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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4
votes
1answer
58 views

Show that the profile of the hill is a cycloid

I'm struggling with this problem: From George Simmons_ Differential Equations At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock ...
3
votes
1answer
51 views

Find vector field given curl

I have an equation $\nabla \times \vec{B} = \mu_{0}\vec{J}$, where $\vec{J} = \left\langle f(x,y), g(x,y), 0 \right\rangle$ and need to solve for $\vec{B}$. I've looked elsewhere on here for how to ...
1
vote
3answers
233 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
1
vote
0answers
44 views

How can I calculate the force that is applied on a tube by an another tube?

Let's say there is two tubes (cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $\ell_1$ and $\ell_2$. These tubes are located along the axis of each ...
0
votes
1answer
25 views

The instantaneous value of current, i amp, at t seconds is given by: i = 15 sin(100π.t + 0.6) Find the value of;

Find the value of; amplitude period frequency initial phase angel value of i when t = 2.5s time when current first reaches maximum value Relevant equations $i=A*\sin(ωt+\phi)$ $i = ...
0
votes
1answer
12 views

How to find time it takes for an object to slide on an incline ramp [on hold]

So I hope I am asking this question in the correct spot. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long ...
2
votes
1answer
39 views

When does a particle with given acceleration change the direction of motion?

A particle moves along the x-axis so that its acceleration at any time $t\geq0$ is given by $a(t)=12t-4$. At time $t=1$, the velocity of the particle is $v(1)=7$ and its position is $x(1)=4$. ...
-2
votes
0answers
20 views

Impuls after collision [closed]

I am trying to understand collision and collision response for two spheres. This is my current knowledge background Collision Response The linear momentum is no problem. But I am stuck with the ...
0
votes
2answers
21 views

Finding vertical displacement

I am being asked to find the distance a shuttle travels upward after a given amount of time. I know that time passed is 79s, the rate of acceleration is 6.244 m/s^2, and the speed at 79s is 493.276 ...
0
votes
0answers
35 views

Strange question about magnetic dipole in a plane at infinite distance

Please allow me to ask something rather unusual and perhaps completely naive. Suppose I have an electric current in a circular loop in a plane. Consider it just in a mathematical sense, i.e. an ...
3
votes
1answer
40 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
2
votes
2answers
43 views

Find the work done by the force field in moving the particle from one point to another

Find work done by the force field F in moving the particle from $(-1, 1)$ to $(3, 2)$ This sounds good till we are given that $\textbf{F} = \dfrac{2x}{y}\textbf{ i }- \dfrac{x^2}{y^2}\textbf{ j }$ ...
0
votes
0answers
9 views

Using Parametric Equations To Simulate Motion [closed]

In the diagram, a large number of subatomic particles are simultaneously emitted from a radioactive substance located at the origin. The particles all pass through a vertical slit with the same ...
0
votes
1answer
18 views

Simplifying $\frac1{gt}\sqrt{g/2h}\,dx$ in free fall equations

The relevant equation: $x(t) = \frac12 gt^2$ , $dx/dt = gt$ , $T=\sqrt{2h/g}$ $dt/T = (dx/gt)\sqrt{g/2h} = 1/(2\sqrt{hx}) dx $ I do not see how $(dx/gt)\sqrt{g/2h}$ turns into $1/(2\sqrt{hx}) dx $ ...
1
vote
2answers
48 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
1
vote
1answer
33 views

How do component wavelengths *add* to wavelength of light color?

Say you have 3 leds at frequencies (or wavelengths) $u_1, u_2, u_3$ in Hz (or nm). Then how do you calculate the apparent or center of, or blah frequency (I don't know what I want really) of the ...
0
votes
0answers
29 views

Using significant figures, what would the answer be?

I've been learning about significant figures and I have a few questions. When you multiply/divide, the number of significant figures in the answer should be the same as the term with the least number ...
2
votes
1answer
51 views

Why does a heating model work?

