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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-3 votes
0 answers
20 views

b) Compare the velocity of the balls when they hit the ground.

Three balls of equal volumes are dropped from rest simultaneously from a height of 40m. The masses of the balls are 5 kg, 10 kg, and 15 kg.
0 votes
0 answers
28 views

How To Measure Work Done Against Friction On A Non-Linear Path?

I've been trying to solve how to find the Work done against friction as a ball rolls down a curve, but haven't been able to find anything matching what I want online. The solution I have came up with ...
15 votes
3 answers
90k views

How to prove the derivative of position is velocity and of velocity is acceleration?

How has it been proven that the derivative of position is velocity and the derivative of velocity is acceleration? From Google searching, it seems that everyone just states it as fact without any ...
5 votes
2 answers
119 views

geometrical/physical interpretation of multiplication of real numbers (including negative)

In calculus we see that the derivative has a physical interpretation as speed, and a geometric interpretation as slope, and that they are helpful when thinking intuitively about that concept. But this ...
-2 votes
0 answers
33 views

Calculate distance from accelerometer .

I'm trying to calculate speed from g-force values from an accelerometer. I get accelerometer readings at 100Hz and want to find the fastest speed over 3 consecutive values (0.03s). I multply ...
1 vote
1 answer
1k views

Two particles moving at consant velocity: how close do they get?

A particle was at point $P_1$ at time $t_1$ and is moving at the constant velocity $\vec{v}_1$. Another particle was at $P_2$ at $t_2$ and is moving at the constant velocity $\vec{v}_2$. How close did ...
0 votes
0 answers
8 views

Metric Multidimensional Scaling for Geometric TDoA Array Calibration

Background I'm following this paper, and this Matlab code by the author (see Slide 4), in an attempt to implement metric multidimensional scaling for the calibration of geometric Time-Delay-of-Arrival ...
2 votes
1 answer
82 views

Performing receiver localization in media with non-trivial refraction properties using TDoA

Problem. I have a radio transmitter, with known location $\langle t_x, t_y, t_z \rangle$, embedded in a medium whose index of refraction varies as a known function of depth: $$n(\text{depth}) = a-be^c$...
0 votes
0 answers
23 views

How To Use A Line Integral To Calculate The Work Done By An Object Falling Down A Parameterised Curve?

I am trying to calculate the work done by a unit mass which falls along a parabola from (5,25) to (0,0) (where the gradient at (0,0) is 0). My solution was to use a line integral. I parameterised the ...
-5 votes
1 answer
84 views

Solving $\ddot r=-\frac{GM}{r^2}$ [closed]

In finding a comet's equation of motion, I derived this: $$\ddot r=-\frac{GM}{r^2}$$ I have never encountered ODE like this before this time. How do I solve $r$ with respect to time, $t$?
-4 votes
0 answers
101 views

A very hard gaussian integral

There is an integral I read in a book that I don't understand. First I have equation $(4.56)$ like this: \begin{align*}& \exp(-\frac{1}{2}\sum_{j=1}^{n_2}\sum_{\alpha_1,\alpha_2\in D} \hat{G}^{\...
1 vote
1 answer
82 views

Gravity Differential Equation

Is it possible to solve this system of differential equations in terms of $G$? $$r''=\frac{-Gr}{\sqrt{\left(r^2+(1-s)^2\right)^3}},\ s''=\frac{G(1-s)}{\sqrt{\left(r^2+(1-s)^2\right)^3}}$$ with initial ...
1 vote
0 answers
27 views

Gravitational geons: an explanation for mathematicians

The Notices of the AMS has a column that is What is...?, I would like to ask in the spirit of this journal about a subject in which I'm interested. I wondered if some user can to expand the ...
0 votes
1 answer
914 views

Direction of acceleration in Simple Harmonic Motion.

A particle of mass = 0.5kg, is attached to a spring of natural length = 0.6m and modulus of elasticity = 60N,and the setup is on a horizontal smooth table. The other end of the string is attached to a ...
0 votes
0 answers
31 views

Simple conservation of momentum question...am I right?

I was doing a very old Applied Mathematics exam (from the 70s... yeah I lead a sad life) and came across the following problem. A shell is fired from a gun mounted on a carriage which is moving ...
-1 votes
2 answers
92 views

How much of the earth can see the moon? [closed]

I framed this into 2d. If you draw two circles, get the common direct tangents, then you need to find the angle between the two intersection points for the two lines and the bigger circle. Except I ...
2 votes
1 answer
2k views

Neumann condition and Dirichlet condition at the same point

I am studying heat equation on a 1-D bar. We now that Neumann conditions at both ends leads to a singular matrix (for finite element methods) in equilibrium. Adding an initial condition can lead to ...
20 votes
10 answers
17k views

Do infinity and zero really exist? [closed]

From the first day that I entered college, I was wondering about the relationship between some basic mathematical abstract concepts and nature. I'm going to explain them here and you may find them a ...
2 votes
4 answers
124 views

Why my expression for acceleration doesn't work?

