All Questions
Tagged with applications physics
67
questions
-1
votes
3
answers
53
views
How to untangle the ODE $\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$? [closed]
In working on this problem, I came up with the following differential equation:
$$
\frac{dx}{dt} = c + \frac{px}{l_0 + pt}
$$
where $x$ is the dependent variable, $t$ the independent, and all others ...
- 4,450
22
votes
5
answers
2k
views
What do physicists mean when they say something is "not a vector"?
It's common for physicists to say that not every 3-tuple of real numbers is a vector:
“Well, isn’t torque just a vector?” It does turn out to be a vector, but we do not know that right away without ...
- 4,450
8
votes
2
answers
805
views
Negative Numbers in Math & Physics
We say that $-4 < -2$ and that $-3 < 0$ and that $-192 < 24$. I'm aware that there are simple, easily understandable definitions for less than / greater than / equal to e.g. $a < b$ iff ...
- 983
2
votes
0
answers
98
views
Heat from a geothermal well: your take?
Imagine digging a cylinder-shaped (vertical) bore-well of depth $L$ and diameter $r$ ($L\gg r$). The (infinitely thin) cylinder-wall is made watertight and we split the well in half using a kind of ...
- 2,455
0
votes
1
answer
93
views
How taut must a stretchable, horizontally-oriented string be in order for a straight line to approximate the string to within a given margin of error? [closed]
My question deals with a string that can stretch due to its own weight. If the string is allowed to stretch then I'd assume there would always be a bit of a bulge due to gravity.
The only progress I'...
- 887
1
vote
0
answers
31
views
Error while calculating force in 2D flow around a circle
This is statement of the exercise:
In this exercise we consider as example the case of a disk of radius R centered at the origin of coordinates immersed in a fluid of density σ and velocity field $u(x,...
0
votes
0
answers
45
views
Cavalieri's Principle in volume calculation
In petroleum engineering, for easier calculation of the volume underlying a specific surface underground, the irregular surfaces are modeled by an equivalent surface with circular cross sections, ...
4
votes
1
answer
387
views
I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
- 1,156
3
votes
1
answer
123
views
Strong solutions of SDEs in electrical engineering
I am currently reading about existence and uniqueness theory for stochastic differential equations (SDE). Two of the main concepts are: strong and weak solutions.
I do understand the difference ...
- 319
0
votes
0
answers
532
views
Application of Graph Theory in Electrical Circuits
I've been learning about electrical circuits, and I can see how Graph Theory naturally lends itself well to problems with circuits.
I was wondering what some examples of applications of Graph Theory ...
- 140
1
vote
0
answers
147
views
Finding optimal 2D trajectory on a simple rocket control without air resistance
My problem is as following:
Suppose we have a rocket ship, which is modeled as a point mass(the mass doesn't matter, but we'll assume it's a constant $m_0$ for simplicity).
It can accelerate in any ...
- 111
1
vote
1
answer
210
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 ...
- 987
0
votes
0
answers
92
views
Derive the equations of motion and determine whether angular momentum is conserved..
Suppose that the gravitational force is not given by the inverse-square law, and instead is
$$ F_{grav}=\left(\frac{A}{r^{2}}+\frac{B}{r^{4}}\right)\hat{r}, $$
where A and B are real constants. Derive ...
- 1
0
votes
1
answer
60
views
Interpretation and use of the logarithmic scale for high school students
Often when we discuss on the logarithms in high school we also talk about a scale called logarithmic.
In the he logarithmic scale: the distance from $1$ to $2$ is the same as the distance from $2$ to ...
- 7,792
0
votes
2
answers
130
views
Invertible polynomial that approaches linearity at large x
I need to approximate a function $y=f(x)$ using a small set of constants $a_0…a_n$, ideally where the number of constants can be arbitrarily increased to improve accuracy. $x$ and $y$ are both real ...
1
vote
0
answers
49
views
Physical significance of 3rd derivative [duplicate]
I am new to calculus and currently learning differentiation. I understood that the first derivative indicates the slope of the function and the second derivative indicates the rate at which the slope ...
- 647
0
votes
1
answer
46
views
Solving time derivative of glycogen dynamics: $17.6{dG\over dt} = 2000 - 13G^2$ [closed]
Can I find G, glycogen level at time t=5, if glycogen dynamics are described by the following derivative:
$$17.6{dG\over dt} = 2000 - 13G^2$$
It's been a long time since I've messed with derivatives ...