I am referring to: $T=T_0 e^{kt}$ where T=temperature,t=time and k=constant. It seems to work, I as just curios to why it works?
0
votes
1answer
58 views

How to calculate the area of a 4 dimensional curve?

I have been searching on Google about it, and I found that given a sample, 4 points, per example, I could find a function and use integral on it. I am sorry if it sounds silly, I am very dummy in ...
1
vote
1answer
82 views

Quantifier problems of equations in physics [closed]

Equations in physics are often written without quantifiers. For instance, from time to time we can see the equation $$E = mc^2$$ is casually written down. To assert that static energy equals mass ...
0
votes
1answer
44 views

Dirac Delta identity proof.

I was working on showing that: $$x \frac{\mathrm{d}(\delta (x))}{\mathrm{d}x} = -\delta(x)$$ using integration by parts. I arrived to a point where I had had as an answer the following: $$ -f(0) - ...
0
votes
5answers
88 views

Assumptions in Word Problems (Calculus)

I just had a small question about assumptions in mathematical word problems. Suppose you are given a calculus problem (related-rates), "A spherical balloon is inflated with gas at the rate of 800 ...
5
votes
0answers
56 views

Symbolic manipulation inside integral

I'm an undergrad who has just completed the standard calculus sequence (1, 2, and multivariable). I've done well in the courses, however, things like the following, which is a derivation of kinetic ...
0
votes
4answers
43 views

Integration, ball throw simple example

I thought that I could do it like this. Given that $$g=9.8m/s^2$$ $$\int -9.8 \, dt=v_0-9.8 t$$ Setting it equal to zero we have: $$t=\frac{v_0}{9.8}$$ $$\int \left(v_0-9.8 t\right) \, dt=-4.9 ...
0
votes
1answer
31 views

Calculate launch angle of projectile

I'm creating a game and am having trouble designing aiming system for AI. How do I calculate all angles at which the projectile can be launched from point $T_0(x_0,y_0)$ with launch velocity $v_0$ to ...
0
votes
0answers
23 views

Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...
1
vote
1answer
50 views

I need some help understanding the tensor algebra done this problem.

I often see equations rearranged across an equal sign and I have no clue what tricks and reasoning they are using to arrive at these solutions. The only resources I can find on tensor algebra only ...
3
votes
3answers
137 views

Explanation of line element formula $dl^2 = dx^2 + dy^2$

I found this in a physics textbook without justification: $$dl^2 = dx^2 +dy^2,$$ where I presume that $l = \sqrt{x^2+y^2}$. Why is this so? By my calculations I obtain $$ dl = \dfrac{\partial ...
4
votes
1answer
42 views

What exactly are the curves that are a best fit to the Harmonic Cantilever?

Let's start with a few references to get an idea: Daniel Goldwater: Harmonic Cantilever Book Stacking Problem Block-stacking problem Harmonic Series and Bricks Interesting related issues: Maximum ...
37
votes
15answers
6k views

Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need ...
1
vote
1answer
21 views

Setting Up an Integral (depends on displacement vector from a long line)

The following is a physics problem, but I don't actually care about the physics right now. I just want to set up the integral, which I'm having a difficult time doing (the problem is from the book ...
0
votes
1answer
36 views

The motion of the particle satisfies $\textbf{v} = \textbf{c}\times \textbf{r}$

Why is the path is contained in a circle that lies in a plane perpendicular to $\textbf{c}$ with centre on a line through the origin in the direction of $\textbf{c}$
6
votes
1answer
104 views

Why do objects that are farther away look smaller?

