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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2
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0answers
55 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. ...
0
votes
1answer
42 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 ...
2
votes
2answers
43 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 ...
0
votes
1answer
52 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 ...
0
votes
1answer
44 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 ...
0
votes
1answer
27 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 ...
-1
votes
1answer
63 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 ...
0
votes
1answer
18 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 ...
0
votes
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 ...
6
votes
1answer
242 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. ...
0
votes
1answer
34 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 ...
1
vote
2answers
26 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 ...
1
vote
1answer
25 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 ...
0
votes
1answer
41 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 ...
0
votes
2answers
123 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 , ...
0
votes
2answers
50 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 ...
0
votes
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 ...
0
votes
0answers
42 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 $∇.E = 0$ ...
0
votes
1answer
24 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 ...
3
votes
2answers
127 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 ...
0
votes
1answer
42 views

Help deriving third order gaussian optics formula.

We are given: $$\frac{n_1}{l_0}+\frac{n_2}{l_i}=\frac{1}{R}(\frac{n_2s_i}{l_i}-\frac{n_1s_0}{l_0})$$ $$l_0=\sqrt{R^2+(s_0+R)^2-2R(s_0+R)cos(\phi)}$$ $$l_i=\sqrt{R^2+(s_i-R)^2+2R(s_i-R)cos(\phi)}$$ ...
5
votes
0answers
51 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 $v_y = -(2v_x+v_x^2)^{1/2}$. ...
0
votes
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 ...
0
votes
2answers
115 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. ...
0
votes
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
votes
0answers
19 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 ...
0
votes
1answer
35 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 $|y\rangle$ ...
0
votes
0answers
34 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 ...
1
vote
2answers
90 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 ...
1
vote
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 ...
2
votes
3answers
198 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 ...
0
votes
0answers
36 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 ...
0
votes
0answers
21 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 ...
0
votes
0answers
47 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 ...
1
vote
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: ...
0
votes
1answer
178 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 ...
0
votes
0answers
34 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 ...
3
votes
1answer
113 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 ...
0
votes
1answer
33 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 ...
4
votes
1answer
130 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 ...
1
vote
2answers
106 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 ...
0
votes
1answer
36 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 ...
1
vote
1answer
102 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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votes
0answers
22 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 ...
-1
votes
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
0
votes
1answer
29 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 ...
0
votes
0answers
15 views

Trouble converting $m^3$/hr to kg/sec

So I'm doing a physics problem on conversions, and having a bit of trouble with the intermediate steps (since I keep getting the wrong answers. The problem is as follows: Suppose that it takes 18.2 ...
1
vote
1answer
53 views

Characteristic of a ring: intuitive explanation

I know the following definition of characteristic of a ring: it is the smallest positive $n$ such that $$\underbrace{a+\cdots+a}_{n \text{ summands}} = 0$$ for every element a of the ring, if $n$ ...
2
votes
1answer
52 views

Find Distance Function from Acceleration Function

The (non-constant) acceleration as a function of time, $a(t)$, is defined and known over $[t_0, t_2]$. It is also known that $a(t)$ is integrable. Also, $a(t)=\frac{dv(t)}{dt}$ and ...
4
votes
2answers
133 views

Why $F(\mathbf q,\dot{\mathbf q},t)$ and not $F(\mathbf q,t)$?

In beginner classical mechanics, which I've just started learning, a particle with coordinates $\mathbf q\in\mathbb R^n$ has its equation of motion specified by $F(\mathbf q,\dot{\mathbf ...