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Questions tagged [physics]

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

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1answer
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calculating constant deceleration with time

The distance between point A and B is 500m, an object is moving at 50m/s, the object will stop exactly at 500m when it's deceleration reaches zero after 5 seconds, the deceleration is constant, how do ...
0
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2answers
33 views

Solve Equation of Motion when gravity is two dimentional

How does one solve the following system of equation for Θ. Only unknown variables are Θ and t. This is the equation of motion when gravity is two dimensional. WolfarmAlpha succeeded to solve but I ...
3
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1answer
84 views

How to prove $\int_{-\infty}^{+\infty} \frac{x^2}{\cosh(x)^2} dx = \frac{\pi^2}{6}$?

I found the integral in the Fermi gas theory. There is an approximate formula for specific integrals: $$\int_{-\infty}^{+\infty}F(\epsilon)\frac{\partial f(\epsilon)}{\partial \epsilon}d\epsilon\...
12
votes
2answers
96 views

Are Transitions in a Hydrogen Atom Unique

So there was a question on a past exam paper of a test I have recently taken and despite the test being over I feel the need to know the answer. I am a physics major and the test was a generic test on ...
3
votes
1answer
32 views

Van der Waals integrated in Clausius-Clapeyron [on hold]

I have inserted Van der Waals equation into Clausius–Clapeyron equation and now Im stuck here. $$\frac{dP}{dT} = \frac{a } { RT^2/P + bT }$$ $P$: pressure $T$: temperature $a$: Delta sublimation ...
0
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1answer
13 views

Proof that $\int_0^{\Lambda}\frac{x^{d-1}}{(1+x^2)^2}dx$ remains finite for $1<d<4$

For a phase transition in Landau theory, I need to show that $$I=\int_0^{\Lambda}\frac{x^{d-1}}{(1+x^2)^2}dx$$ remains finite for $1<d<4$, as $\Lambda \rightarrow \infty$. Now I know, that $$\...
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1answer
38 views

Force exerted on earth in the air vs on the ground

A baseball falls through the air and lands on the ground. Compare the force with which the ball pulls the earth upward in the air and on the ground I don't understand why they wouldn't just be equal?
0
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1answer
13 views

Calculating all components of Projectile motion

I have a Physics project which requires me to find football passes and calculate based on the data given. I need to find the Initial Velocity, Angle of Release, and max height with only the time and ...
2
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1answer
47 views

(-1)^Matrix - general matrix exponential

I am going through a physics lecture where the following is stated: $$(-1)^\hat n = \left( \begin{matrix}1 & 0\\ 0 & -1\end{matrix} \right) := \sigma^z$$ The $\hat n$ stands for the ...
1
vote
1answer
97 views

Units of Function [on hold]

What will be the unit of a function $f(V)=e^V$, where $V$ is in Volts? I mean what will be the unit when the function is written in an implicit format and what will be the units when function has a ...
2
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1answer
60 views

Solving the nonlinear differential equation $ m \ddot x +\alpha x + \beta x^3 = 0$

As the header says: I want to solve the differential equation $ m \ddot x +\alpha x + \beta x^3 = 0$, with initial conditions $x(0) = -x_0$, $\dot x(0)=0$. It comes up in the solution to the equations ...
0
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0answers
53 views

whats the interpretation of $\int y + d(y)/dx$ [closed]

0 down vote favorite Does it make sense to sum the surface defined by a curve and the tangent at some points of the curve? The motivation of this question is that I need the calculate somehow the ...
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1answer
73 views

Calculus and Physics for beginners. Suggestions for books [on hold]

I would like to start brushing up on some math and physics. Mostly math that theoretical physicist use. Want to start with the basics so wanted some suggestions on books that'll help me with this. I ...
0
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1answer
35 views

Physics Problem Involving Trap Door Supported by Rope

A uniform trapdoor shown below is 1.0 m by 1.5 m and weighs 300 N. It is supported by a single hinge (H), and by a light rope tied between the middle of the door and the floor. The door is held at the ...
0
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1answer
31 views

What does the dot product give us?

I am working through some questions and I have an equation for the position vector of a projectile, namely r, and it's given that k is the vector directly vertical to the starting point of the ...
4
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1answer
40 views

Finding moment of inertia of a cone: Why can't I integrate like this?

