All Questions
Tagged with potential-energy homework-and-exercises
394
questions
0
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1
answer
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What are the points to note in a spring+block system? [closed]
This is the solution to a question related to spring+block system, and I have some doubts regarding the concept behind this question
The solution reads
The velocity of the block increases till the ...
- 83
2
votes
0
answers
50
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Energy of a spherical shell
System: spherical shell with surface density.
Objective: calculate potential energy.
I found energy through potential.
Next, I found the formula for energy through the field, which gives two ...
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0
votes
1
answer
59
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Deriving expression for gravitational potential energy around a mass, $M$, using vectors
(I think my question will be somewhat related to this one: Deriving gravitational potential energy using vectors .)
I know the change in the potential energy associated with a conservative force, $\...
0
votes
1
answer
56
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
1
vote
1
answer
130
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Why can we ignore the work done by gravity?
I am working through the problem above, starting with part (d). By the conservation of energy setting the spring in equilibrium as $y_0$ as the difference in length of the unstretched spring to the ...
0
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0
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27
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About reference of potential energy
I have an exercise with a pendulum starting at horizontal position, then we give it a velocity of 5m/s pointing down, $z=0$ at this horizontal position and potential energy = 0. This confuses me ...
5
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3
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2k
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If a car is *accelerating* uphill, does it *gain* kinetic energy?
I had an exam yesterday on physics (9th Grade), there was a question that confused me a lot. It said: "If a Gas Car is accelerating uphill, what happens to its G.P.E and K.E?"
A: It loses ...
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107
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Finding the Equation of motion for a vertical rotating disc with an added mass
I have been trying to figure out the equation of motion of a rotating disc with an added mass fixed on the surface of the disc at a certain distance $r$ from the disc's centre point.
I have ...
1
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1
answer
163
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Why is there a *minimum* energy for a particle to be captured in a $r^{-3}$ potential?
I was stuck in a central force problem from David Morin's Book "Introduction to Classical Mechanics".
The problem states that suppose there is a particle of mass $m$ moving under the ...
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1
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2
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217
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Lagrangian function of a mass-spring-system with deflections in 2D [closed]
I’m looking for the lagrangian function of the following problem (as seen in the picture). We have a mass connected to two springs. We can deglect the mass in two dimensions.
My main problems are:
...
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0
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45
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Question about condition for oscillation of a physical system in Lagrangian mechanics
I can't answer the following question about a (simple) physical system I have studied using Lagrangian mechanic techniques.
So, we have a straight rigid rod in a horizontal plane, symmetrically fixed ...
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1
answer
93
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Potential energy involving both elastic and gravity
A block of mass $m$ is placed against an ideal spring as shown. Initially the spring (of force constant $k$) is compressed by a distance $s$. The block is then released and slides a distance d up the $...
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2
answers
67
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Minimum initial velocity to avoid collision [closed]
I'm having problem with the solution of this question:
Two material points with mass $m$ move along a horizontal axis subjected only to Newton's gravitational force law. At the instant $t_0=0$, one ...
- 237
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1
answer
98
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Triple integral gravitational potential between point and sphere [closed]
Problem for self-study: Gravitational potential between a point $\mathbf a$ and a uniform sphere, leaving out gravitational and density constants
$$
V(\mathbf{a})=\int\int\int\dfrac{1}{\vert\mathbf a -...
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3
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192
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I know that electric potential energy is defined for a system of charges, not for a single charge. But what about electric potential?
My professor explained me in the best manner possible about the electric potential energy and why it is NOT defined for a single charge, BUT my question is as Electric potential is just electric ...
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4
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3
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250
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Why is my answer for height negative?
Question is simple. A ball is thrown upwards with initial velocity $v_0$. How high does it go up?
Assume down is negative and up is positive and no air resistance.
KE at bottom = PE at the top:
$\...
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102
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Change in potential and kinetic energy after a photon is absorbed by a electron
This is a question from the AP Physics 2 2022 FRQ. Why does the potential energy of the atom and the kinetic energy of the electron decrease after a photon is absorbed? Shouldn't both of them increase?...
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1
answer
22
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Finding the spring constant and magnitude of acceleration when it is dropped with the top attached to a ceiling [closed]
I've tried finding the potential energy by using PE = mgh then using PE = 1/2kx^2 to find k and setting PE = KE to find PE using velocity but neither is correct when finding the spring constant. I don'...
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1
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85
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Schrödinger-Propagator for combined linear and harmonic potential
Given the Hamiltonian
\begin{equation}
H = \frac{p^2}{2m} + V(x)
\end{equation}
The propagator for a pure harmonic potential of the form
\begin{equation}
V(x) = \frac{1}{2} m \omega^2 x^2
\end{...
