Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

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What does it mean to differentiate $f(\theta_1)/f(\theta_2) = C$ with respect to theta?

In the book I am reading, at one point they differentiate Snell's Law with respect to ${\theta}$: $$\frac{d}{d\theta}\Bigl(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}=\frac{\eta_{2}}{\eta_{1}}\Bigr),$$ ...
Shane Simms's user avatar
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1 answer
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Minimizing the MSE of a cosine Fourier Series

When approximating an even function with period $2\pi$ by a Fourier-cosine-Series with $m$ terms, it has the error $$E_m=\int_{-\pi}^\pi \left[f(x)-\frac{a_0}{2}-\sum_{n=1}^m a_n \cos(nx)\right]^2 dx$$...
Adam's user avatar
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1 answer
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Formula for continuously dividing by 2

I was helping my daughter with her physics homework. The problem had a bee flying back and forth between two bikes moving toward each other. The question was to see how far the bee traveled. Turned ...
Vaccano's user avatar
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1 answer
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Is my modification to this solution valid?

I have the following problem: I know the center points and radii of three circles. I want to slowly increase each circle's radius until all three circles intersect. They are guaranteed to intersect at ...
10GeV's user avatar
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Understanding Norton' s dome equation

Here is the equation of Norton's dome used to demonstrate an indeterministic system within Newtonian formalism: h(r) = $-\frac{2}{3g}r^{\frac{3}{2}}$ where r is defined as "radial distance ...
Yury's user avatar
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Recommended Linear Algebra Text for Undergraduate Physics and Comp Sci

I'm an undergraduate freshman considering self-learning linear algebra given the free time quarantine has afforded me. I'm looking for an introductory (but comprehensive) textbook which I could use ...
Lucas Brito's user avatar
3 votes
1 answer
5k views

Number of images formed by two plane mirrors formulae derivation.

Derive: Number of images formed by two plane mirrors inclined at an angle of $\theta$ is given by $$\frac{360}{\theta} -1 $$ What I think: Inclined mirror forms images in the circle and one image ...
Wolgwang's user avatar
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4 votes
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Matching a target velocity and position

For a science-fiction computer game I'm writing, I wish to calculate the travel time and accelerations of a ship leaving one (3D) position with an initial velocity, and travelling to a moving target, ...
Robert Rendell's user avatar
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1 answer
381 views

Integrating a velocity field with respect to time, $\vec{i}$ and $\vec{j}$ vectors

When I'm given a velocity vector (they call it "velocity field") that's $a\vec{i} + xy\vec{j},$ its easy to integrate both of them with respect to time separately. Integrating $a\vec{i}$ ...
user242506's user avatar
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2 answers
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What kind of curve does $a*(x+y) = x*y$ form?

If $a$ is a constant, what is the name of a curve of the form $a*(x+y) = x*y$? And how is this equation related to more this curve's more general equations/characteristics? Plotting this curve, I ...
raflex's user avatar
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Defining a metric on plane based on downward gravity force

What is the metric defined on $\mathbb {R}^2$ plane, where downward gravity force ($\overrightarrow {-y}$ direction) causes the brachistochrone curves become its geodesics?
MasM's user avatar
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Compute the commutator, and compare it to quantization of the Poisson bracket.

Can someone please provide an insightful solution or verification of my solution to this question: Compute the commutator $$[p^2,q^2]$$ (in the one variable case), and compare it to quantization $$\...
BrazyOski's user avatar
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Analyzing a Position Function obeying Hooke's Law, and Simple Harmonic Motion

Given the following position function: \begin{equation} x(t) = 4.00 \cos(3.00\pi t + \pi) \end{equation} I have to extract the following information which are the following: Frequency Amplitude ...
Jose M Serra's user avatar
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1 answer
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Simplifying/computing an integral

I am attempting to compute some expectation value in a physics problem. I have computed that given $\psi_n(x)=\sqrt{\frac{2}{a}}\sin(n\pi x/a)$, we get $$\phi_n(k)=\frac{1}{\sqrt{2\pi}}\int_0^a\psi_n(...
Quaere Verum's user avatar
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3 votes
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Game physics of tearing apart

For a game I'm programming I'm looking for a kind of realistic mechanic for simulating the tearing apart of objects. Let me explain: I have a given point $p$ in a 2-dimensional space (possible later ...
man zet's user avatar
  • 197
2 votes
3 answers
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Why are there vectors that cannot span the Bravais lattice?

I'm taking a course in condensed matter physics and have just been introduced to the Bravais lattice. From a mathematical point of view this could be thought of as a vector space where the scalar ...
BoseEinsteinCondensator's user avatar
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1 answer
216 views

Estimating sunset time from Earth's radius [closed]

i have some issues with this. Could anyone explain me if it is right /wrong ? that is the link/image of my work -You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully ...
Msmrx's user avatar
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1 vote
2 answers
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Center of Mass of an Orange Slice

In a question in the book Advanced Problems in Mathematics by Stephen Siklos, the reader is told to assume that the center of mass of a spherical ‘segment’ (orange slice) of radius $a$ subtending an ...
Vishu's user avatar
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Understanding and implementing a multilateration localization algorithm.