I have a cone (vertex at $(x,y,z)=0$) with height $H$ and radius $a$ (radius of the base). Here is a picture: I want to find the moment of inertia around the $z$-axis using calculus. I know the ...
1
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2answers
36 views

Finding maximum height with initial velocity.

An object is projected from the surface of Earth with a velocity of one mile per second. What is the maximum height it will reach? My solution for solving this was to use the following equation:...
0
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0answers
31 views

What shape is a lens?

(I'm not entirely sure whether this should go here on on the Physics stack exchange. Tell me if I'm wrong :)) To my understanding a lens can be made by intersecting two spheres. This causes spherical ...
2
votes
1answer
39 views

Is there an elegant or easier way to solve this system of equations?

This is a physics problem that involves an inelastic collision and a system of equations that I want to solve. I know the values of $v_1,m_1,v',\Delta E$ where $v'$ is the velocity of the two objects ...
0
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2answers
30 views

Net force on ramp

I'm having difficulty understanding the free body diagram for the forces acting on a ramp when a block is sliding down it. Say a block of mass $m$ is accelerating down a ramp with mass M with ...
1
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2answers
19 views

Displacement Equation in a Vector Field

While building a program for a college level Physics course, I have a vector field representing force such that $\vec F = F_x(x,y) \hat{i} +F_y(x,y) \hat{j}$. I am asked to create a program which ...
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1answer
64 views

Finding the distance if speed is $v=\frac{63}{200}t\cos t$

So I have the following exercise: Student is running in the straight corridor with the spdeed $v = \frac{63}{200}t\cos t$ m/s where $t$ is the time that has passed since the student started running ...
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0answers
16 views

Issues concerning the 3-particle phase space in d dimensions

I am not sure whether this problem fits better in the physics section or not. Recently I came across a problem concerning the 3-particle phase space. I am trying to show, that the 3-particle phase ...
2
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1answer
78 views

If I square a value units of radians, is the result in units of radians squared or is it still radians?

I am writing a paper on circular motion. A function given is $$T=Msω^2L$$ The units for $ω$ are $\text{rad}/s$. What are the units for $ω^2$? Are they $\text{rad}^2/s^2$ or $\text{rad}/s^2$? If they ...
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1answer
64 views

What is the number j?

So, I've been hearing that $e$ and $i$ are not the only numbers out there that are represented and known by a single letter in the English alphabet. Apparently, there is also the number $j$. What is ...
0
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1answer
35 views

How to apply integrals and derivatives in physics?

We have learned how to count integrals and derivatives in maths and we were told we would use this in physics but how do I know when to use integral and when I should differentiate? I know that ...
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0answers
41 views

Mathematical calculation of work exercise?

So I have the following exercise: Find the work that is necessary to pump empty the cylindrical motor oil tank, it the tank is placed up on the base. The height of the tank is 202cm, radius of the ...
1
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0answers
44 views

How to calculate force from source on a wall?

I've got the following question I'm trying to answer, however I'm just not really sure where to start. I assume I need to find the pressure on the plate and then integrate over area to find the force, ...
1
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1answer
12 views

Infinite Subcritical Reactor with a plane Source; Deriving analytical solution with boundary conditions

This might as well be a mathematics question since I am only looking for a way to solve a basic model of the neutrondistribution in an infinite plane subcritical reactor. So the model for the ...
0
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1answer
21 views

Find max value from two known points and the average value of all points

From an unknown number of points, I have two points, e.g. (0,105) and (100,108). I also know the average, e.g. 110, of all the unknown and known points. Would it be possible to estimate a maximum ...
2
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1answer
39 views

Difficult Region of Integration Involving Gauss's Theorem

I'm told to use Gauss's Theorem to compute the flux of a field $\vec F = <x,y^2,y+z>$ along the boundary of the cylindrical solid $x^2+y^2 \le 4$ below $z=8$ and above $z=x$. I know by Gauss's ...
2
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1answer
30 views

Finding Projectile Angle With Different Elevation When Velocity And Range Are Known

I'm trying to derive a formula to find the angle $θ$ required to hit a target that may be higher or lower than the initial launch position. My known variables are $g, v_0, y_0, y_f, x_0, x_f$ where: ...
5
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1answer
60 views

Physical dimensions in math

I was interested in the idea of of formalising the idea of physical dimensions with an algebraic structure containing "all physical quantities of any type". You'd need: Scalar multiplication over the ...
0
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1answer
20 views

Magnetic field at points on the circuit

I know magnetic field lines due to a circuit always form closed loops. Therefore $\nabla \cdot \vec{B}=0$ everywhere (even at points on the circuit). However due to singularity, magnetic fields are ...
2
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0answers
23 views

Second order approximation in rocket equation

The simple rocket equation with no external forces can be derived in multiple ways. Assume a rocket with mass $m$ and velocity $v$ at time $t$ that looses the mass $-dm > 0$ with relative ...
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4answers
50 views

Why km$^2$ and not (km)$^2$?

