All Questions
Tagged with potential-energy homework-and-exercises
395
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3
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Electrostatic Potential Energy Integral
I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book:
$$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$
...
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0
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1
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Calculating change in gravitational potential energy [closed]
A satellite mass $500\ kg$ is elevated from altitude $10000\ km$ to altitude $20000\ km$. Radius of earth is $6378\ km$. Mass of earth is $5.97 \cdot 10^{24}\ kg$. Gravity is given to be $9.81\ m/s $
...
- 109
1
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2
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Energy to reach the moon
I've been stuck on this question for a couple of days now.
Given that the potential energy of a 930 kg object on the Earth's surface is -58.7GJ, calculate the minimum energy required for the 930 kg ...
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0
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1
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Comparing work done for two accelerations
Suppose at a time $t_{0}$ a car goes from 0 to 30mph at time $t_{1}$, and then maintains a speed of 30mph until $t_{2}$. After that minute it accelerates, reaching 60mph at time $t_{3}$.
I want to ...
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Computing average force exerted by ground when jumping
Problem: A man of mass $m$ jumps vertically into the air from a sitting position in which his center of mass (CoM) is at a height $h_1$. When his feet are just about to leave the ground his CoM is at ...
- 657
2
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361
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Calculate Potential Gravity Energy converted when star collapses [closed]
We want to calculate how much gravitational potential energy converts to heat, when the star has no nuclear fusion, the gravity will cause the star to shrink in nano seconds.
Now assuming the Sun ...
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2
votes
3
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321
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Potential energy & entropy of three particles
Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question.
Let's consider that we have three free charges that somehow can ...
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How to show that the gravitational potential energy of a two particle system is -2 times the total kinetic energy, without using the virial theorem?
Consider a two-particle system with identical masses, orbiting in circles about their center of mass. I'm supposed to prove that:
$$U_p = -2U_k$$
With $U_p$ potential energy of the system, and $U_k$ ...
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-1
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1
answer
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Calculate amount of energy based on height of object
How can you calculate the amount of energy an object produces that falls from a particular height?
Or water.
In an eg i would like to know how can you calculate the amount of electricity water can ...
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Work done by magnetic field on magnetic dipole
In the above slide, it reads that $W=\int\mu B sin(\theta)d\theta=\mu B cos(\theta)$.
But, I thought that $\int\mu B sin(\theta)d\theta=-\mu B cos(\theta)$ by some calculus calculation.
Can somebody ...
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1
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2
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Who of these cyclist travel takes less time? [closed]
There are two cyclist. They start off with equal velocity $v_0$.
The first one bikes a straight path, while the other bikes through a valley, something like this:
We assume friction doesn't affect ...
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2
votes
1
answer
944
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Finding the Shape of a Hanging Massive Wire
This came from a physics wave book. I have a static, massive wire on the x-axis, with a y-displacement due to a force per unit length $F_y$. I start with the equation $F_y = T_0\frac{\partial^2(\eta)}{...
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6
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2
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Finding the components of the tensor for potential and kinetic energy
I have a rather poor understanding of what a tensor is, but enough to apply it to the biggest part of the classical mechanics I'm studying.
However, I've run into a small problem while studying "Free ...
- 1,373
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0
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182
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Double pendulum find first integral [closed]
Consider the following situation of a double pendulum in 2D.
We found the moving equations as
$$
\ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\
\ddot{\theta}...
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Potential at Center of Earth
If using the surface of the earth as a reference point how much work is needed for gravity to pull me to the center. Is it negative infinity or am I wrong? Also is a single value of potential ...
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1
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Infinite chain of alternating charge
The problem
There is an infinite chain (1d) of alternating charges that are in a distance a from each other. That is there is one charge +q and next to it -q and so on. Now calculate how much work it ...
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1
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Statements about gravitational potential energy contradicting intuition?
So in my textbook I am told:
two masses have gravitational potential energy because work had to be done in order to move one the masses form a position very far away (lets say infinity) to the ...
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Isn't $\varepsilon_0\int_{\text{all space}}\vec{E}_1\cdot\vec{E}_2 \,{\rm d}v$ just the potential energy?
I have two metallic spheres each with a charge of $q_1$ and $q_2$ respectively. What is the value of $$\varepsilon_0\int_{\text{all space}} \vec{E}_1\cdot\vec{E}_2 \,{\rm d}v$$
where $\vec{E}_1$ and $...
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2
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211
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Help understanding the solution to a problem regarding kinetic energy of a group of point charges
The problem provided by my professor goes as follows:
"Now consider a situation in which all charges are equal to q and they simultaneously become "unglued". What speed will each charge have when a ...
