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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1answer
80 views

Finding the ideal angle for the maximum range of a projectile when elevated?

I was thinking about physics, and I thought of something. How do we find the ideal angle for the maximum range of a projectile when elevated? Assumptions: Parabolic flight path No air friction ...
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1answer
36 views

Need help deriving an expression for average acceleration in terms of displacement and time

I'm having trouble with this math problem. Here's what the questions is asking: Derive an expression for the average acceleration of the cart in terms of displacement and time of travel. Write ...
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1answer
57 views

Using definite integrals with velocity and acceleration

Rocket A is traveling 49 ft/sec at 80 seconds. Rocket B is launched upward with an acceleration of $$a(t)=\frac3{\sqrt{t +1}}$$. At time t=0 seconds, the initial height of the rocket is 0 feet, and ...
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1answer
76 views

Does distance increase equally in equal time intervals under the influence of gravity?

Quick question. If an object falls under the influence of gravity near the Earths surface, is the distance traveled increased by equal amounts in equal time intervals? I thought that this would be ...
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1answer
43 views

Finding Orbital Period of an Object

A satellite is launched to orbit the Earth at an altitude of $1.55\times10^7$ m for use in the Global Positioning System (GPS). Take the mass of the Earth to be $5.97\times10^{24}$ kg and its radius ...
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2answers
179 views

Finding Acceleration of Two Objects Touching

Alex is asked to move two boxes of books in contact with each other and resting on a rough floor. He decides to move them at the same time by pushing on box A with a horizontal pushing force FP = 8.7 ...
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1answer
61 views

Heat energy per unit mass necessary to raise temperature in a slice

Suppose that the specific heat is a function of position and temperature $c(x,u)$. show that the heat energy per unit mass necessary to raise the temperature of a thin slice of thickness $\Delta x$ ...
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2answers
72 views

Square Root Yields Different Result After Unit Conversion [duplicate]

This is boggling my mind. The square root of 100 seconds is 10 seconds The square root of ...
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0answers
22 views

Closed form for 3j-symbol ratio

I am working on the spherical harmonic decomposition of cosmic microwave background maps, therefore I often deal with functions that are proportional to Wigner 3J symbols/Clebsch Gordan coefficients. ...
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1answer
49 views

Line Integral to Find Work on Slope (Without Explicit Use of Vector Calculus Format)

Ok, so my math class has introduced the Line Integral as a way to find the work done on a two-dimensional slope by gravity on an object traversing any distance on the slope. This is all supposed to be ...
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0answers
40 views

Geostationary orbit

We have the following governing equations for the motion of a satellite around the earth under gravity: $\dfrac{-GM}{r^2} =\ddot{r} -r\dot{\theta}^2$ $r^2\dot{\theta} = h$ I want to find the height ...
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1answer
84 views

Solving an ODE with Mathematica, using Lagrangian mechanics

Question: The velocity of light above a hot surface decreases with the height from that surface. The velocity is given by $v=v_0(\frac{1-y}{\alpha})$ where $y$ is the vertical distance above the ...
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3answers
39 views

Finding the total distanced covered (physics)

A subway train starts from rest at a station and accelerates at a rate of $1.60\frac{m}{s^2}$ for $14.0 s$ . It runs at constant speed for $70.0 s$ and slows down at a rate of $3.50\frac{m}{s^2}$ ...
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1answer
32 views

Need help deciphering equation that was messed up when used on a thread online

How can I understand what this says? Can someone also tell me what the heck those symbols mean and where they came from? $$\vec{p_e} = 1200 kg \cdot 5 m/s [{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\ ...
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0answers
226 views

Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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0answers
43 views

How to solve this differential equation of the second order

Do you know how to solve this equation? I'm a physicist student and I have initial equation, condition and answer. Unfortunately I need an explanation how this answer was got. I am mew to such ...
4
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2answers
127 views

one-dimensional inverse square laws

I suddenly became curious about the following differential equation: \begin{align*} \frac{d^2x}{dt^2} = \frac{k}{x(t)^2} && x(0) = x_0 > 0 && \frac{dx}{dt}(0) = v_0 \end{align*} ...
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0answers
34 views

Deriving the lagrangian multiplier

Could someone kindly help me with: 1. a step by step method of deriving the lagrangian multiplier 2. what are the uses of the lagrangian multiplier. I'm really new to this and your help will be ...
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1answer
45 views

Oscillation and Damped oscillation program

I am trying to build a simple program where an object undergoes simple harmonic motion, where a force is initially applied, than undergoes SHM until coming to a stop. My problem is that my program ...
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0answers
36 views

Define a plane with double integral

For my transport physics I have to describe how much volume through a rectangular pipe goes. The speed is given by $\displaystyle V_x=V_0 \frac{y}{h}$. But I have to define the plane with a double ...
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1answer
55 views

Finding acceleration at a certain velocity

A race car starts from rest and travels east along a straight and level track. For the first $5.0s$ of the car's motion, the eastward component of the car's velocity is given by ...
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1answer
189 views

Find acceleration at the first instant when a car has zero velocity.

The position of the front bumper of a test car under microprocessor control is given by: $x(t)=2.17m+\left(4.8\frac{m}{s^2}\right)t^2-\left(.100\frac{m}{s^6}\right)t^6$ Find its acceleration at the ...
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1answer
35 views

please help me understand the lecture note? heat equation and fourier series

I don't quite understand equation 3.73 and 3.74. To get $T(x,t)$ I thought I had to multiply F and G. How does that give equation 3.73? I got G as e^{stuff} as in the last bit of equation 3.73. ...
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2answers
34 views

Heat equation. Find $B_n$ (using boundary conditions?)