What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
1
vote
2answers
47 views

Constants for anti-derivatives

Hey StackExchange I'm diving into integral calculus for the first time and I have a few questions about this problem. A steel ball bearing at rest is accelerated in a magnetic field in a line with ...
1
vote
1answer
18 views

Sound and decibels at distance

If I have an object that is 53 decibels at x distance, how many decibels would y objects be at the same distance x, assuming they all created 53 decibels.
0
votes
2answers
30 views

Calculating velocity of an object moving at 12m/s north, with 5m/s wind from the west

An object moving 12m/s passes north and hits an object. Due to the wind from a west direction, it is pushed sideways at 5m/s. Find the resultant velocity. I don't know where to start with this one, I ...
5
votes
2answers
87 views

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Let $\Omega$ be a region in $\mathbb{R}^2$ with $f:\Omega \to \mathbb{R}$ a smooth function. Why is the quantity, $$ \tfrac{1}{2} \iint_{\Omega} \|\nabla f\|^2 $$ Called the "energy" of $f$? I am ...
0
votes
1answer
28 views

Trigonometry in projectile motion

I initially posted this question on Physics SE but got no responses probably because it's more related to maths than physics. A plane surface makes an angle $\bf X$ with the horizontal. From the ...
0
votes
1answer
23 views

How to prove the Hubble law is the unique expansion law compatible with homogeneity and isotropy?

In the book physical foundations of cosmology, it saids that Hubble law is unique and a problem seems to be a hint of proving that. In order for a general expansion law,v=f(r,t), to be the same ...
1
vote
3answers
38 views

By how much should the distance from the source be increased to reduce the surface illuminance to 30 lumens?

This is my problem and I have no idea how to solve it: The illuminance of a surface varies inversely with the square of its distance from the light source. If the illuminance of a surface is 120 ...
3
votes
0answers
63 views

My orbiting body is orbiting about the wrong focus of it's elliptical orbit… why? [closed]

I am coding in c++ and am computing the position of an orbiting body as a function of time. Everything is almost working. I have a nice elliptical orbit. Except, my orbiting body speeds up as it ...
1
vote
1answer
53 views

Question regarding combinatorics of resistance network. [closed]

If you have $N$ $1$Ohm resistors, how many distinct equivalent resistances can you create? Assume that only parallel and series and mixture of them is allowed and no bridging between two parallel ...
1
vote
5answers
54 views

Vector field ${\bf F}$ with $\int_S {\bf F}\cdot{\bf n}\ dS=c$

Find a vector field ${\bf F}$ on $ {\bf R}^3$ with $$\int_S {\bf F}\cdot{\bf n}\ dS=c > 0 \tag{1} $$ where $S$ is any closed surface containing $0$ and ${\bf n}$ is normal Here there is a ...
0
votes
0answers
35 views

What is the density of a homogeneous disk with mass $m$ and radius $a$?

Could someone help me understand why the density of a homogeneous disk is $\dfrac{m}{(\pi a)^2}$? I am trying to understand an example about finding the moment of inertia of an object. The question ...
0
votes
0answers
28 views

translating vectors in polar coordinates to the complex plane [duplicate]

These equations model circular motion. Equation R is the position vector given in polar coordinates. What I've done is represent this vector onto the complex plane via equation (1). Equation (2) and ...
0
votes
0answers
35 views

Derivation of the equations for non-uniform circular motion using complex analysis.

Here http://farside.ph.utexas.edu/teaching/301/lectures/node89.html They use complex analysis to derive the equations of non-uniform circular motion. My confusion is this: In the derivation they ...
4
votes
1answer
58 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
3
votes
2answers
133 views

Gödel's incompleteness theorems

In the last paragraph of Stephan Hawking's speech "Godel and the End of the Universe", he mentioned "... I'm now glad that our search for understanding will never come to an end, and that we will ...
0
votes
0answers
33 views

Subject to in equation

I have the formula below: $$\hat x_2=\arg\min\lVert x\rVert_2\quad\text{subject to}\quad A{x}=y.$$ But I didn't understand what was meant by "subject to" ? does $x$ is replaced by $x_2$? please can ...
12
votes
5answers
757 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...