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

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76
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8answers
21k 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 ...
51
votes
8answers
7k 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 ...
34
votes
4answers
5k views

What is the energy source if a tall water tank is used to transfer floating objects upwards instead of cables with motors?

Suppose I want to transport some logs from the ground to the roof of a tower. Originally I can use a lift, or some cables, or even move the logs upwards manually; then the energy is converted to the ...
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, ...
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 ...
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
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 ...
16
votes
3answers
7k 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 ...
14
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 ...
13
votes
6answers
4k 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
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 ...
12
votes
2answers
751 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
5k 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 ...
10
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 ...
10
votes
4answers
8k 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 ...
10
votes
2answers
52k 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 ...
8
votes
6answers
576 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 ...
8
votes
5answers
16k 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
7answers
3k 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
2answers
3k 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 also,...
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 ...
8
votes
2answers
881 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
3answers
2k 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, work,...
8
votes
4answers
445 views

Is work done by a pseudo force?

If a body is viewed from the frame of another body which is itself accelerating, will work be done by the pseudo force acting on the first body in the frame of second body ( provided the first body is ...
7
votes
4answers
451 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 \underline{\underline{\sigma}}:\mathrm{d}\underline{\...
7
votes
4answers
655 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
577 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
5answers
5k 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 $KE=5,...
7
votes
3answers
2k 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 ...
7
votes
2answers
255 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 ...
6
votes
5answers
20k 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: $\large\frac{1}{2}...
6
votes
5answers
5k 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 ...
6
votes
3answers
39k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar, but why? And why not a vector?
6
votes
3answers
555 views

What does it mean to say work is path-independent when pushing an object in different directions?

If I apply a straight upward(perpendicular to ground) force against gravity of $5\ \mathrm{N}$ and lift an object "A" 10 meters, then the work done is: $$ W = F \times S = 5\ \mathrm{N} \times 10\ \...
6
votes
7answers
6k 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 ...
6
votes
3answers
770 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
3answers
363 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? ...
6
votes
2answers
2k 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
8answers
976 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 ...
5
votes
7answers
5k 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
4answers
10k 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 ...
5
votes
2answers
4k 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 ...
5
votes
5answers
8k 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? ...
5
votes
6answers
10k 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
1answer
6k 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 ...
5
votes
4answers
546 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
1answer
707 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, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
5
votes
1answer
2k views

Why is the maximum work achieved in reversible processes?

Let us consider an ideal gas. Let it be present initially in a state $(p_1,v_1,t_1)$. Now let it be driven to another state $(p_2,v_2,t_2)$. Why is it so that during this process the maximum work can ...
5
votes
2answers
113 views

How is the dot product a generalization of multiplication?

I've seen an interesting explanation for lots of what I previously thought were unmotivated definitions in Newtonian mechanics, namely that power is always defined as effort times flow. But when ...
5
votes
2answers
7k views

Work done by isothermal expansion from two different viewpoints

Consider an adiabatic system as follows. It consists of a gas in a container and a piston. Initially, the system is at equilibrium and the gas inside it occupies a volume $V_i$ at a pressure $p_i$ ...