All Questions
Tagged with differentiation homework-and-exercises
290 questions
0
votes
1
answer
59
views
From infinitesimal momentum volume to infinitesimal rapidity & tranverse momentum
I'm trying to derive a relationship given in a paper which is used to obtained a differential cross-section distribution in function of rapidity and transverse momentum of final state particles,
$$
\...
- 125
0
votes
2
answers
46
views
Phases difference
Recently, I learned in my class about harmonic motion and the difference in phase. According to the wikipedia and many other sources, you find that difference by subtracting the phases. Take a look at ...
0
votes
0
answers
1k
views
Divergence of a radial vector
I'm reading an introduction to the Maxwell Equations. The author states that $\textbf E=\frac{e\textbf r}{4\pi\epsilon_0r^3}$ (r is the magnitude of $\textbf r$). Then he derives the Gaussian law from ...
- 1,052
0
votes
0
answers
28
views
Evaluating derivatives with respect to certain vector axis
So, I am trying to work in Spherical coordinates. I have a predefined fixed axis, $\hat{v}_0$, so that $\alpha=\vec{r}.\hat{v}_0$ Now, I am interested in the following:
\begin{equation}
f(r,\alpha)=\...
- 490
0
votes
1
answer
2k
views
Classical Mechanics, The Theoretical Minimum: error in answer to partial derivatives exercise? [closed]
I'm reading Leonard Susskind's Classical Mechanics, The Theoretical Minimum, and I'm on the interlude on partial derivatives. There is an exercise that asks you to find all of the first and second ...
0
votes
1
answer
72
views
Show $\frac{\partial T}{\partial \dot q_j} = m_i \dot r_i^T\frac{\dot r_i }{\partial \dot q_j} $ [closed]
This is a basic result in lagrangian mecanics. Let $T$ be the kinetic energy, $r_i$ be the position of the $i^{th}$ particle in the system I need to show $$\frac{\partial T}{\partial \dot q_j} = \frac{...
- 1,754
0
votes
1
answer
360
views
a mistake related to variable mass system
I'm having a problem with finding my mistake when trying to find the derivative of the momentum when mass is being ejected in a constant rate.
The problem is this - a body in space is burning fuel ...
- 353
0
votes
1
answer
282
views
What is the infinitesimal work done when the force is given by the gradient of a scalar function that depends both on position AND time?
The title is slightly confusing but I didn't know how else to phrase my question.
Basically, this is the situation:
When the force applied to a particle is given by the gradient of a scalar function ...
- 1,373
0
votes
3
answers
174
views
Question about differentiation of tensors
According to Arnab Rai Choudhuri, Astrophysics for physicists Page 363:
$$\frac{\partial \overline A^i}{\partial \overline x^l}=\frac{\partial A^k}{\partial x^m}\frac{\partial x^m}{\partial \overline ...
- 859
0
votes
2
answers
17k
views
What is the derivative of $\dot{\theta^2}$? [closed]
$$\frac{d}{dt}(\dot{\theta^2}) =? 2\dot{\theta}\ddot{\theta}$$
is this correct, or am I missing something?
- 53
-1
votes
3
answers
493
views
The use of the commutators in quantum mechanics: explanations [duplicate]
Considering that I've never studied quantum mechanics before I have need to understand the operator commutator. My start is: $[A,B]=AB-BA \tag{a}$
Now, why must be
$$\left[\frac{\partial }{\partial ...
- 2,575
-1
votes
3
answers
69
views
Vector question, differentials, Electromagnetism
I was reading this demonstration of electric potential in my book:
Let $q$ be a point charge at point $P$
The Electric field created at point $M$ by $q$ is :
$$\vec{E}(M) = \...
- 685
-1
votes
1
answer
22k
views
Maximum electric field of a circular ring
How do you differentiate the equation for electric field of uniform ring
$$ E_x = \frac{kxQ}{(x^2+r^2)^{3/2}} $$to get the maximum at a point? My book says $x = r/\sqrt2$. I tried differentiating ...