I’m trying to implement a Time Delay of Arrival Multilateration algorithm. However, I’m struggling to understand the concept on the level necessary to produce an actual implementation. For reference, ...
K_M's user avatar
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2 votes
4 answers
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Show that $xy/z$ is constant given conditions on $xy$ and $y/z$.

If $xy$ is constant whenever $z$ is constant, and $y/z$ is constant whenever $x$ is constant, then show that $xy/z$ is constant. ...
across's user avatar
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-1 votes
1 answer
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determining weight of an object given the vectors holding it

Suppose that an object hangs from three ropes which point in the directions of the vectors ⟨2,−1,2⟩, ⟨−2,2,1⟩, and ⟨−3,0,4⟩. (Assume that the positive z-axis points directly upward.) If the tension in ...
cheescake's user avatar
1 vote
1 answer
403 views

How do I integrate this $d^3p$ integral?

I've been attempting to integrate the following: $$\int \frac{d^3 p}{(2\pi)^3} \frac{p}{T} \sin^2 (2\theta) \frac{1}{e^{p/T}+1}$$ to do this I chose to use spherical coordinates which originated the ...
user7077252's user avatar
1 vote
3 answers
148 views

How do I integrate $\int^{\infty}_0 \frac{p}{T} \frac{1}{e^{p/T}+1} dp$ by parts? (if it is by parts)

I've been trying to integrate this equation: $$\int^{\infty}_0 \frac{p}{T} \frac{1}{e^{p/T}+1} dp \tag{1} $$ and attempted to do it by parts following : $u=p^3$ and $dv=\frac{1}{e^{p/T}+1}$ where ...
user7077252's user avatar
0 votes
3 answers
57 views

How to discover the torque of this two stick device?

In Stewart's calculus book he asks about the magnitude of the torque of $F$ applied on $P$. The formula given in the book is $|\tau|=|\vec{r}\times \vec{F}|=|\vec{r}||\vec{F}|\sin\theta$. So my guess ...
user42912's user avatar
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1 answer
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Dimensional Analysis Limitations

Since dimension doesn't depend on magnitude. Hence, if a relation is dimensionally correct then it doesn't mean that it will also be mathematically or physically correct. What will be the vice-versa? ...
Chrishiv Tamta's user avatar
1 vote
2 answers
68 views

$\text{Rate} \times \text{Time} = \text{Distance}$ problem

To drive to the supermarket, Mable drives for $m$ miles, then drives $12$ miles per hour faster for the remaining $\frac{4m}3$ miles. The amount of time Mable spent driving at each of the two speeds ...
Lara Lincy's user avatar
0 votes
1 answer
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Calculate the average speed of a car

A car is traveling from New Haven to Philadelphia. It takes 1 hour and 24 minutes to drive 85 miles from New Haven to New York City. What was the average speed? First I converted the hour and $24$ ...
Eric Brown's user avatar
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How to find the speed of a car ascending on an incline when the mass is a time function?

The problem is as follows: A VW bus is ascending over a ramp as indicated in the figure from below. The bus has a power of $120\,kW$ to ascend over the incline. If the friction with the road and air ...
Chris Steinbeck Bell's user avatar
0 votes
1 answer
90 views

How to find the tilt angle in a square plate when it is tied in one end by a supporting wire?

The problem is as follows: The figure from below shows a golden square plate hanging from a wooded ceiling, the plate sides are $\textrm{ABCD}$. It is known that all sides are equal to $80\,cm$. The ...
Chris Steinbeck Bell's user avatar
1 vote
3 answers
112 views

Does $\frac{d^2x}{dt^2}=-Axe^{-x^2/2}$ have an elementary solution?

I'm trying to find a solution to the following differential equation: $$ \frac{d^2x}{dt^2}=-Axe^{-x^2/2} $$ Or better yet if I can find some function $\xi(x)$ such that $$ \frac{d^2\xi}{dt^2}=-B\xi. $$...
jackzeromega's user avatar
1 vote
1 answer
96 views

Approximating an integral involving a decaying exponential.

I've got this integral in a textbook $\Delta N=\int_{E_{0}}^{\infty} \sqrt{E}(e)^{-\frac{E}{k T}} \cdot d E$with $E_{0}>>K T$. The author approximates it by saying The principal contribution to ...
Kashmiri's user avatar
  • 547
1 vote
1 answer
214 views

Find an expression for the position at time $t$.

Suppose a unit of mass moves on a straight line (in one dimension). The position of the mass at time $t$ (in seconds) is denoted by $s(t)$, and its derivatives, velocity and acceleration, by $s'(t)$ ...
Skm's user avatar
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0 votes
2 answers
348 views

Why are reaction forces normal to the surface?

