All Questions
Tagged with potential-energy homework-and-exercises
394
questions
0
votes
2
answers
3k
views
Gravitational potential energy inside of a solid sphere [duplicate]
I am self-studying classical mechanics. I came across a problem which required me to calculate the gravitational potential inside of a sphere. I found in one of my textbooks that the potential energy ...
- 23
0
votes
1
answer
97
views
Lorentz force from potential- extra term?
I'm trying to verify the E.M potential energy $U= \int{A_\mu J^\mu} = q(\phi - A_j v^j )$ by using the connection:
$$
F= - \frac{\partial U}{\partial r} + \frac{d}{dt} \frac{\partial U}{\partial v}
$$...
- 2,142
0
votes
2
answers
195
views
Marble "rolling" on the graph of a function
Consider a guide for marbles whose profile locally coincides with a function $f(x)$, for example
$f (x) = - \frac{1}{2} x ^ 4 + x ^ 3 + x ^ 2-2x + 1.$
Suppose that the reference system is chosen in ...
- 11
1
vote
0
answers
50
views
Potentials that prevent the phase flow of the system [closed]
I am trying to solve a question that my professor gave.
When a particle moves in one dimension $x$ in a potential $U(x)$ , the resulting motion over a very short time interval is specified by Newton’...
- 9
0
votes
1
answer
330
views
Doubt from Arnold; Mathematical methods of classical mechanics (page 20)
I am trying to do a problem from Arnold; Mathematical methods of Classical mechanics.
But I didn't get the desired result mentioned by the author.
Let $E_0$ be the value of the potential function at ...
- 23
0
votes
2
answers
239
views
Direct calculation of the gravitational potential inside a hollow sphere
I calculated the gravitational potential inside a massive sphere with constant density and got the result:
$$\Phi = -2\pi G\rho R^2 + \frac{2}{3}\pi G\rho R_p^2$$
Where $R$ is the radius of the sphere ...
- 16.6k
4
votes
2
answers
7k
views
Why is the gravitational potential inside a hollow sphere same as that of the gravitational potential on the surface of the hollow sphere? [duplicate]
Gravitational potential inside a hollow sphere is given by $$V(r)=\frac{-Gm}{R}$$ Why is it the same as the gravitational potential on the surface of the hollow sphere, which is given by $\frac{-Gm}{R}...
- 43
1
vote
2
answers
694
views
Lagrange equation of motions for a particle moving in a surface in the presence of gravity
I have to model the dynamic behaviour of a particle solid in a gravitational field.It is for a control theory course. And my background in dynamics is not the greatest. The particle can move left and ...
0
votes
1
answer
382
views
A block starts from rest at the top frictionless slide at a height $h_1$ above the ground and leaves the slide perfectly horizontally
A block starts from rest at the top of a frictionless slide at a height h1 above the ground. The block leaves the side moving perfectly horizontally at a height h2 above the ground. The block ...
0
votes
0
answers
44
views
Why didn't we account for kinetic energy of two stars in conservation of mechanical energy
Two stars of masses 3×10^31kg each, and at distance 2×10^11m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In ...
13
votes
5
answers
4k
views
Why does the incline angle not affect how high a launched object will slide up a frictionless ramp?
I am seeing a problem with the solution given in this book. How did the height of the box have nothing to do with the incline of the ramp? Intuitively it would seem the higher the incline the higher ...
0
votes
1
answer
213
views
Electric Potential, Work, Potential Energy, and Electric Field [closed]
I don't quite understand these concepts. What is the relationship of electric potential with work, potential energy, and electric field?
1
vote
0
answers
71
views
Verifying the equation of motion, expressions of kinetic energy and potential energy and how to examine whether motion confined to a plane or not [closed]
A particle is moving in space such that it is attracted towards a fixed point and is proportional to the distance from the fixed point. Derive the Lagrangian and Hamiltonian of the system. Examine ...
- 111
0
votes
1
answer
205
views
Energy released from destruction of an object [closed]
In the movie “Star Wars: A New Hope”, Luke Skywalker blows up the „Death Star‟. Assume
that the „Death Star‟ is a perfectly spherical spaceship with uniform mass distribution. The mass
of „Death Star‟ ...
- 3
1
vote
1
answer
56
views
Elastic Potential Energy Of Elastic Wire: Two contradictory methods [closed]
Suppose a wire of length $L$, cross sectional area $A$, density $\rho$
and Young's Modulus $Y$ is suspended at one of its ends from a
ceiling, then find its total elastic potential energy due to its ...
- 117