- 1
44
votes
17
answers
9k
views
What is a simple, physical situation where complex numbers emerge naturally? [duplicate]
I'm trying to teach middle schoolers about the emergence of complex numbers and I want to motivate this organically. By this, I mean some sort of real world problem that people were trying to solve ...
- 645
0
votes
0
answers
146
views
Physical interpretation of Dirichlet energy for a membrane.
In the following model of a membrane with a mass particle in it, why does the integral represents the elastic energy of the system?
Let $\Omega$ be an open connected region (the membrane) in $\Re^2$, ...
12
votes
3
answers
864
views
Applications of "finite mathematics" to physics
Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias.
When I think of applications of maths outside of itself, I ...
- 43.9k
2
votes
1
answer
55
views
Could families of "Airys" and "Bairys" of integer "frequencies" be useful?
A very famous family of functions are the complex exponentials and in the case of real valued functions, the sin and cos functions. They are related by the famous Euler formulas:
$$\exp(i\phi) = \cos(...
- 26.1k
3
votes
2
answers
94
views
Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?
Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...
- 26.1k
2
votes
1
answer
170
views
How do I tell the rank of the electric susceptibility tensor (and others)?
I understand that a tensor is a multilinear map from
$V^*\times\cdots\times V^*\times V\times\cdots\times V$ to $V$'s underlying field, where $V$ is a vector space and $V^*$ its dual. This is fine, ...
- 23
0
votes
1
answer
26
views
Can we solve the functions describing the bend of a cable at rest fixed at two positions?
Assume we have a cable which endpoints is attached to two points at $(x,h)$ and $(x+\Delta_x,h)$.
Further assume it has some mass density distribution, $\rho(m),m \in [0,l]$ and is of some length $l ...
- 26.1k
1
vote
2
answers
5k
views
Solution to ODE from Newton's Second Law
I have attempted to explore Newton's second law (F = ma) further into its many differential forms. I am not very familiar with differential equations and was searching for the steps and methods to ...
0
votes
1
answer
4k
views
Amount of work required for pulling rope problem
50 m rope with 8 millimeters in diameter is dangling from an edge. density of rope =40 g/m. how much work to pull it up to edge?
// I've seen different variations of this problem, but I am unsure of ...
- 129
2
votes
1
answer
1k
views
Are there any Applications of Abstract Algebra in Engineering?
As the title suggests, I was wondering whether there are any applications of abstract algebra in the engineering disciplines - and if so, what these are (not including basic linear algebra here, as ...
- 1,416
0
votes
1
answer
92
views
A tank is part of a cone with a 10 foot radius on top, 4 foot radius on bottom 12 feet below the top Water in the tank has depth 5 feet
A tank is part of a cone with a 10 foot radius on top and a 4 foot radius on bottom, 12
feet below the top. Water in the tank has depth 5 feet.
Provide an integral for the work
done pumping the water ...
- 9
1
vote
0
answers
22
views
Dispersion of mid-air particles: scaling laws and similarity solutions of a function
I'm currently looking at some old questions from my undergraduate studies which I may not have fully understood but would like to understand now.
The initial stage of a dispersal process is very ...
- 6,343
0
votes
0
answers
87
views
Applied Maths: Equations of Motion
"A particle of mass m moves in a straight line, so that at time t the particle has a displacement x measured from an origin O. The force acting on the particle is Fsin(ωt), where t is time, and F and ...
- 63
2
votes
0
answers
76
views
whats is the applications of the minimization of eigenvalue in the real life ( physics,the natural sciences...)
let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $
the classical spectrale optimisation ...
- 704
1
vote
0
answers
117
views
Physical meaning of this boundary value differential equation
I am considering the following boundary value problem:
$$-\frac{\mathrm{d}}{\mathrm{d}x} \left[ a(x) \frac{\mathrm{d}}{\mathrm{d}x}(u(x)) \right] + c(x)u(x) = f(x),$$
where $x \in [0,1]$ and $u(0) = ...
- 3,993
9
votes
1
answer
132
views
How many times do you have go back and forth to get out of a deadlock?
Here's a challenging question for you math lovers.
This question was originally asked in Physics SE but I was suggested to post it here.( You can see it here.)
