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

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72
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8answers
19k views

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 ...
49
votes
8answers
6k views

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 ...
13
votes
6answers
3k views

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 ...
13
votes
7answers
2k views

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 ...
25
votes
6answers
7k views

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 ...
1
vote
3answers
33k views

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 = $w -$ ...
17
votes
4answers
5k views

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 ...
9
votes
3answers
2k views

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 ...
7
votes
4answers
646 views

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 ...
3
votes
2answers
894 views

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 ...
2
votes
2answers
5k views

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 ...
5
votes
1answer
677 views

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, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
8
votes
2answers
820 views

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 ...
1
vote
1answer
265 views

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?
8
votes
3answers
1k views

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, ...
6
votes
4answers
528 views

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 ...
6
votes
3answers
643 views

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 * ...
8
votes
3answers
3k views

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 ...
0
votes
2answers
280 views

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 ...
0
votes
3answers
7k views

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 ...
5
votes
4answers
525 views

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 ...
5
votes
2answers
3k views

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 ...
4
votes
3answers
328 views

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 ...
4
votes
4answers
3k views

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 ...
15
votes
3answers
6k views

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 ...
21
votes
9answers
3k views

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 ...
26
votes
4answers
2k views

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, ...
6
votes
5answers
19k views

Why there is a 1/2 in kinetic energy formula? [duplicate]

Possible Duplicate: Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$? Hèllo, I have a question about kinetic energy formula. As you know, in kinetic energy formula, we have: ...
12
votes
4answers
2k views

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 ...
8
votes
7answers
2k views

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 ...
1
vote
1answer
116 views

Trajectories piecewise smooth?

In my studies of calculus and real analysis I have found the proofs of several theorems, commonly used in physics, such as those concerning the conservativity of fields, for example like If ...
3
votes
4answers
1k 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 ...
1
vote
3answers
66k views

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 ...
5
votes
5answers
7k views

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? ...
2
votes
2answers
280 views

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. ...
2
votes
3answers
915 views

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 ...
2
votes
4answers
16k views

What is the difference between dot and cross product?

What is the difference between dot product and cross product? Why do we use cross product to find torque, why can't we use dot product? Also we use dot product to find work done and not cross ...
1
vote
1answer
79 views

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?
0
votes
2answers
988 views

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 ...
0
votes
1answer
6k views

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.
5
votes
4answers
9k views

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 ...
3
votes
2answers
651 views

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 ...
2
votes
4answers
194 views

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, ...
2
votes
3answers
6k views

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 ...
1
vote
2answers
140 views

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 ...
1
vote
1answer
18k views

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?
0
votes
2answers
122 views

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 ...
0
votes
1answer
166 views

Energy density and Carnot cycle

For example, diesel has about 40 MJ/kg, what does it mean? Is that if we burn it we will get 40 MJ of energy per kg, but we can not get all of it to mechanical work? If that is the case, then why ...
4
votes
4answers
682 views

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 ...