1
vote
3answers
52 views

Why does the work done by an internal force differ from the work done by external force?

Let's consider the following situation. We put a body of mass $m$ at a distance $A$ from the center of Earth. We let the Earth attract the body and analyze the situation at a point $B$, closer to the ...
7
votes
2answers
359 views

How does escape velocity relate to energy and speed?

I have several confusions regarding escape velocity. I am sure I am missing something(s) obvious or maybe I am taught wrong. Lets say we throw an object of any mass at exactly escape velocity of ...
1
vote
2answers
99 views

Two expressions for potential energy in the gravitational field of the earth

Let $M$ be the mass of the earth, considered as a point mass, then the potential energy of a point with distance $r$ away from the center (assume $r > \textrm{radius of earth})$ is $$ U(r) = ...
1
vote
1answer
50 views

Why potential energy of external force on particle attached to spring is equal to full force multiplied by full displacement?

I am having quite difficult time to understand the meaning of total potential energy on spring. All references I read say that the total potential energy on particle attached to spring is: ...
1
vote
1answer
42 views

Action Reaction Pairs and Work

Say that a ball is sitting in front of a compressed spring launcher. The spring is then released. The spring applies a force on the ball for a certain distance. This force is accompanied by an equal ...
0
votes
1answer
49 views

Work done by Internal Forces

Why is it that internal forces do not change the potential energy of the system? Assume that a man stands on earth with a dumbell. If the dumbell is the system, when it is raised a height h, the work ...
0
votes
1answer
31 views

How would we find what sort of a force this one is? [closed]

The potential energy for a force field is given by $U = -Kxy$, where $K$ is a constant. The body moves in an $x$-$y$ plane. Find the force vector. $i$ is the unit vector along the $x$ axis, $j$ is ...
2
votes
2answers
77 views

Explanation for $M{\ddot{r}}=-\nabla \phi$

Could someone please explain this equation $$M\bf {\ddot{r}}=-\nabla \phi$$ Where $\bf r$ is a position vector and $\phi$ is the potential function. Could someone brief explain the potential function ...
-1
votes
1answer
24 views

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 ...
3
votes
2answers
136 views

What is the mathematical definition of work?

I'm looking for the pure mathematical definition of work, but I haven't yet learned line integrals. My book says that the work due to a force ${\bf F}$ from point $A$ to point $B$ is $$ W= |AB|\cdot ...
3
votes
2answers
193 views

Potential energy of a rotating bar

I have a bar of length $L$, mass $m$, and negligible width. The bar can rotate along an axis through its center of mass (the rotation is in the $x$-$y$ plane), and also can move up and down (in the ...
2
votes
4answers
317 views

Why can't the work done by a non-conservative force be zero?

Why can't the work done by a non-conservative force be zero? The displacement along a closed path is always zero. So, whatever be the type of force, variable or constant, the work has to be zero. Why ...
0
votes
2answers
57 views

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 ...
2
votes
0answers
35 views

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),\\ ...
2
votes
2answers
137 views

Gravitational potential energy negative?

Can the gravitational potential energy be negative? $PE=mgh$, we kind of have the same fig as this (minus the car)! and we choose the arbitrary point to be the G of the pendulum (point of ...
16
votes
6answers
1k views

Why does a system try to minimize potential energy?

In mechanics problems, especially one-dimensional ones, we talk about how a particle goes in a direction to minimize potential energy. This is easy to see when we use cartesian coordinates: For ...
2
votes
2answers
123 views

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 ...
3
votes
2answers
87 views

Internal potential energy and relative distance of the particle

Today, I read a line in Goldstein Classical mechanics and got confused about one line. To satisfy the strong law of action and reaction, $V_{ij}$ can be a function only of the distance between ...
1
vote
2answers
77 views

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 ...
1
vote
2answers
101 views

Energy of a damped oscillator

$$ E=\frac{1}{2}m\left(\frac{dx}{dt}\right)^2+\frac{1}{2}m\omega_0^2x^2. $$ This is the equation for the energy of a oscillator. The second term is the potential energy. Now, my question is, will ...
3
votes
1answer
108 views

Where does energy in a field come from?

Let us consider for example Earth's gravitational field. If we put a ball somewhere in this field, the ball starts to accelerate due to the gravitational force exerted on it. I understand the ...
1
vote
1answer
418 views

Why doesn't the potential energy of any object equal 0

Consider a particle on the ground. This particle is raised by a force of magnitude $mg$ to a height $h$ above the ground. At this point, the work done on the particle by the force is $mgh$, which is ...
-1
votes
4answers
996 views

Is potential energy and “work done” the same thing?

Is potential energy and "work done" the same thing? If they are not one and the same thing then why is potential energy always associated with "work done"? Could you explain me with some examples?
2
votes
1answer
431 views

Dominos vs. Conservation of Energy

In this video a single flick of a finger tips 116000 dominos. Domino video I understand the work that needs to be done to move 116000 pieces (at least 100 kilos) of plastic is greater then that ...
1
vote
2answers
223 views

Potential and Kinetic Energy

In engineering school you learn the basic swing problem. Essentially that there is a transfer of kinetic energy (as seen in the velocity at the bottom of as swing) to potential energy at the top of ...
0
votes
2answers
3k views

Relation between work, kinetic energy and potential energy

We derived two equations in class. The work done between two points $A$, $B$ is equal to the difference between the kinetic energy at the last point and the one at the first point. The work done ...
0
votes
1answer
270 views

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 ...
3
votes
4answers
669 views

Potential energy sign conventions

Almost every book on physics that I read have some weird and non-clear explanations regarding the potential energy. Ok, I do understand that if we integrate a force over some path, we'll get a ...
2
votes
2answers
2k views

Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
1
vote
2answers
307 views

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 ...
0
votes
2answers
149 views

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 ...
1
vote
1answer
835 views

Gravitational potential energy of mass between two planets

Suppose I want to launch a rocket from earth to some point $O$ between the center of earth and the center of moon (on a straight line connecting their centers), where the gravitational force of the ...
1
vote
1answer
819 views

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. ...
1
vote
2answers
171 views

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 ...
1
vote
0answers
212 views

Potential energy of a spring

I have a little problem with the potential energy of a spring... I hope you can help me! I have two coupled pendula, given by two masses $m$ fixed to two rigid bars (that haven't any mass) and with ...
0
votes
1answer
241 views

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 ...
2
votes
5answers
831 views

Is there a mathematical derivation of potential energy that is *not* rooted in the conservation of energy?

For simplicity I'll consider only gravity, but in general this question only applies to conservative forces. As per my understanding, the way one gets to the equation for gravitational potential ...
2
votes
2answers
572 views

Lever Mechanics - How to formulate an ideal lever launch

Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
1
vote
3answers
612 views

What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass?

As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A ...
1
vote
2answers
262 views

Could someone remind me what this means again? $\nabla U = \pm F$

You know that for a potential function (conservative force/fields) that $\nabla U = \pm \vec{F}$ In math, we don't have that minus sign, we have only the plus one. What does it mean if you get rid ...