So i have an object that moves in a straight line with initial velocity $v_0$ and starting position $x_0$. I can give it constant acceleration $a$ over a fixed time interval $t$. Now what i need is ...
0 votes
2 answers
41 views

Prove when Instaneous Velocity is equal to Average Velocity with Constant Acceleration

Assume constant acceleration. It seems that average velocity over some time interval [t1, t2], will be equal to the instantaneous velocity at the midpoint t = 1/2[t1 + t2]. I'm wondering how you might ...
0 votes
1 answer
53 views

Solving $\int_{-\pi}^\pi \delta[E-A-B\cos x-C\cos (2x)]$

I'm trying to evaluate a delta function integral for the density of states- $$g(E)\propto \int_{-\pi}^\pi \delta[E-A-B\cos x-C\cos (2x)]$$ I don't know how to go about this. There's also one subtle ...
-2 votes
0 answers
19 views

Find the velocities after impact and the loss of kinetic energy. [closed]

A sphere of mass 3 lbs., moving with a velocity of 7 ft./sec., impin ges directly on another sphere, of mass 5 ha.. at rest after the impact, the velo cities of the spheres are in the ratio of 2:3. ...
0 votes
1 answer
22 views

Find a formula/function based on dataset

I have an example dataset with each row having two variables. The shown data uses Time and Distance Time Distance 0.2388839976 212.54885537138 0.3349551193 337.83087805091 0.3703744125 398....
2 votes
2 answers
97 views

How can I solve a differential equation of the form $c_1 \ddot{x}^2 + c_2 \ddot{x} + c_3 \dot{x}^2-c_4 =0$?

The solution to it will give us the eqs. of motion of a car moved by a constant force due to combustion of fuel at the engine that produces the main torque at the wheels and that is "fighting&...
0 votes
1 answer
43 views

Understanding complex exponentials as solutions to differential equations

I am a physics undergraduate working through of Jackson E&M (3ed)'s section on solving Laplace's equation in cylindrical coordinates. I am consciously asking this question on Math stack. I have ...
0 votes
0 answers
11 views

Diffraction Intensity = Fourier Transform of the Autocorrelation

I'm trying to understand how x-ray diffraction intensity is related to the Fourier Transform autocorrelation function. In the work below, $\rho(\mathbf{r})$ is the electron density of a molecule/...
1 vote
1 answer
38 views

Mechanics of a weighted rod held at one and

We need to show that the tension in the rope, T, is = to 2Mgcos(theta) I've taken Moments about A but keep getting T = (1/2)Mgcos(theta). I've ignored the moments at C as they are in equilibrium ...
0 votes
1 answer
43 views

Work of weight force

I'm trying calculating the work of weight force of a punctiform mass, free falling from an height L . We know that total work along the path is given by dot product between force and displacement, ...
0 votes
1 answer
61 views

Physical interpreation regarding heat equation

I have included image of a problem from Oxford. I was able to do the question. However, i am stuck at the last part which asks about the physical interpretation. I don't have a good background in ...
4 votes
1 answer
400 views

Ampère's law with ellipse

Background information first: Using Ampère's law we can find the magnetic field due to a current, I. We do this with a line integral around a closed path encompassing the current (e.g. long straight ...
0 votes
1 answer
37 views

A particle is executing oscillations about the origin on the X-axis. Its potential energy is $U(x)=k|x|^3$.Find ansatz of integral wrt parameter.

A particle of mass $m$ is executing oscillations about the origin on the X-axis. Its potential energy is $U(x)=k|x|^3$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then ...
0 votes
1 answer
1k views

Given the density of water and the gravitational force of the earth, calculate the force

So I'm taking calculus 2, having never taken physics and I'm having some trouble understanding the problems we are at. I'm trying use integrals to calculate the force required to pump a container of ...
1 vote
0 answers
53 views

Systematic way of solving this charge-placement problem without brute force

This is a problem I encountered on an exam. I understand the problem and what needs to be done but I cannot figure out a way to solve it systematically other than brute forcing. It deals with physics ...
1 vote
1 answer
48 views

Deriviation of terminal velocity with faulty results, under condition that $f=-cv^2$

Note: There's a similar problem to this (https://math.stackexchange.com/questions/2796694/how-to-derive-an-equation-for-terminal-velocity-assuming-air-resistance-is-some#:~:text=Taking%20proper%20sign%...
1 vote
1 answer
35 views

the centroid of a plane area - how to interpret 1/2 in the summation formula for Mx?

