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

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57
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8answers
14k 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 ...
47
votes
8answers
5k 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 ...
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, ...
26
votes
6answers
6k 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 ...
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 ...
17
votes
4answers
4k 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 ...
14
votes
3answers
5k 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 ...
12
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 ...
12
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 ...
12
votes
2answers
681 views

Does energy expenditure require movement? [duplicate]

In every formula I've seen that involves energy, I've also seen a distance element. Is there nothing that doesn't involve movement? For instance if I hold my arm out parallel to the ground with a ...
10
votes
2answers
3k views

Calculating the force required to lift a weight with a screw

I am trying to learn physics by myself as I do not have a good teacher at school. I've been reading Feynman Lectures on Physics and I can't figure out how he found out this number. Here is an excerpt ...
9
votes
2answers
465 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 ...
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 ...
8
votes
3answers
1k 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 ...
8
votes
5answers
11k views

Why does work equal force times distance?

My 'government-issued' book literally says: Energy is the capacity to do work and work is the product of net force and the 1-dimensional distance it made a body travel while constantly affecting ...
8
votes
2answers
265 views

Internal energy of an ideal gas as a function of volume

Okay so I've been reading a bit on Thermodynamics and I found something that I couldn't wrap around my head. For an ideal gas, the change in internal energy is equal to $$\Delta U = Q + W$$ And ...
8
votes
3answers
2k 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 ...
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, ...
7
votes
3answers
810 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 ...
7
votes
4answers
438 views

Is there a fundamental reason not to define the work vice-versa

My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as: $$W=\int_\Omega ...
7
votes
4answers
596 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 ...
7
votes
4answers
4k views

Is energy the ability to do work?

Here was my argument against this, the second law of thermodynamics, in effect says that, there is no heat engine that can take all of some energy that was transferred to it by heat and do work on ...
7
votes
2answers
34k views

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 ...
7
votes
4answers
494 views

On the definition of work

Work is defined as $$W = \vec{F}\cdot\vec{s}$$ But what what exactly is $\vec{s}$? Is it the displacement of the body on which the force is being applied? Or is it the displacement of the point of ...
7
votes
3answers
1k views

Energy equation for an open system

I teach undergraduate thermodynamics and I was quite ashamed that I couldn't explain to a student, the following. I thought I'd bring it to physics.SE in hope of providing my student a good ...
6
votes
5answers
13k 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: ...
6
votes
4answers
343 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
430 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 * ...
6
votes
2answers
745 views

What's the difference between work in thermodynamics and mechanics?

What is the difference between work in thermodynamics and work in mechanics?
6
votes
5answers
2k views

Kinetic energy vs. momentum?

As simple as this question might seem, I failed to intuitively answer it. Let's assume there is a $10,000$ $kg$ truck moving at $1$ $m/s$, so its momentum and KE are: $p=10,000$ $kg.m/s$ and ...
6
votes
8answers
704 views

Energy and work

I don't quite understand the concept of energy and work. We can define energy as the ability to do work. An object moving at constant speed has kinetic energy. Does the object have the ability to do ...
6
votes
2answers
195 views

While holding an object, no work done but costs energy (in response to a similar question)

I read the answer to Why does holding something up cost energy while no work is being done? and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of ...
5
votes
7answers
3k views

In calculating work done by a constant force over a constant distance, why doesn't the subject's initial velocity matter?

Assume a point-mass $m$ is travelling in a straight line, and a force $F$ will act on $m$ (in the same direction as $m$'s velocity) over a constant distance $d$; why doesn't $m$'s velocity matter to ...
5
votes
6answers
6k views

What is $vdp$ work and when do I use it?

I am a little confused, from the first law of thermodynamics (energy conservation) $$\Delta E = \delta Q - \delta W $$ If the amount of work done is a volume expansion of a gas in, say a piston ...
5
votes
5answers
3k views

Is there work being done if no displacement occurs?

So the definition of work is $W = \vec{F}\cdot\vec{s}$. Say I have a point mass which is being pushed on both sides by equal forces and therefore does not move. Does this mean that no work is being ...
5
votes
7answers
3k views

Intuitively, how can the work done on an object be equal to zero?

To my understanding the work done on an object is defined mathematically as: $$W = \vec{F}\cdot\vec{S}=|\vec{F}||\vec{S}|cos\theta$$ This, I understand. My problem is that I don't understand that if ...
5
votes
4answers
467 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
7answers
5k views

If the net work on a particle is zero, can the speed change?

The following question was on a quiz in physics class: If the net work done on a particle is zero, which of the following statements must be true? a) The velocity is zero b) The velocity is ...
5
votes
1answer
319 views

First law of thermodynamics?

The first law says that the change in internal energy is equal to the work done on the system (W) minus the work done by the system (Q). However, can $Q$ be any kind of work, such as mechanical work? ...
5
votes
1answer
605 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, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
4
votes
3answers
1k views

Work = Force x Distance vs Displacement

The difference in using Distance vs Displacement is demonstrated in this example: Work = Force x Distance If I carry an object to and fro 10 metres, the work done would be Force x 20 metres. ...
4
votes
4answers
421 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 ...
4
votes
2answers
156 views

Conservative Force and $1/r^2$

Does the inverse square law have anything to do with conservative behavior of the central forces?
4
votes
4answers
4k 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 ...
4
votes
4answers
1k views

Sign of Work and potential energy in electrostatics

Conceptual question: Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive. I'm kind of rusty with my mechanics, ...
4
votes
2answers
2k 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
303 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
1answer
4k views

How to understand the work-energy theorem?

How to understand the work-energy theorem? I took a short lecture on physics for engineering last week. The lecturer emphasized that the work done on an object will cause the kinetic energy change as ...
4
votes
2answers
302 views

What's wrong with my derivation for the spring constant? [duplicate]

An $8.00\ \mathrm{kg}$ stone at rest on a spring. The spring is compressed $10.0\ \mathrm{cm}$ by the stone. What is the spring constant? I used conservation of energy to solve this problem. The ...
4
votes
2answers
1k views

Is any work done when I walk?

I am trying to figure out the amount of work done when I walk X miles or for X minutes. So I got Work=Force x Distance and Force=Mass x Acceleration and Acceleration=(change in velocity)/time. I am ...