- 141
1
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1
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26
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Right displacement in spring potential energy [closed]
I have a doubt in general, the above problem is an example.
Here , the elastic string can be treated as a spring and we know the potential energy of a spring is $\frac{1}{2} k (x_f-x_i)^2$
So , ...
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3
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67
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How do velocities become equal when potential energy is maximum? [closed]
I was given this diagram and asked to find the maximum potential energy during the subsequent motion if one of the blocks is projected with a kinetic energy K initially.
So I did reach upon the answer ...
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1
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24
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Restriction to a region of potential energy [closed]
A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when?
(A) U(x) > E.
(B) U(x) < E.
(C) U(x) = 0.
(D) U(x) ≤ E.
I ...
-1
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1
answer
128
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From my reference frame, why does the Earth need a huge kinetic energy [$0.5M_E(11200)^2=3.75*10^{32}$ joules] to escape me? [closed]
I wake up screaming into the void, when I see the Earth almost touching me but going away from me at 11.2 $km/s$.
I don't remember what happened before I woke up. I faintly recollect being cannoned up ...
- 1,419
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2
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519
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Gravitational potential energy of an object on Earth compared to Moon
The gravitational potential energy of a $200\,\text{kg}$ satellite $3000\,\text{km}$ above the surface of the Earth is $U=-\frac{GMm}{r}=-8.5 \times 10^9\,\text{J}$.
Would the gravitational potential ...
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1
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434
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Finite potential well and nature of its solutions
The question I have is about nature of solutions, not a solution or a specific answer that I am looking for. If we define a potential well centred at $x=0$ as the following,
$$V(x) = \left\{ \begin{...
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5
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1
answer
114
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Insecurity about introductory classical mechanics [closed]
This is a problem I encountered, but not a homework assignment, I'm not only just looking for solutions here... This is my first time encountering questions like this, I'm sure you remember the first ...
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1
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49
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How do I visualize total potential energy of charges?
In the following exercise from University Physics with Modern Physics (Young, Hugh D.; Freedman, Roger A..)
Two point charges are at fixed positions on the $x$-axis, $q_1 = -e$ at $x = 0$ and $q_2 = ...
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2
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50
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Orientation of gravity force in energy [closed]
My apologies in advance if this is a stupid question.
A 0.20 kg rocket in a fireworks display is launched from rest and follows an erratic flight path
to reach the point P, which is 29 meters above ...
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1
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1
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62
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Two charged spheres connected by a wire and one is inside the other [closed]
Two charged spheres are connected by a wire, a small sphere is located inside a bigger one. Both spheres are charged and connected through a wire. The charge of the small sphere is 20µc and the charge ...
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1
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2
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64
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Position equation of $U(x)=-U_1[(\frac{x}{x_1})^3-(\frac{x}{x_1})^2 ]$
If $U(x)$ is given by $$U(x)=-U_1\left[\left(\frac{x}{x_1}\right)^3-\left(\frac{x}{x_1}\right)^2 \right]$$ can I find the position equation without harmonic aproximation?
I'm having problem with the ...
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2
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3k
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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 ...
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1
answer
97
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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
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2
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195
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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 ...
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1
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0
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50
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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’...
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1
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330
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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 ...
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2
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239
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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 ...
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4
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2
answers
7k
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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}...
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1
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2
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694
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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
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1
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382
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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 ...
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0
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44
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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
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5
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4k
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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
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1
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213
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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
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0
answers
71
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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 ...
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1
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205
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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‟ ...
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1
vote
1
answer
56
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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 ...
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4
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1
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769
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Energy electrostatic of a charged sphere
I am reading the Feynman books.
In 8.1, we have shown that the energy of a charged sphere of radius $a$ is
$$U = \frac{4\pi\rho^2a^5}{15\epsilon_0}.$$
I tried to get this result using the following ...
- 145
1
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1
answer
629
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Textbook question on calculation of potential difference between two points
My textbook has the following question
What is the potential difference between two points that are 50cm and 80cm respectively from a point charge of 2uC?
Unfortunately, the textbook has not taught ...
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1
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166
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Binding energy for a uniform sphere bound by a Yukawa potential rather than an inverse-square-law potential?
The binding energy of a uniform sphere that interacts through a force that follows the inverse square law is proportional to $a\frac{C^2}{R}$, where $C$ is whatever charge determines the strength of ...
- 1,405
1
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3
answers
1k
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A rolling stone on a rollercoaster
A ball rolls from point $A$ ($v_0 = 0 \; m / s$) to the right along a friction-less path. We can then calculate the speed of the ball at the points $B$ and $C$ using the law of conservation of ...
- 45
-1
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1
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271
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Configuration corresponding to lowest potential energy [closed]
Figure shows a small magnetised needle P placed at a point O. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) ...
- 33