant (in direction and absolute ...
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0answers
44 views

Find the magnitude, angle of acceleration and the angle of a particle's direction of travel

So I'm doing a Physics problem and have run into a snag with the online homework - every answer I've tried keeps getting rejected and I'm down to my last shot and I don't know what I'm doing wrong. ...
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1answer
34 views

how do you find position vector?

So at time zero a particle is at x= 4 m and y= 3 m and has a velocity of $${ v= \left( 2.0 \ \boldsymbol{\hat{\imath}}-9.0 \ \boldsymbol{\hat{\jmath}} \right) \text{m/s}}$$ The acceleration of the ...
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2answers
42 views

Help in Differential Equations - find velocity at t seconds…

Hello Everyone I am stuck where I am , Would like to know if I'm going the write path, and any hints on how to proceed would be greatly appreciated !! Question: A boat carrying 7 people is being ...
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1answer
48 views

Harmonic Oscillation using Gaussian Quadrature [closed]

Assume that the potential is symmetric with respect to zero and the system has amplitude $a$ suppose that the potential $V(x)=x^4$ and the mass of the particle is $m=1.$ Write a java function that ...
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1answer
35 views

Where should the fire man place the hose for the water to reach its maximum height?

Water leaves a fireman’s hose (held near the ground) with an initial velocity ${v_0 = 22.5 m/s}$ at an angle θ = 35° above horizontal. Assume the water acts as a projectile that moves without air ...
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1answer
22 views

Compute the specific heat capacity of ideal gas under constant $V$ and $p$

Compute the specific heat capacities at constant volume and constant pressure for air at standard temperature and pressure, assuming it is diatomic ideal gas and a molecular mass of 28u. I have ...
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1answer
56 views

Water leaking from box and the relationship of volume and height.

Suppose we have a container that has a base of area $b$ and we fill it up with water. Volume of water = $b \cdot h$, where $h$ is height. Hence, $\mathrm{d}v/\mathrm{d}t = b \cdot ...
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1answer
15 views

How do you calculate a percent of precision?

What does it mean when "calculating a percent of precision can be found from the ratio of your mass sensitivity to the equilibrant mass for each case." My ratio of sensitivity is .010 kg. My ...
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1answer
33 views

Problem Analysis - Answer but no procedure - Differential Eq.

I stumbled with this problem in a notebook that has been bothering me...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you know how to analyse the ...
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1answer
209 views

Derivation of the Boltzmann factor in statistical mechanics

I have seen similar derivation of the Boltzmann factor many times before, (http://micro.stanford.edu/~caiwei/me334/Chap8_Canonical_Ensemble_v04.pdf , just for example), which I think is incomplete. ...
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1answer
28 views

what is the position and acceleration at the instant when its velocity is zero?

The position of an object is given by $${x(t)= 2.17+4.80t^2-0.100t^6}$$ Would I have to take the derivative of that in order to find velocity? But from there how would I find the position and ...
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2answers
22 views

How much is does it take for the stone to reach the bottom?

So a stone is thrown vertically upward with a speed of 10.0 m/s from the edge of a cliff 65.0 m high. So, just making sure I have all my variables right Vinitial: 10 m/s V: 0 m/s g: -9.8 m/s^2 ...
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1answer
21 views

How do I correctly introduce a time parameter into this equation?

So, for the past few years it's been my goal to create an equation that would give me the position of an object in a gravitational field at time $t$, given it's initial position and velocity. At first ...
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1answer
38 views

Differential Equation Concerning Torricelli'$s^2$ Principle

We have $v = \sqrt{2gh}$ where $g$ is acceleration due to gravity and $h$ is height. By equating the rate of outflow to the rate of change of liquid in the tank, show that $h(t)$ satisfies the ...
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2answers
101 views

Moment of inertia of semi circular disc with hole

Suppose we have semi circular disc of radius $R$ with semi circular hole of radius $R/2$ , how can I find moment of inertia from axis thru $H$ I fail to see any symmetry so I cannot integrate , ...
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2answers
37 views

Angle at which a body bounces off a sphere

Suppose a solid body approaches a sphere of radius $R = 1$ and height $z$, how do I calculate the angle $\theta$ at which the body bounces off the sphere? I am writing a java code where the ...
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1answer
28 views

Solving for $T$ in this Algebra problem

I'm taking Physics E&M and I'm trying to solve the following equation for $T$. I feel like the algebra I'm doing is correct but I cannot get the solution in the book which is $53.1 $C ...
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0answers
41 views

How do you take divergence of this field?

