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

learn more… | top users | synonyms

-2
votes
0answers
41 views

Speed of light and relativity [on hold]

I have been thinking about the speed of light and relativity and I have a question I would like to get an answer to. If two vehicles are side by side and they start moving forward at 100 mph and ...
1
vote
0answers
43 views

Physical or geometric meaning of the trace of a matrix

The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too. Is there ...
6
votes
0answers
62 views

Examples of useful, insightful and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
-4
votes
0answers
22 views

physics question [on hold]

A car travels 11.5 km west at a speed of 40 km/h, then travels 15.6 km south at a speed of 50 km/h and finally travels 19.1 km east at a speed of 45 km/h. What is the magnitude of the average velocity ...
0
votes
1answer
36 views

Interchange of derivatives

Given Euler-Lagrangian equation $$\frac{d}{dt}\frac{\partial L}{\partial \dot q}-\frac{\partial L}{\partial q}=0$$ Can I equivalently write as $$\frac{\partial \dot L}{\partial \dot q}-\frac{\partial ...
1
vote
2answers
38 views

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of … [on hold]

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of 10 km / 6 miles per hour in 7 seconds. I found the following: http://en.wikipedia.org/wiki/Thrust-to-weight_ratio ...
0
votes
3answers
44 views

Work done to fill up a spherical tank

A spherical tank of radius $12$ feet is $40$ feet above the ground. How much work is done in pumping water into the tank until it is full? I obtained $$ w= \int_{16}^{40}[12^2-(40-y)^2y] \, dy. ...
3
votes
1answer
19 views

mechanics piston problem involving rotational motion.

The above figure shows a piston driving a crank OP pivoted at the end $O$. The piston slides in a straight cylinder and the crank is made to rotate with constant angular velocity $ \omega $. Find ...
1
vote
3answers
55 views

Geometric Algebra/ Calculus for Physics

I don't know if this would be a better question for physics.SE, but I'll try here first: There is at least one good book on classical mechanics using the geometric algebra/ calculus (GA): New ...
0
votes
2answers
84 views

How did they solve for a here?

Consider the following algebraic steps: $$ F - (M_1 a + \mu_k M_1 g) - \mu_k M_2 g = M_2 a $$ $$ F - \mu_k M_1 g - \mu_k M_2 g = (M_1 + M_2) a $$ $$ a = \frac{F - \mu_k M_1 g - \mu_k M_2 g}{(M_1 + ...
1
vote
0answers
29 views

Solving 2 equations (Projectile motion)

The question is from Physics, but all I need is help on solving maths. So basically, i am trying to find out the optimal angle for projectile motion from a certain height and I end up with these two ...
0
votes
0answers
17 views

How to describe the motion of a mass point?

Consider a mass point moving around a fixed point on a circle with radius $r$ with constant angular velocity $ω$. At a certain moment of time, the connection is removed, and the point mass is flying ...
1
vote
2answers
52 views

How to find $\theta$ at which $d$ is the maximum possible?

I have an equation: $$d=\dfrac{v\cos \theta}{g}\left(v \sin \theta + \sqrt{v^{2} \sin^{2}\theta + 2gh} \right),\ g≈9.81 \dfrac {m}{s^{2}}$$ How to find $\theta$ at which $d$ is the maximum possible? ...
6
votes
1answer
75 views

Dirac Gamma matrix identity

In my library's (old -- 1996) copy of Peskin and Schroeder, there's an identity I'm struggling to prove. In my copy it occurs on page 42, between equations 3.28 and 3.29, but I don't know how well ...
0
votes
1answer
34 views

How do I calculate the centripetal force?

In this experiment, a brown rubber weighs 42.2 grams and was spun at a velocity of 4.66m/s with a radius of 40cm and masses of 200g...the answer should be about 1.96N and I got 2.3. Can someone ...
0
votes
1answer
12 views

$\int_C (\alpha x, -\alpha y) . dr = 0$ where C is the unit circle

Circulation is given by $$\int_C u . dr$$ I want to show that the circulation around the unit circle is $0$ for $u = (\alpha x, \alpha y)$. Ie. $$\int_C (\alpha x, -\alpha y) . dr = 0$$ How would ...
3
votes
2answers
114 views

Is “mixed math” a useful way to learn math?

