All Questions
5
questions
-1
votes
3
answers
118
views
How can mechanical energy be preserved if the potential energy is negative? [closed]
If I set the upwards direction as positive, the gravitational acceleration $g$ will be negative (and thus, $mgh$ will be negative if $h$ is positive). Thus, the potential energy will be negative, but ...
- 248
0
votes
0
answers
80
views
Substituting the conservation of angular momentum into the Binet formula results in contradiction [duplicate]
Background Information
The lagrangian of a particle in a central force field $V(r)$ is
$$
L=\frac12m(\dot r^2+r^2\dot\theta^2+r^2\sin^2\theta\dot\varphi^2)-V(r).
$$
The particle must move in a plane, ...
- 675
6
votes
3
answers
230
views
Inconsistency of PE to KE conversion in moving reference frames [closed]
Here's a nice trick question to keep you amused over the weekend.
A trolley of unit mass with light frictionless wheels is released to roll down a ramp onto a smooth level surface. The PE lost equals ...
- 26.4k
17
votes
2
answers
7k
views
Lagrangian of an effective potential
If there is a system, described by an Lagrangian $\mathcal{L}$ of the form
$$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$
where $T$ is the kinetic ...
- 377
0
votes
2
answers
453
views
In a CMCS 2-body system, why does the speed of the particles after collision stay the same?
A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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