I forgot how to do divergences 3 years ago, this one is very confusing. We used to take them with respect to $x,y,z$ but this one doesn't have them. Help me with this question Prove that $∇.E = 0$ ...
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1answer
23 views

Relation between Diffusion equation and 1st order linear ODE

I'm studying PDE with a book written by Walter A Strauss. In sec 3.3, we tried to guess what is the solution of diffusion equation with a source. In analogy, they brought 1st order linear ODE ...
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2answers
108 views

How do I deal with reflections inside an ellipse?

Suppose I have an ellipse with foci $F_1$ and $F_2$. How do I show that any ray of light which intersects the segment connecting the foci will have subsequent reflections that always are tangent to ...
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1answer
42 views

Help deriving third order gaussian optics formula.

We are given: $$\frac{n_1}{l_0}+\frac{n_2}{l_i}=\frac{1}{R}(\frac{n_2s_i}{l_i}-\frac{n_1s_0}{l_0})$$ $$l_0=\sqrt{R^2+(s_0+R)^2-2R(s_0+R)cos(\phi)}$$ $$l_i=\sqrt{R^2+(s_i-R)^2+2R(s_i-R)cos(\phi)}$$ ...
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42 views

Vector Laplace equation with constraint

I want to solve Laplace equation for a vector $\boldsymbol v=(v_x,v_y)$: $$\nabla^2 \boldsymbol{v}=0$$ but under the constraint that $$(1+v_x)^2+v_y^2=1$$ which becomes $v_y = -(2v_x+v_x^2)^{1/2}$. ...
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0answers
28 views

Calculus Problems - Analysis [closed]

Thank you for your time! I have come across 3 problems I can't put together but I would like to understand. (The book has the solution, but not the actual step of how to get the solution...hence me ...
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2answers
90 views

Why does randomness exhibit a pattern in the long run?

!!! Layman here so please avoid complex math and answers. Random (usually pseudorandom) events are usually characterized along these lines: Each outcome in a trial experiment must be i.i.d.; i.e. ...
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1answer
15 views

Calculate the value of the error (only) with two decimal places for: (5.1 +/- 0.4) / (2.5 +/- 0.2)

Calculate the value of the error (only) with two decimal places for: Z = (5.1 +/- 0.4) / (2.5 +/- 0.2). I tried finding $Z_{max}$ = 5.1(1+0.078)/(2.5(1-0.08)) which gives 2.04 + 0.335 and I ...
2
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0answers
18 views

Matrix index notation confusion in physics

$\newcommand{\diag}{\operatorname{diag}}$I'm confused about converting between explicit matrix expressions and index notation. Take $\eta_{\mu\nu}=\diag(-1,1,1,1)$ and $A$ some $4\times4$ matrix. For ...
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1answer
33 views

Determining a matrix representation

Determine a $2\times 2$ matrix $\mathbb{S}$ that can be used to transform a column vector representing a photon polarization state using the linear polarization vectors $|x\rangle$ and $|y\rangle$ ...
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30 views

Why use class multiplication in Homotopy groups?

This is a related to a physics question Why use class multiplication to describe topological entangling and merging?. In physics, the homotopy theory is used to describing topological defects in order ...
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2answers
74 views

Physics: Help me understand this vector problem?

So I'm doing Physics homework - and I already have a rather crappy understanding of vectors, this problem just frustrates me because I have literally 0 idea of what to do with the information it gives ...
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1answer
26 views

Find the speed required for a boat to “catch” a key dropped from a bridge.

So I'm doing a simple Physics homework problem, and I'm honestly unsure if I'm using the proper formulas for each step. The problem is as follows: A key falls from a bridge that is 47 m above the ...
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3answers
149 views

Projection operator is Hermitian

Use Dirac notation (the properties of kets, bras and inner products) directly to establish that the projection operator $\mathbb{\hat P}_+$ is Hermitian. Use the fact that $\mathbb{\hat ...
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34 views

Intercept planet following an elliptical path (i.e. interplanetary space travel)

So, just as in this question (Intercept path to object following an elliptical path) I have a simple game where I want spaceships to intercept planets, which follow elliptical paths (in my case ...
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17 views

Express Kirchoff's first law using power flow.