I was reading a book about how mathematics was taught in Cambridge in the 19th century, and it struck me how much physics was included in the syllabus, and it wasn't optional but everyone had to learn ...
0
votes
1answer
26 views

Work required to pump water out of tank in the shape of a paraboloid of revolution

This is the problem I have been assigned: A water tank has the shape of a paraboloid of revolution: its shape is obtained by rotating the parabola $y=x^2/4$, for $0\le x\le 4$, around the ...
0
votes
0answers
31 views

intersecting point of two lines

The circle has R radius and and ellipse is intersecting the circle. I need to findout $x_c$ and $y_c$, which is the midpoint of the 2 intersected point of ellipse.Line 3 is the tangent of the ...
3
votes
1answer
42 views

A formal justification for this “physicism”?

I gave a presentation for a seminar class yesterday on Fourier analysis, and introduced the sawtooth function as a counterexample, for a function whose Fourier series is not termwise differentiable. ...
0
votes
1answer
39 views

Tough second order differential equation2

I have asked similar question before but it turns out that the $E_0$ depends on (r,z). It makes the solution complicated. Any comments appreciated. ...
0
votes
0answers
8 views

Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations

My instructor asked me to prove that the real and imaginary parts of the electric susceptibility derived from Lorentz Model satisfy the Kramers-Kronig relations using the residue theorem. The problem ...
1
vote
0answers
9 views

Potentials and Markov Processes

Given a resistive electrical circuit $G$, i.e. a graph with nonzero weights attached to each edge whose reciprocal we call the "resistance," we can define a reversible markov chain on the graph, ...
0
votes
3answers
49 views

$\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $

Show (in cartesian coordinates) that $\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $ I am not really sure how to calculate this. Do I just assume ...
1
vote
0answers
27 views

Ode with Piecewise function

We can write this $$12x"+36x'+48x=f(t)$$ my main problem is how to solve this non-homogeneous ODE I know how to do this as 2 different ode unfortunately its not in a syllabus which doesn't use ...
1
vote
1answer
28 views

Heat equation fundamental solution

The following is from a book of PDEs and I have cannot seem to figure out a particular step in it with regard to the derivation of the fundamental solution of the heat equation. I have highlighted it ...
0
votes
0answers
7 views

Converting a boolean expression into CNF and DNF

Is there any systematic way to convert the following boolean expression (QUBO) into CNF or DNF? Here, $x_1, \ldots, x_n \in \{0, 1\}$, $a_1, \ldots, a_n \in \mathbb{Z}$ and $b_{1,1}, \ldots, b_{n,n} ...
0
votes
0answers
64 views

All $f(x)$ on $[0,1]$ such that center of mass of the function (uniform density) is on its graph

So, as the title describes, I'm trying to find a way to express all $y=f(x)$ differentiable on $[0,1]$ such that the center of mass of the function, assuming it has uniform density, will be a point on ...
0
votes
1answer
15 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
1
vote
1answer
35 views

Equations of Motion of a Satellite

I'm working on a control problem where I need to know the equations of motion for a satellite orbiting the earth about a central axis. Using Newton's second law, I was able to show that ...
1
vote
1answer
36 views

Calculation of a spread light on a surface

Suppose we have a light of power $P$ distributed on a plane $(x,y)$. The distribution of the power is of the form: $$P=f(x,y)$$ If we have a lens conjugating every point of the plane $(x,y)$ in ...
2
votes
1answer
73 views

Solve $\int_0^T f(t) dt =1$ for T.

I have to solve this equation for a physics problem and I don't know where to start: $$\int_0^T f(t) dt =1 \quad\text{and}\quad f(T)=C$$ Where $T>0$, $C>0$ and $f(t)>0$ we can suppose that ...
1
vote
0answers
31 views

Computing the Initial Velocity of an orbiting body [migrated]

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...
0
votes
0answers
15 views

Approximation for uniform load on parabolic cable along its arc length

I am doing analysis for cable structures. Let's say that the cable stretches from point A to point B and carries a vertical ...
2
votes
2answers
44 views

Is it possible to build a fiber bundle whose fibers are different? (Or we should not call it a fiber bundle?)