I've been studying mechanics for a while now, but I still don't know a very basic point: why is it that when a body is in contact with a plane that the reaction/contact force acts perpendicular to the ...
A-Level Student's user avatar
0 votes
1 answer
1k views

Calculus $2$: Lifting Barbell And Chain Problem

A weightlifter holds a $1,300 $N barbell $1$ meter above the ground. One end of a $2$-meter-long chain hangs from the center of the barbell. The chain has a total weight of $600$ N. How much work (in ...
Insatiable Suffering's user avatar
1 vote
0 answers
108 views

Struggling with the integral of $\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)^3 \mathrm{d}$t

I'm doing a physics problem in which I need to find the energy dissipated from air resistance. The straightforward equation which could be solved is $$\Delta E = k\int_0^T \left(\frac{\text{d}x}{\text{...
MurderOfCrows's user avatar
3 votes
1 answer
350 views

Why is the Volume integration & Surface Area integration of a sphere different?

For both volume & surface area, the sphere is split into many discs and the area or circumference of the discs are summed up in an integral. But the summation process uses $dy$ for volume & $r\...
Vignesh Sk's user avatar
1 vote
1 answer
195 views

Criterion to see if you can neglect air drag in projectile motion

In physics education you often consider "real world problems" with projectile motion. Most times in introductory courses you neglect air drag. But how can students (knowing nothing about ...
Julia's user avatar
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1 vote
0 answers
133 views

Understanding the order-n correlation function algorithm

I am referring to the algorithm from Chapter 4, section 4.4.2 of Understanding Molecular Simulations: From Algorithms to Applications by Frenkel and Smit. This algorithm is simply called the order-n ...
megamence's user avatar
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1 vote
0 answers
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Deriving electrostatics from Maxwell equations

When all electric charges are stationary (i.e. $\frac{\partial\rho}{\partial t}=0$ and $\mathbf{J}=0$), the Maxwell equations $$\pmb{\nabla}\cdot\mathbf{E}=\rho/\varepsilon_0,$$ $$\pmb{\nabla}\times\...
apadana's user avatar
  • 191
1 vote
1 answer
4k views

How can I solve initial velocity for a projectile given the max height and distance

I'm trying to find the initial velocity of a tennis ball (magnitude and angle) given the initial height, max height and max range. I believe this is possible with the equations below but I'm ...
Adrian Taylor's user avatar
0 votes
0 answers
21 views

Understanding instability in a boundary value problem

I am numerically solving the following boundary value problem: $$ \begin{align} y'_1 &= F(x)+x^2\rho(x) y_2\\ y'_2 &= -c\frac{\rho(x)}{x^2 P(x)}y_1 \end{align} $$ with the boundary conditions $...
rhombidodecahedron's user avatar
0 votes
1 answer
27 views

How do I go about finding how y relates to a specific variable in this integral?

I'm not sure on the proper descriptions for what I'm trying to do here. Essentially, if at all possible, I want to simplify this as much as possible to obtain something along the lines of $\Lambda \...
ch4rl1e97's user avatar
  • 101
6 votes
0 answers
196 views

3blue1brown Playing Pool with Pi Variation.

I often like doing variations of math puzzles and riddles. For this one though, it's extremely hard for me to find a simulation runner to solve this variation, and this variation also is a lot tougher....
user avatar
0 votes
1 answer
122 views

How to find the angular speed of the cylinder spinning when a bullet strikes against it?

The problem is as follows: The figure from below shows a cylinder spinning. Find the angular speed of the cylinder so that the perforations made in a minimum time by the bullet carrying a linear ...
Chris Steinbeck Bell's user avatar
0 votes
1 answer
18 views

How to find the elapsed time between two collars when they are sliding over a thin wire?.

The problem is as follows: The figure from below shows two brass cylinders sliding through a wire as a guiding line to hit the ground. The cylinders are released from point $P$. Assuming that the ...
Chris Steinbeck Bell's user avatar
4 votes
0 answers
68 views

Where to start with physics? [duplicate]

So I already have a degree in math and am working on a masters, but I’ve taken no physics since grade 12, and I think it would be really interesting. I’m not trying to get an official degree, I’m just ...
archaicmushroom's user avatar
-1 votes
1 answer
29 views

What will be the elapsed time for a person standing a railway can listen a beep?

The problem is as follows: A shinkansen which cruising with a constant rate across a railway in Tokyo emits a warning beep during $2\,s$. Find for how long (measured in seconds) a student standing ...
Chris Steinbeck Bell's user avatar
1 vote
1 answer
918 views

Calculate the tension in OA and OB

A $200\ \text{lb}$ weight and a $100\ \text{lb}$ weight are held in static equilibrium by cables $OA$ and $OB$ as shown below. The pulleys are frictionless and you may neglect the pulley weights. ...
AL vees's user avatar
  • 163
0 votes
2 answers
48 views

Calculating the length of a train

In the above question, I tired to calculate the length of the train as 300/1200 + 3/1200 = 11/400 Km But they are subtracting the above length. I'm not sure why they are doing so.
Simran's user avatar
  • 447
1 vote
1 answer
164 views

Simple calculus question re: the Work-Energy theorem (change of variables)

I have the following proof for the Work-Energy theorem (with the usual notation). Where I'm getting lost is basically at the line break, clearly just missing something very obvious. How is it that we ...
G G Veracruz's user avatar

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