If we just know the power flow in and out of a junction node, can we say that $\sum\limits_{p: e\in p, i\in e^-} f_p = \sum\limits_{q:e\in p, i\in e^+} f_q, \forall i$, where $f_p$ is the power flow ...
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0answers
36 views

Convert position and velocity vector to TLE for propagation

I have a set of position and velocity vector for a satellite at time t0. I want to propagate position and velocity of the satellite at time t (t>t0) I converted these vectors to Keplerian Elements ...
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0answers
30 views

What is the root structure of the Diffeomorphism Group?

Being a physicist, I think it'd be cool to have Coxeter plane projections of the root systems of the symmetry groups associated with the fundamental forces hanging on my walls (example for E8: ...
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1answer
115 views

Calculate how long a ball will be in the air after being thrown

So I'm doing some online homework, and have done this specific problem 3 different times and gotten the same answer, but the answer I get seems to be wrong? The problem is as follows: (a) With ...
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0answers
32 views

Stiffnes tensor, Hooke's law

Let's have a deformed body of an isotropic homogenous material. How is it possible that we can write the free energy in the form $$F=F_0+\frac12\lambda\left(\sum_i ...
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1answer
110 views

Differentiating position with respect to 'modified time'

I've been reading a book on orbit determination, and I've hit a block with the calculus. Why do this? He defines tau, called modified time, as follows: $\tau \equiv k(t - t_0)$ Where $k$ is the ...
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1answer
31 views

Effective Acceleration for Non-Constant Acceleration Motion

This question uses the same symbols as "Effective Acceleration" is Distance-Averaged Acceleration?. One of the kinematics formulas for constant acceleration is: $\Delta x=v_0*\Delta ...
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1answer
129 views

Finding $\mathbf{10}\otimes \mathbf{8}\otimes \mathbf{8}\otimes \mathbf{8}$ in $SU(3)$

I know that in $SU(3)$ $$\mathbf{8}\otimes \mathbf{8} = \mathbf{27}+\mathbf{10}+\mathbf{\bar{10}}+\mathbf{8}+\mathbf{8}+\mathbf{1}. $$ How can one use this to compute $$\mathbf{10}\otimes ...
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2answers
86 views

Significance and physical meaning of diagonalization of linear maps and bilinear forms, eigenvalues and eigenvectors

In linear algebra, I have studied the diagonalization of a linear map and of a bilinear form; and also the concepts of eigenvalues and eigenvectors. However, the importance of diagonalizing a linear ...
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1answer
33 views

Second order differential equation, physics.

I need your input on this exercise I'm doing: "A 2-kg mass is suspended from a string. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 50 cm. If the mass ...
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1answer
79 views

“Effective Acceleration” is Distance-Averaged Acceleration?

My question involves simple math, but to be precise on what I'm asking, I need to write a lengthy description. Let us define the following symbols: $t$: time $x(t)$: distance as a function of time ...
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0answers
19 views

Issues Calculating Average Acceleration?

So I'm doing a Physics problem here and I'm down to my last answer and I honestly can't figure out where I'm going wrong. The problem is as follows: From t = 0 to t = 4.22 min, a man stands ...
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2answers
53 views

What are the degrees of freedom of $F=ma$ and $F =mdv/dt$? [closed]

I read in http://en.wikipedia.org/wiki/Degrees_of_freedom, the definition of "degree of freedom" for equations. However, I am consfused about what is the degree of freedom of the two known physical ...
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1answer
30 views

How can I take the derivative of $Q=C \cdot \Delta T$

How can I take the derivative of $$Q=C \cdot \Delta T$$ with respect to time $t$? note: $C$ is heat capacity and $T$ is temperature
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1answer
25 views

Shifting Velocity and Position functions

I'm given a function $A(t)$ that defines the acceleration of an object w.r.t. time $t$ and am tasked with finding the position function and velocity function for that object. Finding the functions ...