All Questions
69 questions
0
votes
1
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129
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Why does $W = \int F\cdot \mathrm{d}s$ rather than $\int s\cdot\mathrm{d}F$ [duplicate]
Conventionally, infinitesimal work is defined as $\delta w = F\cdot ds$ and its integral as the work $$w(P_1 \to P_2) = \int_{P_1}^{P_2} F\cdot ds \tag{1}.$$
The word work, of course, can be assigned ...
- 53
5
votes
1
answer
410
views
Clarification Regarding a Possible Typo in David J. Griffiths' Introduction to Electrodynamics
Question:
I am currently reading Introduction to Electrodynamics by David J. Griffiths, and I’ve encountered a point of confusion in Section 2.4 on page 91.
Why is $W=\int_a^b\textbf{F}\cdot d\textbf{...
-2
votes
1
answer
65
views
Work understanding [closed]
I was reading about work. My thoughts are that work is the quantity somewhat related to the total momentum transfer over a distance. This is a way to predict an objects path over another distance. ...
4
votes
3
answers
648
views
Why isn't work a state function?
I've heard the example, that work is path dependent. But whether I climb a mountain directly or in serpentines, in the end it's the same amount of work, with the one difference that it takes me longer ...
- 153
1
vote
1
answer
58
views
Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]
John Taylor's Classical Mechanics says this...
I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
- 97
0
votes
2
answers
105
views
How can work be a function of position when non-conservative forces don't act the same way at each point?
My textbook and wiki/online articles all claim that work is given by the integral
$$W=\int_\gamma\vec{F}\boldsymbol{\cdot}\text{d}\vec{s}$$
where the $\text{d}\vec{s}$ is some infinitesimal step along ...
- 179
1
vote
2
answers
1k
views
What is the difference between work done against gravity and work done by gravity?
Work done "BY" a force,from my understanding,is:
•positive when the direction of displacement is same as the direction of force.
•negative when the direction of displacement is opposite to ...
- 57
-1
votes
2
answers
104
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Motivation for definition of work [closed]
Why do we take the dot product in the work energy theorem? Consider the integral
$$\int\vert\vec F\vert\vert d\vec r\vert$$
Why don't we define this to be work done for example, instead of $\int\vec F\...
0
votes
1
answer
88
views
${}$Conservative and Non-Conservative Forces
For work done by conservative forces ($W = F.S$), we consider $S$ as the displacement and not the actual path travelled. However for non conservative forces we consider the total path length and not ...
1
vote
2
answers
705
views
Why does small work done mean $dw=f.ds$ and why not $dw=df.ds$ and why not $dw=s.df$? [duplicate]
Work, power and energy questions.
Why does small work done mean:
$$dw=f.ds$$
and why not:
$$dw=df.ds$$
and why not:
$$dw=s.df \ \ ?$$
1
vote
2
answers
222
views
Work done by non-continuous force
How work done is really understood?
I know that $W=F\cdot d$. I am interested in the meaning of force here i.e.
Is it a continuous force applied till displacement? like the case of pulling trolley ...
- 101
-1
votes
3
answers
64
views
Definition on type of work [closed]
A man carries a bag hanging it in his hand and he moves horizontally. The bag does not move up or down. What is the work done on the bag? The man gets tired after some time of the movement. Why?
0
votes
1
answer
711
views
Formula for work done for both conservative and non-conservative force are different?
We know that the formula for Work Done by an constant force is
W.D = Force x displacement x (cosine of angle between force and displacement).
Situation: A mass m travels 10 meters towards +ve axis ...
- 1
0
votes
1
answer
47
views
How to know what force to plug in for work?
Suppose I have a positive charge $+Q$ at some point, and I want to see how much work I need to do to bring a negative charge $-q$ to a distance $r$ from that point. The direct calculation is done via ...
- 163
4
votes
3
answers
866
views
How can an object do work?
I read in many sites that the concept of mechanical energy is the ability of an object to do work, but how can an object do work? Isn't it rather the force applied to that object the one that produces ...
- 179
1
vote
3
answers
115
views
Clarification on the displacement in the definition of Work
I'd like to ask a question about work. The definition of work gives us a way to calculate the work done by a force along a path but in practice it's not always clear what path to take in consideration....
