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
40 views

Example of using the Hadamard's matrix to determine the superposition

I've came across those notes for Quantum computation from John Watrous. I am having troubles understanding the last example. We have those two vectors, or if I understood correctly, from now on ...
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0answers
16 views

Light attenuation through water at an angle

I know that light intensity decreases exponentially governed by \begin{equation*} \frac{dy}{dx} = -ky \end{equation*} where $y$ is the intensity and $x$ is the distance. Now what happens when light ...
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0answers
13 views

Finding the magnetic field

A mechanical pendulum is made of a metal rod, one end of which is attached to a string. The mass of the rod is $m$ and the string length is $l$. The oscillation period of the thus obtained pendulum ...
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1answer
28 views

Integration — Work done in pulling an elevator using a rope [on hold]

An elevator weighing 3000 lbs. is supported by a 12 ft. cable that weights 14 lbs./ft. Find the work a which has to do by pulling the rope to lift the elevator 9 feet. I eventually figured out ...
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0answers
37 views

First fundamental theorem of calculus for line integrals [on hold]

Please, could someone look at this tricky question? Find the work done by force $F(x,y)=(3y^2+2) \hat i+16x \hat j$ in moving a particle from $(-1, 0)$ to $(1,0)$ along the upper half of the ellipse ...
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2answers
28 views

Calculate Speed from Distance, Time, Acceleration Time and Deceleration Time [on hold]

I'm trying to find a formula for working out the speed for an object with a given distance, overall time, acceleration time and deceleration time. The object starts and stops at a standstill. I know ...
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1answer
37 views

Is there a method to check if two curves (non-linear) are identical

I have two data sets of pollutant concentration on simultaneous days. I have to check whether these two curves follow similar pattern or not ( there might be some time lag between both) on daily ...
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13 views

Mph conversion question [on hold]

If i throw a baseball at 68mph from 15 feet away, what is the pitch speed at 60.6 feet away?
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2answers
65 views

Calculate moment of inertia of Koch snowflake

That's just a fun question. Please, be creative. Suppose having a Koch snowflake. The area inside this curve is having the total mass $M$ and the length of the first iteration is $L$ (a simple ...
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1answer
24 views

Calculus Velocity and Acceleration

Here's the question: I know that: $a(t) = -9.8$ So I integrated the acceleration function to find the velocity: $v(t) = -9.8t + c$ And because $v(0) = -5$, I can determine that $c = -5$, thus: ...
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1answer
29 views

Prooving Kepler's Second Law through vectors.

I am taking a multivariable calculus lecture online provided by MIT OpenCourseWare. ...
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2answers
27 views

Freefall with terminal velocity - expressions for velocity and position

A body weighing 29 kg is dropped from a height of 30 m with an initial velocity of 3m/sec. Assume that the air resistance is proportional to the velocity of the body. if the limiting velocity is known ...
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1answer
18 views

Find springs position at the time

A force of 13N is needed to keep a spring with a 2 kg mass stretched 0.25m beyond its natural length. The damping constant of the spring is c=8. If the mass starts at the equilibrium position with a ...
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0answers
15 views

Need to find stretched springs location [closed]

I have to find out the position of the string after it has been stretched out. Here is the picture of the assigement. http://prntscr.com/71txpf
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2answers
24 views

Linear Motion: Initial velocity [closed]

How long does it take a car traveling with an initial velocity of 25 m/s and accelerating at a rate of 5 m/s2 to travel 1500 meters? Need some help answering this question
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0answers
11 views

1-D Motion , direction of air resistance in N2L

I cant seem to understand why mcx(dot) is not positive on the RHS of ma=F because it is acting in the same direction as the weight, but the answer doesnt agree, please help, I can get the DE but with ...
1
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1answer
65 views

Group theory argument

I'm reading Group Theory in Physics by Wu-Ki Tung and on page 69 in the proof of Theorem 5.3 he makes a group theory statement that I don't get. Let me try give some notation and explanation ...
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1answer
27 views

Integral equation involving Planck radiation formula

I am stuck in solving the following integral equation: $$\sigma T^4=\pi\int_{\lambda_0}^{\lambda_1}d\lambda W_{\lambda,T}$$ where: ...
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0answers
21 views

Tension on the string of a drawn bow.