- 307
-1
votes
1
answer
4k
views
Lennard-Jones potential, distance $r$ for minimum energy
I'm sorry if the question seems stupid. I found (wikipedia) that the Lennard-Jones potential has it's minimum at a distance of
$$r = 2^{\frac{1}{6}}\sigma.$$
If $U(r)_{min} = -\epsilon$
$$U(r) = 4\...
- 137
-1
votes
2
answers
88
views
Change in areal element
Example 1.7
Calculate the surface integral of $\mathbf{v}=2xz\hat{\mathbf{x}}+(x+2)\hat{\mathbf{y}}+y(z^2-3)\hat{\mathbf{z}}$ over five sides (excluding the bottom) of the cubical box (side 2) in Fig. ...
- 1
-1
votes
1
answer
96
views
Finding solution to this differential equation
In this paper http://arxiv.org/abs/hep-th/9506035 equation (3.11) was written as: $$\frac{\partial L}{\partial u}\frac{\partial L}{\partial v} = -1$$
The author then said p.9 that "approximate ...
- 215
-1
votes
1
answer
149
views
Basic vector calculus: Show that $\nabla \vec{r} = \vec{1}$ [closed]
Show that $\nabla \vec{r} = \vec{1}$
My instructor in my E & M class put the $r$ and $1$ in bold. I am not sure what a bold one means. From my work I get $1ii + 1jj + 1zz$.
- 119
-1
votes
1
answer
569
views
Confusion in differentiation in physics problem [closed]
Here, we had to find theta such that the denominator has the maximum value. Being new to differentiation I basically didn't understand how differentiation solved the purpose:
I basically didnt ...
- 997
-1
votes
1
answer
762
views
Uncertainty in Range of Projectile [closed]
If we are given that a projectile is launched with velocity 10m/s at an angle of $45^\circ$ and uncertainty in angle is of $0.5^\circ$ . What is the uncertainty in the range of projectile.
The problem ...
- 53
-1
votes
1
answer
507
views
Finding the divergence of this force [closed]
I've got to find the divergence of this force,
$$
\mathbf F=\left(x^2+y^2+z^2\right)^n\left(x\hat e_x+y\hat e_y+z\hat e_z\right)
$$
I would know how to do it if the $n$ superscript wasn't there. Any ...
- 9
-1
votes
1
answer
164
views
Given a Postion-time curve/function, how do I find the time spent per unit position?
I have recordings of the position time curve for a given 1D actuator.
I'm trying to find out the time spent per unit length.
To get this relationship, I tried to take an example of a linear function:
$...
- 57
-1
votes
1
answer
51
views
Proving the relation $\frac 1 2 \left[\nabla^2,r \right] = \frac 1 r + \frac \partial {\partial r}$ (quantum mechanics exercise) [closed]
I'm trying to prove this relation in my quantum mechanics exercise book
$$\frac 1 2 \left[\nabla^2,r \right] = \frac 1 r + \frac \partial {\partial r}.$$
Here's my attempt:
Expand the Laplacian ...
- 301
-1
votes
2
answers
418
views
Wave Function Probability calculation [closed]
Redited
The wave function of the particle at a certain instant is given as $$\psi(x)=Ae^{(-\frac{x^2}{a^2}+ikx)}.$$
If $P1$ and $P2$ denote the probabilities of finding the
particle in the range $a$ ...
-1
votes
1
answer
98
views
How we can prove this vector identity?
I was trying to rederive the formula of the angular momentum of electromagnetic field, and all the steps are clear for me except this one which I took from
"Photons and Atoms: Introduction to ...
- 11
-1
votes
1
answer
309
views
Connection between algebraic and analytic method of quantum harmonic oscillator
I am studying Quantum harmonic oscillator,
There are 2 methods to solve Harmonic oscillator one is algebraic method and another is analytic method , Wave functions derived from 2 methods are ...
user212422
-1
votes
2
answers
3k
views
Vector Calculus Computation: Finding the divergence [closed]
Mathematical Methods for Scientists and Engineers page 309, problem 6.
This question asks the reader to show that the divergence of (r/r $^3)=0$, provided that r is not 0. Well, r, I suppose, is the ...
- 101
-1
votes
2
answers
273
views
How can I show that the acceleration vector for uniform circular motion undergoes uniform rotation?