- 465
4
votes
2
answers
1k
views
Proving if a force is conservative and non-conservative
recently I have studied conservative forces and non-conservative forces in halliday book and while doing some exercise I saw some questions asking for proving if a force is conservative so after doing ...
- 45
0
votes
2
answers
403
views
What does potential energy really mean?
I have a lot of doubts regarding the potential energy definitions
First of all,I would try to express my Understandings(they might be wrong)regarding the issue
I was told that if Work done on a body ...
- 462
-3
votes
2
answers
251
views
Why is work done force times displacement? [duplicate]
Why is work done the product of force and displacement? Why not force and time?
- 13
0
votes
4
answers
4k
views
Why do we multiply $\cos θ$ in the formula for work? [duplicate]
I know that the formula for work, $W = FS\cos\theta$, where $F$ is the applied force, $S$ is the displacement of the object and $\theta$ is the angle between the applied force and the displacement of ...
1
vote
3
answers
332
views
Is the $d$ in $W=F*d$ displacement or distance?
My textbooks say that work=force times displacement but when I was considering conservative and non-conservative forces I got a bit confused. I know that the work done by non-conservative forces onto ...
0
votes
3
answers
2k
views
Work done on a frictionless surface
Imagine that we apply a force $F$ on a frictionless surface to move a body by a distance $d$. (The body starts at rest and is stopped after moving a distance $d$.)
Is the work done $F d$?
But from ...
- 49
-3
votes
1
answer
61
views
Is energy, as we know it, "persistent"? [duplicate]
Suppose I raise a ball (with my hand) to some height. I am doing some work against gravity and storing potential energy in the ball.
However, once I loosen my grip, or just sweep my hand away from ...
- 71
3
votes
4
answers
411
views
How is the definition of work motivated?
For most dynamical variables in classical physics, I can understand how one may have decided to introduce them as a result of some "incompleteness" in Newton's laws of motion. For example:
...
- 366
4
votes
7
answers
662
views
What comes first: Work or kinetic energy?
Suppose we have a body initially at rest. Now a force ($F$) is continuously applied on it and it gets displaced by some distance $x$.
My tutor said that from work energy theorem it gains kinetic ...
- 8,456
2
votes
4
answers
218
views
Basic question: intuition about $W = F \cdot T$
I find it written many places that "you can find the work along a short segment of the path by taking the dot product of the force and the tangent vector."
I can solve these problems, but I ...
- 53
20
votes
3
answers
4k
views
Conditions for a force to be conservative
Taylor's classical mechanics ,chapter 4, states:
A force is conservative,if and only if it satisfies two conditions:
$\vec{F}$ is a function of only the position. i.e $\vec{F}=\vec{F}(\vec{r})$.
The ...
- 1,325
1
vote
1
answer
150
views
How to choose the sign of the differential?
I know this is a very simple question, and I have searched it too. How to avoid incorrect symbols in calculation results.I don’t understand how to choose the sign of $ds$.
An object moves from a to b,...
- 35
1
vote
3
answers
239
views
Work=Force Displacement Displacement relative to what?
Ok, taking the equation W=FD. Say a 30N force is acting on a 10kg object over 10s, causing it to move 150 metres over a frictionless surface. The work done by this force will be 30(150)J. However, if ...
- 11
3
votes
7
answers
2k
views
Work done when lifting an object at constant speed
A previous post (What Is Energy? Where did it come from?) defines work qualitatively as "a process in which energy is transformed from one form to another form". And mathematically, work is ...
-1
votes
2
answers
369
views
Please explain work done
We have learnt that when an force displaces object along its direction then it is work done. so there is dot product in its formula (I guess). So is it also right to say that work done is cross ...
3
votes
9
answers
4k
views
Why is work equal to force times displacement?
This is how I think of what work is.I am sure I am wrong somewhere because I shouldn't be coming to the conclusion that I am coming to.It would be helpful if you would point out where this conceptual ...
- 1,043
0
votes
3
answers
260
views
Deep meaning of work integral formula [duplicate]
I want to understand very deeply the meaning of the work integral formula:
$$ \int m\frac{d\bar{v}}{dt}d\bar{l} \, .$$
It is not enough for me to know that it was defined in this way, I want to know ...
- 401
1
vote
4
answers
1k
views
Work when there is more than 1 force
I know that for an object with an applied force, the work done is
$$W = Fd \cos \theta.$$
I was wondering what would happen when there is another force (e.g. friction)? Is it better to say that the ...