An archer's bow is drawn at its midpoint until the tension in the string is 0.881 times the force exerted by the archer. What is the angle between the two halves of the string? *Edit: some context, ...
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0answers
6 views

What force should be applied to each axis given a forward angle and a left/right direction?

I have three parameters: up/down angle, left/right angle, and power. The up/down angle can range from 0-90. It determines the forward force applied to my object. 0 means it moves straight forward ...
1
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1answer
30 views

Invertibility of inertia matrices

The inertia matrix is defined, for a discrete body composed of material points $P_i$ of mass $m_i$ whose position vector $\overrightarrow{CP_i}$ with respect to the centre of mass $C$ has Cartesian ...
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2answers
58 views

Velocity and Acceleration

I'm currently studying applications of calculus to the physical world in mathematics. I don't understand how a particle with zero velocity can have a positive acceleration. If the particle is at rest, ...
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1answer
40 views

Physics/Math conversion

I'm having difficulties solving this conversion. I know what to do at first but the way to set this up is a bit confusing:
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2answers
67 views

Mechanics problem. [closed]

A bottle is dropped from a blimp whose height is 1200m. Assume that a= 9.81m/s/s, find the time it takes the bottle to reach the ground.
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0answers
28 views

Notation for Christoffel symbols used by Gödel in “An example of a new type of cosmological solution of Einstein field equations of gravitation”

I have difficult to understand the meaning of the notation used by Gödel in the article cited in the title of this post. You can find it here: http://www.lygeros.org/10552b.pdf In the second page ...
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0answers
15 views

Algebraic determination of asymmetric unit (aka irreducible wedge) in Brillouin zone of lattice

In Solid State physics the reciprocal space is of utmost importance to predict the band structure and thus most of the electrical transport parameters like effective mass, etc. The First Brillouin ...
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1answer
27 views

Impact of weight of the dice

If you throw a 6-sided die there is a probability of 1/6 to throw any specific value. However, this assumes that dice are exactly symmetrical, and we all know that they are not, in reality. Let's ...
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1answer
20 views

Calculate a jetplane's distance from my location

So i was sitting outside my workplace and saw this jet flying. I was really curious if there is a way to calculate the jet's distance between the jet and my location. (I have very little knowledge ...
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1answer
66 views

Trouble with a Statement in Arnold's “Mathematical Methods of Classical Mechanics”

On Pg 6 of Arnold's Mathematical Methods of Classical Mechanics (2nd Edition), there is a line which reads One can speak of two events occuring simultaneously in different places, but the ...
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3answers
2k views

How to solve this problem with trigonometry and by using vectors?

In an assignment I'm asked this: A boat needs to sail to a port that is on a bearing of 065°. The boat sails in still water at a speed of 35km/h. There is a current, moving the water at a speed ...
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2answers
31 views

Physics- Horizontal Displacement

Currently working my way through a maths problem, and I've hit a brick wall. A circus acrobat is launched from a cannon that is aimed at 75 degrees above the ground. He leaves the barrel at a ...
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1answer
27 views

Uniform Circular robot motion

Here is the initial diagram: The robot is moving counter-clockwise around the circle. I am having trouble seeing how they derived the centers of the circles. They have defined the center of a ...
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1answer
43 views

(Integration) Physics problem to find the time before a collar comes to rest on a ring with friction.

