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

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311 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 ...
3
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1answer
1k views

Area under a $pV$ diagram

What does the area under a Pressure volume diagram equal? I read in my textbook it equals 'external' work done, but why is this? First of all, what exactly is external work? Can you get it ...
3
votes
1answer
98 views

Could $\int (\ddot\phi + \mu\dot\phi^2)d\phi$ ever be negative? How to show it?

I am working on the following problem: Given a mass $m$ at rest at the base of an incline surface shaped like 1/12th of a circle with radius $R$. The mass is pulled up the incline by a rope that ...
3
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4answers
206 views

Definition of force, kinetic energy and momentum

I've edited the post. Q1 and Q4 are the important ones but I didn't delete Q2 and Q3 since some older answers would not make sense anymore. To begin with, the formula of the kinetic energy $T$ is ...
3
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2answers
2k views

work done by tension

The problem statement, all variables and given/known data Consider the following arrangement: Calculate the work done by tension on 2kg block during its motion on circular track from point $A$ to ...
3
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1answer
221 views

Intuition behind Work

I have a doubt in understanding the intuition behind the concept of work. First of all, I think this isn't duplicate, I've searched on the site, and the closest thing I've found was this post which is ...
3
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2answers
231 views

When work is performed solely by magnetism, is there an equivalent loss of energy from the magnetic field?

When two magnets are placed within appropriate proximity and released, the attractive force will perform work and bring them together. Work is performed overcoming friction. Can we measure a ...
3
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2answers
92 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
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6answers
598 views

Centripetal Force Acceleration

In uniform circular motion, acceleration is $\frac{v^2}{r}$ and time which it acts $\rightarrow 0$. So $\Delta v = 0$, but then why/how does direction change, when the acceleration should be ...
2
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1answer
211 views

Work Done to click a mouse?

Is there any good research done to find out the work done in clicking a mouse button. any link to that would be greatly appreciated. P.S. i am not too sure whether this question belongs here or ...
2
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4answers
343 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 ...
2
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6answers
2k 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 ...
2
votes
5answers
915 views

Is there a mathematical derivation of potential energy that is *not* rooted in the conservation of energy?

For simplicity I'll consider only gravity, but in general this question only applies to conservative forces. As per my understanding, the way one gets to the equation for gravitational potential ...
2
votes
1answer
434 views

What is the difference between $Q=\Delta U+W$ and $\Delta U=Q+W$?

Is $Q=\Delta U+W$ for when the the work is done from the system while $\Delta U=Q+W$ is for when the work is done by the system? Will anybody explain this to me, please? When do we use $Q=\Delta ...
2
votes
2answers
128 views

If an asteroid were threatening the Earth, could I deviate it just by jumping on it?

An impact by a 10 kilometres asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets coming ...
2
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4answers
103 views

Why work $W$ and heat $Q$ are different concepts?

I understand heat as the flow of energy (through radiation, convection or conduction) from one body to another. When I think about conduction (for example) I visualize particles that jiggle a lot ...
2
votes
4answers
93 views

Is work done by how much velocity is changed or how much displacement is done?

A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat? The answer key is "No" according to the work energy theorem about work is done when ...
2
votes
3answers
110 views

How do I relate $ds$ to $dx$?

A block of mass $5\text{ kg}$ is kept on an inclined plane with angle of inclination $37°$, attached to a spring with spring constant $10\text{ N/m}$ kept at the base of the incline. The ...
2
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2answers
191 views

Mechanical work to required battery power

I have a very practical question where I've calculated the mechanical work needed by a simple mechanical system by solving the line integral $W = \int_C \ F \ dx$. However, since I have a black spot ...
2
votes
3answers
144 views

Why is it mandatory to 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 ...
2
votes
3answers
168 views

Joules to do something

If my very limited understanding is correct, then, not accounting for gravity: 1 Newton can move 1 kilogram 1m But, can 2 Newtons move 1 kilogram 2 meters? Is this because 1 Newton = acceleration ...
2
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1answer
41 views

Work done or not in this case?

I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any ...
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2answers
717 views

Having trouble understanding the work energy principle intuitively

I'm having trouble understanding the work energy principle intuitively. This is what I'm solid on so far: If you have a ball rolling down a hill, it loses potential energy and gains kinetic energy. ...
2
votes
1answer
2k 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 ...
2
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1answer
160 views

Is work is equal to $mv^2$ (without $\frac{1}{2}$)?

I was trying to come up with an equation for work that doesn't include time, because I don't know time. Here's what I did: $$ work = Fd = mad = m{v\over t}d = m{v\over\left({d\over v}\right)}d = ...
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3answers
107 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
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2answers
208 views

Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions?

What are the conditions in order for the equations: Entropy $dQ = TdS$ and Work $dW = -p dV$ to work? I think for $dQ = T dS$, it must be a reversible process? But for $dW = -p dV$, shouldn't it ...
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3answers
95 views
+50

Why do the agents of conservative force return work done against them to the body that worked on them?