- 11
0
votes
2
answers
758
views
Why is work defined with respect to distance rather than time? [duplicate]
The common way of finding the work done on some object is by applying the equation: force*displacement.
However, suppose we apply a force of F newtons on an object of mass M for a duration of T ...
- 892
0
votes
4
answers
577
views
Why is Work equal to Force * distance? [duplicate]
I totally get the mathematical part, but I cannot imagine how this works. I apply a force to a ball. Why does the distance over which it moves matter to me? Sure, if I calculate the kinetic Energy of ...
- 101
33
votes
11
answers
9k
views
Why does work depend on distance?
So the formula for work is$$
\left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right]
\,.
$$
I'm trying to get an understanding of how this represents energy.
...
8
votes
3
answers
1k
views
What does the 'displacement' refer to in the definition of work?
The definition of work given in books is The work is said to be done by a force on a body, when the body is moved by the force through some 'displacement'.
Now let a body of mass $m$ at rest. When a ...
- 714
1
vote
3
answers
2k
views
What is the "displacement" of the object in the definition of work?
Work in physics is mathematically defined as force $F$ applied on an object multiplied by the displacement $d$ it covers in the direction of the force. In a system where, a restrictive force exists ...
- 13
4
votes
1
answer
145
views
Conservative force definition [duplicate]
Classical Mechanics, by John Taylor defines a conservative force $F$ as a force that satisfies:
$F$ depends only on the particle's position and no other variables.
Work done by $F$ is the same for ...
- 163
5
votes
1
answer
367
views
Understanding conservative forces
I'm trying to better understand conservative forces. I have a decent intuitive idea of what they are, but I've recently learned the mathematical rigor behind it which has made me have some questions. ...
- 3,240
-1
votes
2
answers
216
views
What is work definition exactly? [duplicate]
i learn about work and most book define force x distance. The definition given not very informative and the book don't describe much about it. All they do is give above definition and then a lot of ...
- 17
1
vote
3
answers
104
views
Understanding the equation for Potential Energy
I am having a hard time understanding why Potential Energy can be calculated in the following way:
$$ \Delta U = U_f - U_i = -\int_{x_i}^{x_f} F_x dx $$
In particular, I don't understand why there ...
- 35
4
votes
2
answers
339
views
How can we show Power = $\mathbf{F}\cdot \mathbf{v}$? [duplicate]
How can we say that $$\text{Power} = \mathbf{F}\cdot \mathbf{v}$$
We know that small work done by a force $\mathbf{F}$ to displace an object by '$\mathbf{x}$' is
$$W = \mathbf{F}\cdot \mathbf{x}$$
...
- 319
0
votes
2
answers
1k
views
How has the definition of gravitational potential energy been derived?
The definition of gravitational potential energy is - The gravitational potential energy of an object at a point above the ground is defined as the work done is raising it from the ground to that ...
0
votes
2
answers
113
views
A More General Potential Energy
It occurred to me this morning that the notion of work and of spatial potential energy can be generalized to a more abstract form. In particular, work can be defined in terms of an abstract force ...
- 236
1
vote
2
answers
2k
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In the formula for work, $W=\vec{F}\cdot \vec{d}$, is $\vec{F}$ the resultant force?
Is the force $F$ the resultant force on the object, or exactly the force needed to move the object?
e.g.: I might 'need' only 1 N to move an object over 1 metre, but if I apply a 10 N force to that ...
- 209
-2
votes
1
answer
80
views
Clarification of the definition of potential at a point
My textbook defines the potential at a point to be equal to the work done in bringing a unit positive charge from infinity to that point, and then explains that the point contains another unit ...
- 101
5
votes
6
answers
3k
views
Why is differential work given as $dW=\vec{F}\cdot d\vec{r}$?
Why is differential work given as $$dW=\vec{F}\cdot d\vec{r}~?$$ Because, as I know the work done by a constant force is given as $W=\vec{F}\cdot\vec{r}$, so if the point of application of force is ...
- 305
8
votes
5
answers
2k
views
Confusion between two different definitions of work?
I'm doing physics at high school for the first time this year. My teacher asked us this question: if a box is slowly raised from the ground to 1m, how much work was done? (the system is only the box)
...