Many a times we have been inside a ...
user504401
2
votes
2
answers
252
views
Probability density for velocity in mechanical energy
To be sure my basic physics isn't rusty...
Consider a 2-D bowled shaped classical potential well within which a classical particle of mass m is rolling.
In this system the conservation of energy ...
- 6,343
2
votes
2
answers
1k
views
Prove $v = \sqrt{\frac{2gRh}{R + h}}$ from Given (below)
Given:
$$F = \frac{mgR^2}{(x + R)^2}$$
$m = \text{mass}$
$g = \text{Acceleration due to gravity}$
$x = x(t)$ is the object's distance above the surface at time $t$.
I believe this is the ...
- 141
1
vote
1
answer
7k
views
Hydrostatic force problem with trapezoids?
If I have a trapezoid with a $4$m and $8$m base that is partly submerged vertically in water so that the top is $2$m above the surface and the bottom is $2$m below the surface; how do I express the ...
- 575
0
votes
1
answer
4k
views
UNRESOLVED: Pushing oil out of a tank using work integration
I have a tank of oil with a density of $900\frac{kg}{m^3}$. My tank has a spout that is $2$ meters tall and the general radius of the tank is $6$ meters. It is half full of oil and I want to find the ...
- 575
0
votes
1
answer
112
views
How to show something does not vary with time?
Consider a glider flying at velocity $\bf u$ (giving $u = |\bf u| $ on its speedometer) at an angle $θ ∈ (−π, π]$ to the horizon.
Positive angle $θ ∈ (0, π/2)$ coincides with the glider’s nose ...
- 145
0
votes
2
answers
1k
views
Tacoma Narrows bridge collapse : mathematical explanation. [closed]
What is the exact mathematical reason behind the Tacoma narrow bridge collapse ?
I have googled about the collapse , but I didn't get a correct reason and a mathematical model.
- 73
6
votes
1
answer
2k
views
Applications of group theory to classical mechanics
Today, a friend and I solved a classical mechanics problem using group theory. The problem was the following:
Around a circumference, there are $N$ children evenly spaced. In the center, there is a ...
- 2,965
8
votes
1
answer
360
views
How can one tell if a PDE describes wave behaviour?
I have been looking at a lot of different non-linear PDEs which describe waves lately and have come to the realisation that I don't know what it is about these PDEs that make them behave like waves. ...
- 93
1
vote
0
answers
80
views
Heat problem with an internal source of heat for which the maximum principle doesn't hold.
Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it...
$$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
- 3,766
3
votes
1
answer
5k
views
Applied Mathematics: Spherical Polar Coordinates and Newton's Second Law
I've been attempting this question but can't seem to find a solution.
Question:
A particle of mass $m$ moves under the influence of a force which, in spherical polar coordinates, only acts in the ...
- 455
0
votes
1
answer
46
views
Locus Equation $f(r) = \frac{-h^2}{r^3}$?
For the Locus equation
$$\frac{\mathrm{d^2}u }{\mathrm{d} \theta^2} + u = - \frac{1}{h^2u^2}f\left(\frac{1}{u} \right )$$
How do I find the solution for $f(r)= \frac{-h^2}{r^3}$ and sketch the ...
- 455
1
vote
1
answer
224
views
When is $0$ ever used in real life?
I've just been going through an equation, which is as follows:
$(x+4)^2 = 16$
Lets work through it:
$$x^2 + 8x +16 = 16$$
$$x^2 +8x = 0$$
$$x^2 = -8x$$
$$x = -8$$
However, as i've just found ...
- 2,110
1
vote
1
answer
1k
views
Can anyone answer this with the steps of Assumption > Given > Formula > Solution?
The height in feet of a bottle rocket is given by the function $h(t)=160-16t^2$, where $t$ is the time in seconds. How long will it take for the rocket to return to the ground? What is the height of ...
- 11
1
vote
1
answer
3k
views
How do I calculate the gravitational force exerted by a thin ring of uniform mass M?
I'm working on a problem and can't seem to get it.
Find the gravitational force exerted by a thin uniform ring of mass M and radius a on a particle of mass m lying on a line perpendicular to the ...
user1054
0
votes
0
answers
51
views
partial differential equation applicational problem
As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from yt(...
- 259
7
votes
1
answer
251
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 ...
- 1,167
2
votes
0
answers
286
views
Basis representation for non-negative, compact support, reasonably smooth spectral function
I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
- 21