Why don't km$^2$, cm$^3\ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.
2
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0answers
19 views

solving a system of 2nd order differential equations with 3 variables

I'm creating a simulator for spacecraft that models orbital mechanics. It's simple enough to find the magnitude and direction of gravitational force, but I want to be able to time accelerate without ...
0
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0answers
19 views

Einstein: Is invariance of the sum of squares of coordinate differences of a rigid separation sufficient to determine Euclidean space?

I didn't include my source in my original version of this posting because I didn't want to get an answer that was out of deference to the the source rather than based on reason alone. But I didn't ...
0
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4answers
33 views

$A = 5\sin120\pi t$, find rate of change at $t = 1s$.

I'm in grade 12 advanced functions. Here's the question I'm having trouble with; The current in a household appliance varies according to the equation $A = 5 \sin 120 \pi t$, where $A$ is the current,...
0
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0answers
19 views

Identity for a set of Gaussian distributed variables

For a problem in magnetism, I have to calculate the expectation value (average) for the variable $S_x=\cos \theta$ such that $$\langle \cos\theta\rangle = \mathfrak{R}(\langle e^{i\theta} \rangle)= \...
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1answer
54 views

Tension Force on The Cable [closed]

I've been given a problem. I need to work out the tension force on the cable. Imagine there's a cylinder and it has a height of 0.51m and diameter of 7.9m and a density of $550kg/m^3$ Also, the ...
0
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0answers
19 views

What does it mean by leading contribution in error calculation?

I have an error as 0.012480556357032935 The question asks to find propotionality to another variable and the leading contribution in error? Would that mean 0.012?
1
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1answer
23 views

Resolving vector equations to find angle

Say we have a beam hinged to a wall. The beam is length $l$, and of mass $2m_1$. The other end of the beam is supported by a rope which goes over a pulley and is connected to a weight of mass $m_2$. ...
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0answers
26 views

Transform a non-linear second order ODE

Hi I'm stuck on the following problem: Given a projectile with position $\mathbf{r}(t)=[r_x(t),r_y(t)]$, velocity $\mathbf{v}(t)=[v_x(t),v_y(t)]$ and acceleration $\mathbf{a}(t)$, we can approximate ...
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2answers
49 views

Solve a differential equation in a radioactive decay system

I have a radioactive decay system to solve for $x(t)$ and $y(t)$ (no need for $z(t)$): $$\begin{cases}x'=-\lambda x\\ y'=\lambda x-\mu y\\ z'=\mu y\end{cases}$$ with the initial conditions $x(0)=1,y(0)...
0
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1answer
50 views

Horizontal angular rotation speed

Below is the question I'm not sure I've properly solved. A smooth bead of mass 100g is threaded on a light inextensible string of length 70 cm. The string has one end attached to a fixed point A and ...
0
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2answers
28 views

Need verification for this integral

I have to solve an integral. It's the equation to calculate the rectified value of the output voltage generated by a controlled half-wave rectifier (with a thyristor). $$U_{d}(\alpha) = f(U, \alpha) $...
0
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1answer
32 views

Select 6 mirrors on 6 faces of a room (a cube),when you go to the center, how many selves you can see from one mirror?

Select $6$ mirrors on $6$ faces of a room (a cube),when you go to the center, how many selves can you see in one mirror ?
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2answers
33 views

How do you evaluate the tension force if the coefficient of friction between the objects K and L is $0.6$?

How do you evaluate the tension force if the coefficient of friction between the objects K and L is $0.6$? So the system is accelerating, whence we have to consider that $$\sum F_x = m_1a$$ $$...
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0answers
19 views

Gauge invariance of the Hamiltonian for particle on external electric field

Let us assume we consider a problem of free electrons in an external electric field $$\hat{H}(\mathbf{r})=-\frac{\hbar^2}{2m}\nabla^2-e\Phi(\mathbf{r},t),$$ where $-\nabla \Phi(\mathbf{r},t) =E\...