- 518
1
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2
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Potential and kinetic energy on spherical surface
A small particle of mass $m$ is atop of a semi-sphere as shown in the figure. A little push was given to the particle. Prove that the particle will leave the spherical surface at a height of (2/3)$R$.
...
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3
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Potential energy of an infinitesimal length of elastic rod
I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area $A$. The picture shown below is an element of the rod that ...
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2
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Using an electric winch to compress a spring and launch an object
I'm having trouble grokking the relationship between a winch's pull/torque and a spring's potential energy.
I would like to compress a spring using an electric winch and figure out how far it will be ...
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votes
1
answer
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Help understanding a potential energy problem [closed]
Apologies if the following problem does not seem to involve potential energy, it is a homework problem that is labeled under the potential energy chapter.
Question
While a roofer is working on a ...
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1
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Electrical Potential Energy and Electric Force [closed]
Under certain circumstances, potassium ions $(K+)$ move across the $8.0 nm$ thick cell membrane from the inside to the outside. The potential inside the cell is $−70 mV$ and the potential outside is $...
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0
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1k
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Hamiltonian function for classical hard-sphere elastic collision [closed]
I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$.
Everything I've read on the topic (e.g. this ...
2
votes
1
answer
1k
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Gravitational binding energy and integrated potential energy not the same?
Before looking up the formula for the gravitational binding energy of a uniform sphere, I simply figured that the general formula for binding energy of an arbitrarily-shaped mass distribution would be ...
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2
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Capacitor's voltage
Imagine I have two plates that form a capacitor, so the magnitude of the charge in each plate is, let's say, $Q$. So, the force, in respect to the distance $d$, is gonna be:
$$F(d) = k\frac{Q^2}{d^2}$$...
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0
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254
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Deriving the curve of a cantilever
Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
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Potential energy of the dipole-dipole interaction for two parallel dipole moments
I am looking for an equation that gives me the potential energy of the interaction between two parallel dipoles.
- 1,880
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2
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1k
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The "stationary potential energy" condition for static equilibrium in mechanical systems
I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the ...
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1
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Calculate magnitude of force acting on some area by falling object
I have simple question: is it possible to calculate magnitude of force acting on some area by falling object?
Let's say I have an object with mass $5\text{ kg}$. I drop that object in height 1 meter....
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2
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Kinetic energy of two charged balls at infinite distance between them
If I have two balls with masses and charges $m_1, q_1^{+}$, $m_2, q_2^{+}$, initially held at distance $d$, and then released, how can I know the kinetic energies of each of the balls at infinite ...
- 295
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3
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Center of mass problem
According to the definition of potential energy, we use $U= mhg .
$
In the figure below ,
A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot ...
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2
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1
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Center of mass error - calculating systematic error in change in PE
Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error.
\begin{align}
\Delta PE = m*g*h_1 - m*g*...
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2
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557
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Escape velocity to intersection of two gravitational fields
Find the minimal velocity needed for a meteorite of mass $m$ to get to
earth from the moon. Hint: the distance between the center of earth
and the center of moon is $\approx 60 R_E$, and the ...
- 685
1
vote
1
answer
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Given a potential energy function, find expression of the force of a particle?
This comes from an AP review packet. I'm given a potential energy functon, $$U(r)=br^{-3/2} + c,$$ where $b$ and $c$ are constants, and need to find the expression for the force on the particle.
...
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2
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644
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Potential energy during vertical fall
Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
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votes
1
answer
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Work done by gravity on Water
Now according to me we would see change in potential energy of system and equate it to the work done by gravity.
But when we see this the first column lowers by $H/2$ and right one rises by $H/2$ and ...
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4
votes
2
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Problem $\S12$ $2(b)$ of Landau & Lifshitz "Mechanics" Integration of the Equations of motion [closed]
I'm studying Landau, Lifshitz - Mechanics. Could someone help me with this problem ? =)
Problem $\S12$ $2(b)$ (Page 27 3rd Edition) Determine the period of oscillation, as a function of the energy, ...
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2
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Shape of a string/chain/cable/rope/wire? [closed]
The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
- 1,550
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663
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exercise concerning the inclined plane
I have an exercise to ask yourself.
A ball of mass m = 5 g starts at rest and travels 50 cm along a ramp
inclined at 45 ° to the horizontal. a) If we imagine frictionless motion
of the ball along the ...
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1
answer
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What is the energy of interaction between a point charge and an infinite cylinder?
I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject.
I know, that I can consider the cylinder as a wire with the same charge density (...
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1
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Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
- 175
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2
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Charge, velocity-dependent potentials and Lagrangian
Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
- 1,133
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1
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342
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Atomic weight in respect to the binding energy?
My book says that the weight of helium (with the nucleon number of 4 and proton of 2) is that of $6,6447*10^{-27}$ kg. Earlier the book stated that if the proton number is left out it means that the ...
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