If unclear, scroll to the end integral which needs to be evaluated. I need to find $\tau$ from this integration/differential equation but I'm stuck. $$\int\frac{-{\rm ...
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1answer
30 views

2 Second Pendulum Length on The Moon [closed]

This was a physics bonus assignment. I have been trying to solve it for the last 2 hours. Let's say that the density of The Moon and The Earth are the same. Moon radius:Earth radius is $0.273:1$! How ...
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2answers
319 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
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1answer
42 views

Coordinate systems in physics problem (damped pendulum)

A simple pendulum of lenght $\ell$ is vibrating freely (with small oscillations). The pendulum is set into forced vibration by moving its point of suspension horizontally with a Simple Harmonic ...
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0answers
16 views

Quantum Harmonic Oscillators [migrated]

I'm having trouble with quantum harmonic oscillators and I'm not sure how to approach these questions: . I'd really like to get my head around these concepts but I'm struggling to understand fully. ...
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0answers
23 views

determining the fermi velocity via density of states

The problem is to determine the Fermi velocity for a fermion gas at absolute zero. the problem using integrating a function that looks like $$ v = \frac{4\pi V}{h^{3}} m^{3} \int_{0}^{\infty}{ ...
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0answers
25 views

How does the Schrodinger's potential transformer if the metric conformally transformers?

Given Schrodinger's equation $$ (-\nabla^2+V)\psi=E\psi $$ and the conformal transformation $\tilde{g}_{mn}=e^{2\phi}g_{mn}$, how does the Schrodinger's potential $V$ transformer if the metric ...
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1answer
46 views

How to calculate solid angle of a rectangular detector of 20cm x 10cm?

I have an detector of $20cm*10cm$, how can i calculate the solid angle subtended by the detector if the detector is placed at $30$cm apart? Because directly i cannot use the formula ...
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0answers
17 views

How to prove y component of the field is zero throughout the motion?

This is a pure mathematical question, here is a little background for the interested reader, you can jump directly to the mathematical part if you are not interested. background Imagine we have ...
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0answers
42 views

Dealing with negative work [migrated]

Dumb question, I'm working with vector fields right now, and one question on here tells me to assume an object can take on three paths from a to b. (paths not listed here) for times in [0,1] Now ...
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0answers
30 views

How to solve an overconstrained system of equations?

What is the easiest codeable way to solve an overconstrained static model? How does Force Effect https://forceeffect.autodesk.com do it? Given a 10m long bar angled as the hypotenuse of a 3, 4, 5 ...
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1answer
27 views

Finding the range of a cannonball- proof verification.

I asked such a question before but I do learn best by mistakes and corrections.(I didn't fully understand it yet.) I could really use your verification: A cannonball is being fired with a velocity of ...
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1answer
660 views

Damped Harmonic Oscillator and Response Function

This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a driven damped harmonic oscillator, show that the full ...
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0answers
10 views

Calculating line of motion based on turn-rate acceleration

Given initial time, velocity, position, forward acceleration, and (uniquely to my question, it seems) turn acceleration; and given max forward and turn acceleration; and given the time that has ...
3
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1answer
77 views

Definition: Mathematical way to define the “left” and the “right”

How do we define the left and the right, (such as left/right handness) from a mathematical way of definition? How can we explain this definition to some inhabitant of a distant stellar system who has ...
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2answers
3k views

What is the resistance between two points a knights move away on a infinite grid of 1-ohm resistors

On an infinite grid of ideal one-ohm resistors, what's the equivalant resistance between two nodes a knights move away? (please fix the tags, I didn't really know where to put it)
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2answers
86 views

What are some tips/techniques that might help me solve this (brutal) differential equation?

I've been working on a certain physics problem involving differential equation for two years. I've made some progress on it recently, but I've come across another roadblock, namely an integral that I ...
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4answers
6k views

Deriving an equation for the orbital period of a satellite

I'm combining three equations from my physics text book: Newton's law of gravitation: $F = -\frac{GMm}{r^2}$ The centripetal force equation: $F = \frac{mv^2}{r}$ The equation for the speed of an ...