Can anyone help me with (b)(i)? I've done the first part of it. I've tried putting some boundary conditions in but cannot find $B_n$ What fact should I use? An infinite slab of material, of ...
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1answer
44 views

Initial conditions of a second-order ODE

This may look like a physics problem, but everything physical is explained below and I am looking for a mathematical solution. An RLC circuit (pictured above) is governed by two equations: $$ ...
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1answer
33 views

Can you add potentials if charge redistributes?

Let say we have charged conductor $M$ and we know its potential energy function $V_m(r)$ when $M$ is isolated from any charges. We also have charged conductor $N$ with potential energy function ...
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1answer
39 views

Twin paradox spacetime intervals

I've very recently started to try to understand special relativity. I want to get a decent understanding of the twin paradox. I'll post what I've done so far and highlight what's gone wrong for me. ...
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1answer
50 views

Infiniteness of a knot energy

I am going through the paper, Physical Knots, by Jonathan Simon. Initially, on page 10, he describes the electrostatic energy of two charged stick, X and Y in space as follows. $$ \int_{x \in X} ...
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1answer
57 views

Starting velocity by distance, time, and friction

I am writing a game in Javascript, and I just got a big math problem, where $\text{friction} = 0.97$. This is what is being looped every $1000$ / $60$ milliseconds, to make the projectile move all ...
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1answer
108 views

Pendulum with angular velocity

I have another pendulum problem again but this time it's with angular velocity. My question is: If a pendulum is initially at its unstable equilibrium position, then how large an initial angular ...
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2answers
44 views

Re-arranging variables

In physics, you can say that: $T-m_2 g = m_2 a$ And that $ m_1 g - T = m_1 a$ So this, when combined, should equal: $a = \frac{m_1}{m_1 + m_2} \cdot g$ How do they arrive at that conclusion? I ...
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0answers
78 views

Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
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0answers
39 views

Cross Product - Moments :: Dynamics 2

This problem is related to Cross Product - Moments :: Dynamics Please look at that link for the background on the problem I am faced with right now, I have linked a pdf of the book that I am using ...
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1answer
42 views

Linear algebra and special relativity

I'm going over an exam I had a couple months back, over the exercises I didn't manage to get right and I'm kinda stuck with the following subtask: Let $\xi$ be a 4-vector with the Minkowski scalar ...
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2answers
31 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
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3answers
63 views

Boxes on a slope [closed]

A box with friction slides down a slope and takes 2 times longer than a similar box with no friction takes to slide the same slope. What is $ \mu $ (the coefficient of friction)? I'm pretty lost. I ...
0
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1answer
27 views

Trying to understand free body diagram [closed]

Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly ...
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1answer
98 views

Physics Vector Problem - Airplane

Heres the question: A plane leaves the airport in Galisto and flies $140$km at $68.0^∘$ east of north and then changes direction to fly $255$km at $48.0^∘$ south of east, after which it makes an ...
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2answers
53 views

Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
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2answers
55 views

Fundamental roles that astronomy played in the development of mathematics

I'm currently a third year undergrad maths student, and am particularly interested in how astronomy changed maths as we know it today? Are there any particular sources that could be recommended? Or ...
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0answers
16 views

Using Invariance of Lorentz interval and constant speed of light to prove the Lorentz transformations

By the invariance of the Lorentz interval and the fact that the speed of light is the same in both frames we have \begin{align*} -c^2 dt^2 + dx^2 = -c^2 dt'^2 + dx'^2 \end{align*} By considering the ...
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1answer
34 views

1-D heat diffusion in a bar with fixed temperatures at the edges

I'm trying to calculate the temperature gradient in a bar of metal with a heater at either end. Initially, the bar is at room-temperature $T_0$, then at $t=0$ the heaters are turned on: $u(0,t)=T_1$ ...
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3answers
110 views

Interpretations of $\frac{\infty}{\infty}$

I am trying to understand the physical sense of the mathematical construct $\frac{\infty}{\infty}$ Suppose we have a function $f(x)$ representing some physical construct depending on a "quantity" $x$ ...
5
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0answers
64 views

Earnshaw's theorem

Proposition Suppose $U\colon\Omega\to\mathbb R$ is a non-constant harmonic function, i.e. $U\in\mathcal C^\omega$, i.e. analytic, and $\Delta U=0$, where $\Omega\subseteq\mathbb R^n$ is a region. ...
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1answer
55 views

Forces and line of action

A force $F_1 = i - 3j -2k$ at the point $r_1 = -2i + 9j$ another force $F_2 = 2i + j -3k$ at the point $r_2 = i + yj -k$ and a third force $F_3$ are equivalent to zero. Find y for this to be possible. ...
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1answer
63 views

Problem with friction [closed]

Imagine two boxes stacked on top of each other. The bottom box is larger than the top box and it rests on a surface. So: Between the boxes is a friction force constant $\mu_s$ and between the ...
0
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1answer
38 views

What is the most tension I could get [closed]

Look at the following picture: Imagine that mass "m" is very large. What is the maximum tension we can get on the rope? I'm not sure how to understand this. The rope is indestructible I guess, so ...
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1answer
47 views

How to determine the magnitude of a resultant vector?

I was able to determine a resultant vector based on the sum of two vectors and told to express them in vector units. Here is my answer that was correct: ...
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0answers
21 views

Dynamic flows on sphere

How to draw a vector field on $S^{7}$ in the evolution? My own answer to this question is placed in the book in Russian http://socionet.ru/publication.xml?h=repec:rus:gulthb:7 Let I want to draw a ...
2
votes
1answer
41 views

Angle that car is at after angular acceleration

A car starts from rest on a curve with a radius of $150m$ and tangential acceleration of $\displaystyle 1.5\frac{m}{s^2}$. Through what angle will the car have traveled when the magnitude of its ...