All Questions
18 questions
-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
10
votes
7
answers
2k
views
What can go wrong with applying chain rule to angular velocity of circular motion?
Lets say I have a circular motion, like this:
I know that:
$$\omega = \frac{\text{d} \phi}{\text{d}t}$$
Mathematically, what I am doing wrong, when I attempt to apply the chain rule in the following ...
- 597
4
votes
3
answers
2k
views
What does "Just before" and "Just after" really mean in physics problems?
So I'm stuck in a dynamics problem that asks what is the acceleration of a body just after A, where A is the point that separates the motion of the body from a curvilinear path to projectile motion. ...
1
vote
1
answer
177
views
Find $v(t)$ and $x(t)$, How do I treat $δt$? [closed]
We apply a force to a particle with a mass $m$ and inicial velocity $v_0$:
$$ F(t) = \left \{ \begin{matrix} 0 & \mbox{ $t<t_0$}
\\ \frac{p_0}{\delta t} & \mbox{ $t_0<t<t_0 +\...
- 39
0
votes
2
answers
1k
views
Prove the Total Mechanical Energy of the System is Conserved via Differential Equations [closed]
Consider the dynamics of a particle P shown: Particle in 3D space with Radius r
Newton's second law states that:
$$\frac{d}{dt}(m\dot r) = \mathbf F$$
where, $\boldsymbol{r}$ is the position vector ...
- 129
1
vote
1
answer
287
views
A problem in newtonian physics [closed]
Hello! I have solved problem 89 using analytic way, i.e, the length of the string will always be constant, so repeated substitutions and differentiating will make way(i got answer as "c"). But is ...
user228422
0
votes
1
answer
213
views
Lagrange's equation derivation Kinetic energy
I'm trying to reach Lagrange's equations by D'alembert's principle.
$$\sum_{i=1}^N (m_i\ddot{\mathbf{x}}_i - \mathbf{F}_i)·\frac{\partial\ddot{\mathbf{x}}_i}{\partial q^\alpha}=0$$
or
$$\sum_{i=1}^N ...
- 39
0
votes
1
answer
274
views
Kinetic energy derivation: Why is $\frac{d \mathbf v}{dt} \cdot \mathbf v= \frac 12 \frac{d}{dt}(v^2)~?$
In Goldstein's Classical Mechanics 3rd edition, page 3, the Kinetic energy is derived by considering the work done on a particle by an external force $\mathbf F$ from point $1$ to point $2$ $$W_{12}=\...
user138458
1
vote
1
answer
64
views
Angular dependence of the element of mass of an ellipse
I have an ellipse (a ring, not a disk; its center of mass in $C$) with a constant linear density and mass $m$, with semi-axes $a>b$; $\alpha$ is a dynamical angle describing the orientation of the ...
- 155
-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
-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
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
2
votes
1
answer
122
views
a problem on finding acceleration by differentiation
The displacement of particle along the $x$ and $y$ axis is
\begin{cases}
x(t)=\omega t-\sin\omega t\\
y(u)=1-\cos\omega t
\end{cases}
Upon differentiation, the velocity is
\begin{cases}
v_x(t)=\omega\...
2
votes
2
answers
318
views
Derivation of velocities in the Coriolis force
In Fitzpatrick's Newtonian Dynamics book on the Coriolis force, he states
\begin{align}
v_{x'}&\simeq V_0\cos\theta-2\Omega t V_0\sin\lambda~\sin\theta \tag{433}\\
v_{y'}&\simeq-V_0\sin\...
- 1,629
1
vote
2
answers
66
views
Trouble with derivation in an equation for Newton's Law of Angular Motion
I'm an autodidact and can't follow the part after "it is easily seen that"... which is the 31st equation:
Shouldn't it be:
$m_i\,{\bf r}_i\times \frac{d^2{\bf r}_i }{dt^2}= \frac{d}{dt}(m_i r_i \...
- 13
2
votes
1
answer
1k
views
Taylor series expansion of $\ln$ and $\cosh$ in distance fallen in time $t$ equation
I want to find the Taylor expansion of $y=\frac {V_t^2}{g} \ln(\cosh(\frac{gt}{V_t}))$
I have tried using the fact $\cosh x= \frac {e^x}{2}$ for large t, which works, I just need help on small values ...
- 345
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
1
vote
1
answer
384
views
Question concerning the Feynman Lectures of Physics
I am reading the Feynman lectures and at this point http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S3 it says as follows:
The time derivate of the potential energy is
$\begin{equation}
\...
- 527