Let a body moves & a conservative force opposes its motion by applying an opposing force on it. Therefore, by Newton's third law of motion, the body will also exert reactive force on the agent of ...
2
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2answers
148 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 $p_i$ ...
2
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2answers
197 views

Question related to work done and energy

Suppose you lift a box from the ground over your head. You will be using energy as there is work done. But when you keep the box lifted over your head, aren't you using any extra energy?
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2answers
587 views

Work done by Lorentz Force in case of motional emf

In the classical example of the slidewire generator where the rod slides on a U-shaped conductor in a magnetic field, we get a charge separation due to the Lorentz force. The way the induced emf is ...
2
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2answers
311 views

Signs in proof of gravitation potential energy (GPE)

Proof of gravitational potential energy. Work done by gravity in bringing mass from infinity to a distance of $r$ between masses. When we use the integration formula and arrive at the answer we ...
2
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2answers
305 views

Does a different opposing force affect work?

Suppose a man exerts $10~N$ as he lifts a $1~kg$ box a distance of $2~m$ against Earth's gravity. To determine work we can use the following equation: $$ W = F \cdot d \\ W = (10~N) \cdot (2~m) = ...
2
votes
1answer
267 views

A dielectric table is being inserted between a plate capacitor and $\triangle U<0$ how to deduce the table is attracted to the plates?

I am practicing for an exam in my Physics $2$ course. One of a previews exam questions described a plate capacitor and asked to calculate the initial energy $U_{0}$, then a dielectric table was ...
2
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1answer
937 views

Thermodynamic cycles, when is the work negative/positive?

ever since I begun calculating thermodynamical cycles, I've had problems with determining the sign of the work along a particular bit of the cycle. Of course, I guess that an arbitrary cycle is ...
2
votes
1answer
205 views

Work done by gravity on Water

Now according to me we would see change in potential energy of system and equate it to the work done by gravity. But when we see this the first column lowers by $H/2$ and right one rises by $H/2$ ...
2
votes
1answer
116 views

Conservative forces intuition

Take a gravitational field (with all the field lines pointing inwards) and a perfectly circular curve as an object's trajectory. To find the work exerted by the force on the object, compute the line ...
2
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1answer
202 views

Understanding Work and the conservation of energy

We have a car with a mass of $780 kg$ with travels with a speed of $50 km/h$. The car brakes and after $4,2m$ is stops completely. Warmth is created. Calculate the friction. I solved this easily, by ...
2
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1answer
218 views

Moving along friction surfaces

If a particle moves along a one dimensional surface with constant friction. As the particle moves from point $A$ to point $B$ it loses an amount of energy equals $E(A,B)$. Consider that the particle ...
2
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3answers
1k views

How do I find work done by friction over a curve represented by a polynomial?

I am facing a problem in Physics. Problem: What will be the work done by the frictional force over a polynomial curve if a body is sliding on this polynomial($a+bx+cx^2+dx^3+\ldots$) curve from rest ...
2
votes
2answers
207 views

In continuum mechanics, what is work potential in the context of total potential energy?

I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh–Ritz method. The book ...
2
votes
1answer
474 views

What is the relationship between Force and Kinetic Energy?

I am an Middle-School (Grade 8) student, who is self-learning classical mechanics. I saw this equation from Classical Mechanics: $\vec F=m \vec a$, the following equation is pretty straight forward ...
2
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1answer
26 views

Minimum Power Required

Here is a question, I found two methods to solve it, differing in the answers and I'm not sure why a method is incorrect. Question: A fire hose of cross section area ...
2
votes
1answer
56 views

Work Done On a Body When It is Not in Contact with the agent of the Force

Is it necessary for work to be done on a body that the agent of the force remains in contact with the body? For example, if I hit a football with my foot with a small amount of force and it moves a ...
2
votes
2answers
439 views

Falling chain with friction

I really need some help with a physics problem, and I guess my doubt is more conceptual, than question based. But still, let me pose it to you: A uniform chain of mass $M$ and length $L$ lies on ...
2
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1answer
1k views

Does moving something horizontally in gravity do no work?

Bill’s job is to lift bags of flour and place them in the back of a truck, which is parked next to him. Sally is loading the same bags of flour into a similar truck that is located 10 m away. ...
2
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3answers
3k 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 ...
2
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4answers
117 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 ...
2
votes
0answers
51 views

Connection: Work on dipole <-> optical absorption

If I consider a two-level system with a ground and an excited state, I can compute the instantaneous rate at which work is being done on the dipole $\mu(t)$ by an electric field $E(t)$: $\dot{W} = ...
2
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2answers
367 views

Why can't the units of work and torque be interchanged? [duplicate]

When I'm studying about work and torque, I found that their unit are the same. But, why don't we use Joule (unit of work) instead of Newton-meter (unit of torque)? Since $\mathrm{1\ Joule = 1\ Nm}$, ...