# Tagged Questions

The product of the force on an object and the displacement the object undergoes along the direction of the force.

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### Why does holding something up cost energy while no work is being done?

I read the definition of work as $$W ~=~ \vec{F} \cdot \vec{d}$$ $$\text{ Work = (Force) \cdot (Distance)}.$$ If a book is there on the table, no work is done as no distance is covered. If I ...
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### How can Magnets be used to pick up pieces of metal when the force from a magnetic field does no work?

I learned that the force from magnetic fields does no work. However I was wondering how magnets can be used to pick up pieces of metal like small paperclips and stuff. I also was wondering how magnets ...
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### Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?

For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$\frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$ From this, it ...
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### How can energy be useful when it is 'abstract'?

The topic which haunted me for two years until I gave up on it. But now I am doing engineering and this topic suddenly popped out of my textbook from nowhere. I seriously need to understand this topic ...
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### Does a magnetic field do work on an intrinsic magnetic dipole?

When you release a magnetic dipole in a nonuniform magnetic field, it will accelerate. I understand that for current loops (and other such macroscopic objects) the magnetic moment comes from moving ...
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### Thermodynamics - Sign convention

I use the sign convention: Heat absorbed by the system = $q+$ (positive) Heat evolved by the system = $q-$ (negative) Work done on the system = $w +$ (positive) Work done by the system = $w -$ (...
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### Bird flying in a cage

Assume that you are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of ...
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### How can we move an object with zero velocity?

Consider there is a box of mass $m$ at rest on the floor. Most books give an example that we need to do a work of $mgh$ to lift the box $h$ upward. If we analyze this work done, the external force ...
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### Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...
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### What exactly is $F$ in $W = \int_{a}^{b} F dx$?

I am trying to teach myself some basic physics, here is something I do not really understand about the definition of work: When moving from $a$ to $b$ (in one dimension), the work done is defined to ...
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### How to calculate wasted energy

Suppose you are pulling a weight along a track at an angle (in the picture 45°). If the object is dislocated by a distance $D_{45}$ let's assume that the mechanical work done on/energy transmitted to ...
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### Work done against gravity [closed]

The work done against gravity is $mgh$, well at least that's what my textbook says. I have a question: I can apply a force say 50N, so total work done = $mgh + mah$. Where $ma$ = Force. But the truth ...
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### A Question about Virtual Work related to Newton's Third Law

In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
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### What is the mechanism by which magnetic fields do work?

I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example. Do magnetic fields do work directly, or is it their induced electric fields that do ...
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### How can I understand work conceptually?

I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?
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### How can tangential acceleration from a radial force be explained?

A mass is attached to a rope, and put into a circular motion. If I pull the string from the center, the tangential speed of the mass will increase (by conservation of angular momentum). I am ...
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### How was the definition and the formula of work derived? Is it the best possible?

Work done is defined as the dot product of force and displacement. However, intuitively, should it not be the product of force and the time for which the body is acted upon by the force (force * ...
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### Number of planks required to stop the bullet [closed]

A bullet looses (1/n)th of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be? Logically, to me the answer seems to be infinity, as always a ...
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### Proof of conservation of energy?

How is it proved to be always true? It's a fundamental principle in Physics, that is based on all of our currents observations of multiple systems in the universe, is it always true to all systems? ...
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### Work, Energy & Power - Body slides down a hemisphere

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. There is no friction between the surface of the block and the hemisphere. The height at which the body loses contact ...
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### If Earth starts moving when attracted by an object, where does the energy come from?

Suppose a body(very big but not bigger than Earth) moves against gravitational force of Earth. The force will do negative work on the body decreasing its kinetic energy. The decreasing energy is ...
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### Is any work done if I walk in a circle?

My friend and I were arguing about this and I was wondering if someone out there could settle this for us. Basically, he and I were walking to buy some stamps. When we were on our return trip he ...
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### Why must a body lose energy to an opposing force?

A body must do work against an opposing force to continue motion. I have found this statement many times. But what is the reason behind it? Suppose $F_1$ is acting on a body to accelerate it (to ...
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### Work done by the Magnetic Force

The magnetic part of the Lorentz force acts perpendicular to the charge's velocity, and consequently does zero work on it. Can we extrapolate this statement to say that such a nature of the force ...
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### When can one write $a=v \cdot dv/dx$?