Does it suffice to show that the dot product between the acceleration vector and the derivative of the acceleration vector = 0?
- 39
-1
votes
1
answer
61
views
Simple 2D motion vectors [closed]
I am curious if the initial velocity of $x(t)=-3-4t+2t^2$ can be calculated from only this given in another way than just differentiation, by using the constant acceleration formulas perhaps?
- 1
-1
votes
1
answer
100
views
What is $\frac{\delta (\partial_\kappa \sqrt{g})}{\delta g^{\mu\nu}}$?
Title says it all, is there a closed expression for
$$\frac{\delta (\partial_\kappa \sqrt{g})}{\delta g^{\mu\nu}}$$
where $g = \det g_{\mu\nu}$?
- 1,323
-1
votes
1
answer
518
views
Forced damped harmonic motion, angular frequency at which amplitude is maximum. differentiation [closed]
$$A_0 = \frac{(F_0/m)}{\sqrt{(\omega_0^2-\omega_d^2)^2+b^2\omega_d^2/m^2}}$$
How would I differentiate this with respect to the driven angular frequency (equating to zero) in order to obtain the max ...
- 1
-1
votes
2
answers
89
views
For how long is an objects velocity it's instantaneous velocity at time $t$?
Basically I'm asking if an object's instantaneous velocity at time $t$ is $8m/s$ and its instantaneous velocity at time $t^+$ (idk latex, but basically the t + an infinitely small number) is $10m/s$, ...
-2
votes
3
answers
29k
views
Derivative of kinetic energy [closed]
I read that the derivative of kinetic energy=$F\cdot v$. I tried to differentiate (1/2) mv^2 with respect to time but each time I am getting $m*v$ and not $m*a*v$ which solves to $F*v$.
My efforts are ...
- 274
-2
votes
1
answer
286
views
To prove, $\nabla.(\nabla\phi \times \nabla\psi)$ =0 [closed]
Please Help me solving the problem using levi-cevita symbol :
Prove That, $\nabla.(\nabla\phi \times \nabla\psi)$ =0 where $\phi =\phi(x,y,z)$ & $\psi=\psi(x,y,z)$
- 300
-2
votes
1
answer
3k
views
What is the General formula of gradient of $r^n$? [closed]
so, the question is that r is the separation vector from a fixed point $(x',y',z')$ to the point $(x,y,z)$ and let $r$ be its length.
the answer to the question of what is the general formula of $$\...
- 17
-2
votes
2
answers
250
views
Car Drag Strip Simulation [closed]
I have written an iPhone App for to our local drag strip.
I'm trying to write a physics based information and simulation page duplicating the time slip you receive when you make a pass at a 1/4 mile ...
- 11
-2
votes
1
answer
92
views
Using Gauss' theorem [duplicate]
I am working through some questions and I am stuck on the working of this one:
Where the working to the answer is here:
Can someone explain the highlighted section as I can't see where it comes from?...
- 161
-3
votes
2
answers
118
views
Explain this equation mathematically
$$\Bigl( \frac{\partial S}{\partial T} \Bigr)_H = \Bigl( \frac{\partial S}{\partial T} \Bigr)_M + \Bigl( \frac{\partial S}{\partial M} \Bigr)_T \Bigl( \frac{\partial M}{\partial T} \Bigr)_H$$
How can ...
- 446
-3
votes
2
answers
290
views
Kinematics problem invloving position and time [closed]
An object is moving along X axis with position as a function of time given by $x = x(t)$. Point $O$ is at $x = 0$. The object is definitely moving towards $O$ when
1. $\mathrm dx/\mathrm dt < 0$
...
- 199
-3
votes
1
answer
69
views
Show that $dE/dt = -bv^2$ (Help with differentiation) [closed]
The question is:
Show that $$dE/dt = -b (dx/dt)^2.$$
And the solution is:
...
- 1
-4
votes
1
answer
74
views
Find out which coordinate changes at faster rate [closed]
Suppose we have a particle, which moves along a path (in x-y plane) and say its path is the curve, $ 12y = x^3 $ .
I need to find out which coordinate (x or y) changes at faster rate at any given ...
- 193