Suppose there is a fiber bundle $E$. The base space is $M$ so that $\pi:E\rightarrow M$ is the projection. By the definition, the bundle has a typical fiber $F$ such that the local trivialization over ...
6
votes
1answer
37 views

Is there always an equilibrium point in a field?

For instance, considering a set of planets represented as point masses that create a gravitational field, will there always, no matter what set of points, be a place where I can stand with no net ...
1
vote
1answer
46 views

Derivation of Simple Projectile Motion with Drag

Given the initial velocity $v_0$ and angle $\theta$ of a projectile on the ground, using Newton's second law and the acceleration due to gravity $\mathbf g=\left\langle0,-g\right\rangle$, I was able ...
1
vote
0answers
46 views

Calculating Hydrodynamic Interaction Tensor

I'm a bit of a newbie when it comes to Tensor calculus. Please excuse me as I learn... Given the Oseen tensor, $\mathbf{T}(\mathbf{R}) = (8\pi \eta R)^{-1} \left[ \mathbf{I} + ...
0
votes
0answers
35 views

Calculating force per unit width

Question: A line source of strength $2πm$ is located a distance $a$ above a horizontal plate. Find the force per unit width on the plate, ignoring gravity and taking the pressure below the plate to be ...
3
votes
0answers
39 views

Kinematics of gravity in a non uniform field

I am a first year physics student. I am trying to figure out how to compute position in terms of time for an object falling through non uniform gravity towards the earth, and by extension towards any ...
0
votes
0answers
8 views

How to solve a factorized Helmholtz equation?

I am reading a paper on optics an in appendix A2 they split the Helmholtz equation into two parts and write down the solution for one of those parts (link). Helmholtz Equation where the Laplacian is ...
0
votes
1answer
40 views

Inverse of a 3x3 matrix error!

I have this 3x3 matrix $$E_{ij} = g_{ij} + \bar{\epsilon}_{ijk}z^k$$ and want to derive its inverse. I know that its inverse is given by $$(E^{-1})^{ij} = \frac{1}{1+z^2}(g^{ij} + z^{ij} - ...
0
votes
0answers
14 views

What is the difference between initial launch velocity and launch velocity

Are they mathematically the same? If I have initial launch velocity, can I calculate time of flight and other projectile anomalies?
0
votes
0answers
19 views

Is my maths correct about Projectile Motion?

The initial launch velocity of a projectile is determined using R = 2$u^2$ / g. From this, can we calculate maximum height and time of flight if we know the initial launch velocity derived? I ask ...
2
votes
1answer
40 views

Charge distribution on an arbitrarily shaped conductor

From physics we know that given a charged conductor put in vacuum (no external electric fields), the charge distribution on its surface is approximately proportional to the curvature of the surface on ...
0
votes
0answers
21 views

Physical interpretation of the integral formula for the solution of Laplace equation with Dirichlet/Neumann boundary condition

Suppose we have a bounded domain $D$ with smooth boundary, with $G(x,y)$ being the Green's function for the Poisson equation on $D$, i.e. $G(x,\cdot)=0$ on $\partial D$ and $\Delta_y ...
4
votes
1answer
56 views

What are the equations modelling a vertical spring system with two masses?

Modeling a vertical spring system with one mass is a pretty common problem. I looked around online and found some horizontal spring systems with two masses, but no examples of a vertical one. I'm ...
0
votes
0answers
11 views

Calculate ratio of volumes in mixture with given ratio of masses

I have two components of a mixture: $a$ and $b$. I know that using $3.5 \text{ kg}$ of component $a$ and $0.5 \text{ kg}$ of component $b$ will give a proper mixture, and its density will equal $1.45 ...
0
votes
0answers
35 views

Why does this graph produce a straight line? [duplicate]

When we graph the sin and cos of theta against the range of a projectile, we get a straight line. When we graph range against angle, we get a hyperbola. Why does the sin and cos of theta against ...
-1
votes
2answers
33 views

Is launch speed of a projectile maximum at 45 degrees? [closed]

I hear that range is maximum at 45 degrees, would that mean launch speed (velocity) is too?