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.
5,946
questions
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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 ${\theta}$:
$$\frac{d}{d\theta}\Bigl(\frac{\sin(\theta_{1})}{\sin(\theta_{2})}=\frac{\eta_{2}}{\eta_{1}}\Bigr),$$
...
0
votes
1
answer
68
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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
$$E_m=\int_{-\pi}^\pi \left[f(x)-\frac{a_0}{2}-\sum_{n=1}^m a_n \cos(nx)\right]^2 dx$$...
1
vote
1
answer
4k
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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 ...
1
vote
1
answer
32
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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 ...
1
vote
0
answers
43
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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 ...
1
vote
0
answers
169
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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 ...
3
votes
1
answer
5k
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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 ...
4
votes
0
answers
361
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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, ...
0
votes
1
answer
381
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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 $a\vec{i}$ ...
0
votes
2
answers
95
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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 ...
1
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0
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32
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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?
1
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1
answer
56
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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 $$\...
1
vote
0
answers
24
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Analyzing a Position Function obeying Hooke's Law, and Simple Harmonic Motion
Given the following position function: \begin{equation} x(t) = 4.00 \cos(3.00\pi t + \pi) \end{equation}
I have to extract the following information which are the following:
Frequency
Amplitude
...
1
vote
1
answer
53
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Simplifying/computing an integral
I am attempting to compute some expectation value in a physics problem. I have computed that given $\psi_n(x)=\sqrt{\frac{2}{a}}\sin(n\pi x/a)$, we get
$$\phi_n(k)=\frac{1}{\sqrt{2\pi}}\int_0^a\psi_n(...
3
votes
0
answers
31
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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 ...
2
votes
3
answers
180
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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 ...
0
votes
1
answer
216
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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 ...
1
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2
answers
223
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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 ...
0
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0
answers
212
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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, ...
2
votes
4
answers
124
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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.
...
-1
votes
1
answer
548
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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 ...
1
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1
answer
403
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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 ...
1
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3
answers
148
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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 ...
0
votes
3
answers
57
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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 ...
-2
votes
1
answer
46
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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?
...
1
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2
answers
68
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$\text{Rate} \times \text{Time} = \text{Distance}$ 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 ...
0
votes
1
answer
39
views
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 $24$ ...
0
votes
1
answer
130
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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 ...
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 ...
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
$$
\frac{d^2\xi}{dt^2}=-B\xi.
$$...
1
vote
1
answer
96
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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 ...
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 $s'(t)$ ...
0
votes
2
answers
348
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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 ...
0
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1
answer
1k
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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 ...
1
vote
0
answers
108
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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
$$\Delta E = k\int_0^T \left(\frac{\text{d}x}{\text{...
3
votes
1
answer
350
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Why is the Volume integration & Surface Area integration of a sphere different?
For both volume & surface area, the sphere is split into many discs and the area or circumference of the discs are summed up in an integral. But the summation process uses $dy$ for volume & $r\...
1
vote
1
answer
195
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Criterion to see if you can neglect air drag in projectile motion
In physics education you often consider "real world problems" with projectile motion. Most times in introductory courses you neglect air drag. But how can students (knowing nothing about ...
1
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0
answers
133
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Understanding the order-n correlation function algorithm
I am referring to the algorithm from Chapter 4, section 4.4.2 of Understanding Molecular Simulations: From Algorithms to Applications by Frenkel and Smit. This algorithm is simply called the order-n ...
1
vote
0
answers
60
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Deriving electrostatics from Maxwell equations
When all electric charges are stationary (i.e. $\frac{\partial\rho}{\partial t}=0$ and $\mathbf{J}=0$), the Maxwell equations
$$\pmb{\nabla}\cdot\mathbf{E}=\rho/\varepsilon_0,$$
$$\pmb{\nabla}\times\...
1
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1
answer
4k
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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 ...
0
votes
0
answers
21
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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 $...
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 \...
6
votes
0
answers
196
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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....
0
votes
1
answer
122
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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 ...
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 ...
4
votes
0
answers
68
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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 ...
-1
votes
1
answer
29
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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 ...
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. ...
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.
1
vote
1
answer
164
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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 ...