Referring to unidimensional motion, it is obvious that it doesn't always make sense to write the speed as a function of position. Seems to me that this is a necessary condition to derive formulas like:...
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### Is the normal force a conservative force?

Most of the time the normal force doesn't do any work because it's perpendicular to the direction of motion but if it does do work, would it be conservative or non-conservative? For example, consider ...
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### Why can we cycle faster than we can run? [duplicate]

This seems obvious: faster long-distance runners hit ~20 km/h (marathon records) while fastest cyclists can do ~40 km/h (Tour de France stats). But on the physical/biological level this doesn't seem ...
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### The physical definition of work seems paradoxical

So this is possibly a misunderstanding of the meaning of work, but all the Physics texts, sites, and wiki that I've read don't clear this up for me: In the simplest case with the simplest statement, ...
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### A confusion regarding an example in The Feynman Lectures

In The Feynman Lectures, In the chapter entitled Work and potential energy, Feynman states: The work done in going around any path in a gravitational field is zero. This is a very remarkable ...
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### Why does a conservative force return the work done against it by a body to that body?

Newton's 3rd law of motion: Newton's third law of motion or the law of action and reaction implies that there is no isolated force in nature. Whenever there is any force at all , there must be ...
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### What is the sign of the work done on the system and by the system?

What is the sign of the work done on the system and by the system? My chemistry course book says, when work is done on the systems, it is taken positive. When work is done by the system, it is taken ...
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### Conceptually, what is negative work?

I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
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### What is the work done against a force?

Suppose a particle travels a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ subject to a force $\mathbf{F}: \mathbb{R}^3\to T\mathbb{R}^3$, then we know that we define the work done by the force ...
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### Where does this formula for sagging of a beam come from?

In one of my physics textbooks there is a chapter on the elasticity of materials which contains pretty basic outline about Young's modulus, stress-strain, elastic potential energy and related stuff. ...
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### What is Work? What does the quantity suggest intuitively? [duplicate]

The mathematical formula for work says that work is force into displacement, but what is the philosophy behind it? I mean what does the quantity suggest?
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### Work done by magnetic field [duplicate]

I know Lorentz force don't do any work. but I want to know whether any type of magnetic field do a work or not.
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### Is work done in rolling friction?

I am confused by rolling friction. Suppose you have a cylinder rolling which starts at rest at the top of an incline plane and begins to roll down the plane without slipping. Is work done by the ...
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### Wrong calculation of work done on a spring, how is it wrong?

So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring ...
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### How to reconcile the two definitions of work? (mechanical and thermodynamical)

When studying classical mechanics, work is defined as: $W_M=\int F_{tot} \hspace{2 mm} dx$. However, for thermodynamics, work is defined as: $W_T=\int -F_{ext} \hspace{2 mm} dx$. I'm having trouble ...
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### Net work done on the body when we lift it and put it on the table is zero?

I'm little confused here. Work done on the body when we lift it and put it on the table is zero, because according to work energy theorem, change in kinetic energy of the body is zero. So, the net ...
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### If velocity is constant, how can $p = F\cdot v$ be non zero?

If an airplane of mass $m$ is flying at a constant speed $v$, the power of the airplane is $$P = m\cdot v\cdot g$$ where $g$ is the acceleration of gravity and therefore: $$F = m\cdot g,$$ but, ...
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### How much work is needed to compress a certain volume of gas?

I want to know the formula (and what does the symbols stand for) for how much work is needed to compress a certain volume of gas?
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### Confusion with Grounded Conductor: bringing in a point from infinity

Suppose, for sake of argument, we have a spherical grounded conductor at the origin. Additionally, let our reference voltage be at infinity. Now, I view the potential of a point in space as being the ...
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### Can I define the term energy in terms of work?

Recently, I'm doing my personal task which is to formalize every definition and concept in physics, by means of formal language and of course with intuitional notes. Because I found myself that the ...
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### Intuitively Understanding Work and Energy

It is easy to understand the concepts of momentum and impulse. The formula $mv$ is simple, and easy to reason about. It has an obvious symmetry to it. The same cannot be said for kinetic energy, work,...