Please explain why "1/2" appears in the following summation. My understanding is that Mx = y*(dA), so I'm looking for an interpretation of the 1/2 factor there especially, as for y=f(x) and ...
1 vote
1 answer
22 views

Full derivation of impulse formula for collision response

The wikipedia page says that the equation for impulse-based collision response is: \begin{equation} j_r = \frac{ -(1 + e) v_r \cdot n } { {m_1}^{-1} + {m_2}^{-1} + ({I_1}^{-1}(r_1 \times n) \times ...
1 vote
0 answers
51 views

Two operators multiplication in the Baker-Campbell-Hausdorff Lemma

When I was learning the transformation from the Schrodinger picture to the interaction picture in quantum mechanics, I have to use the Baker-Campbell-Hausdorf Lemma, \begin{align} e^ABe^{-A}=B+[A,B]+\...
0 votes
0 answers
36 views

How would we calculate the density of particles inside a 1 dimensional Universe?

How would we calculate the density of particles inside a 1 dimensional universe. The particles can only interact with each other through Newtonian gravity and will pass right through each other. the ...
0 votes
1 answer
47 views

What mathematics books would be good to get an understanding of Lie Groups and how they relate to the symmetries of fundamental particles?

I have a math background and am familiar with multivariable calculus but seem to get lost when I read how it may be related to "gauge symmetries" of fundamental particles. The nuts and bolts ...
3 votes
1 answer
98 views

Equilibrium problem with 3 unknown forces | Hanging mass

This problem is related to my previous question on the generalized Lami's theorem. I would like to see how you solve this problem and compare with my solution. My motivation for this problem is that I ...
2 votes
2 answers
30 views

Double delta function value

I have a question from a past paper of a university physics course. "Calculate $\int_{-\infty}^{\infty}\delta(y-x)\delta(y-z)dy$" We believe the answer is $1$ only if $x=z$, otherwise the ...
0 votes
1 answer
97 views

It is possible for a (electromagnetic) wave equation to have as a solution a finite-duration/compact-supported function? Any closed-form examples?

A) It is possible for a wave equation to have as a solution a finite-duration function? Any closed-form example? (please share the specific wave equation with its finite-duration solution, showing how ...
0 votes
0 answers
34 views

additivity of elements in Baker–Campbell–Hausdorff formula

When I was learning the interaction picture of the Hamiltonian, the usual way to convert it from the Schrodinger picture is using the Baker–Campbell–Hausdorff formula, \begin{equation} e^ABe^{-A}=B+[A,...
-1 votes
1 answer
32 views

Questions on direction of dot product

So i am having problems with understanding that if two forces (suppose in parallelogram law of addition of two vector) the resultant has the same direction as the diagonal between them. So theta (...
1 vote
0 answers
35 views

Equation containing $\arcsin$ as well as square root.

I was studying physics for an upcoming exam and found this in a practice sheet : A source S is oscillating between A and C with its position varying with time as $\displaystyle y (\text{in metres})=...
1 vote
1 answer
926 views

How to calculate drag force vector

I am trying to calculate drag in 3D, and I came across the formula $$F_d = \dfrac{1}{2}\cdot C_d \cdot \rho \cdot v(t)^2 \cdot A$$ I understand how this formula is reached, as a proof is given ...
0 votes
2 answers
1k views

Linearize Shifted Exponential Decay

I'm just having trouble linearizing a quick function I'm graphing. The function is of a shifted exponential decay from a capacitor : $V(t) = V_0e^{-t/\tau}+V_1$. I previously had the function without ...
2 votes
2 answers
92 views

Is curl of a particle's velocity zero?

The question Consider the motion of a particle specified by $\mathbf{x} (t): \mathbb{R} \mapsto \mathbb{R}^3$, where $\mathbf{x} = (x_1,x_2,x_3)$ in cartesian coordinates. The curl of its velocity $\...
1 vote
1 answer
290 views

Verlet Integration to Approximate Planetary Orbit: The First Time Step

I'm currently working on a simulation of a planet orbiting binary stars, which I want to use Verlet integration to approximate. The formula is as follows: $\mathbf{p}(t_2) = 2\mathbf{p}(t_1) - \...
0 votes
1 answer
66 views

How to calculate the new position at time t of bodies with variable acceleration?

Intro For an N-body simulation of calestial bodies I need to calculate on the one hand the accelerations of the calestial bodies based on the received gravitational forces [done] and on the other ...

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