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

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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 $H/2$ ...
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2k 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 ...
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130 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 ...
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3answers
2k 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 ...
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2answers
211 views

How can magnetic fields have energy and yet be unable to do work with that energy? [duplicate]

Magnetic fields can't do work. However, we use the following equation to describe the energy density of a magnetic field. $u = \frac{B^2}{2\mu_0}$ The term energy density suggests that the magnetic ...
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3answers
347 views

Line integral definition of work clarification

So I am kind of confused about the role of force when calculating work. Specifically, when defining work using a line integral. There is a paragraph in my calculus book that is really throwing me off ...
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2answers
132 views

Is the coefficient of restitution frame independent and energy conservation?

In this question I am ignoring relativistic effects. The following statements I think are true: change in Kinetic energy is not invariant under change of frame Force is invariant under change in ...
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2answers
931 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 ...
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829 views

Energy of electron spinning in a magnetic field

When an electron travels in circles in a uniform magnetic field, it must lose energy because all accelerated charges radiate, and must therefore spiral down to the center. Is this energy compensated ...
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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 ...
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470 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 ...
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266 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 ...
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3k 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. ...
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235 views

How to calculate the work of the electrostatic forces in a parallel-plate capacitor?

The expression of the energy stored in a parallel-plate capacitor is: $$U = \frac{e_0\cdot A \cdot V^2}{2d}$$ with $e_0$ the vacuum permittivity, $A$ the surface of the capacitor, $V$ the applied ...
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0answers
174 views

How much work can a single grain of rice do? [closed]

I found a website saying a grain of rice contains 1/10 kcal. I'm not a physicist and haven't done maths for a long time. But here's what I came up with: E = m * g * h One small calorie equals ...
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6answers
846 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 ...
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1answer
406 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 ...
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1answer
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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 ...
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5answers
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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 ...
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3answers
953 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 ...
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4answers
17k 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 ...
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3answers
246 views

Is there an intuitive explanation of the work formula?

Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
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4answers
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Does stopping the same bike and rider at the same velocity with the front brake require less energy than the back brake?

It's the same body made by the rider and the bike moving at the same speed. So, even though braking on the front/back alters the normal forces on the opposite wheels thus creating more friction with ...
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1answer
70 views

Does the line integral definition of Work involve distance or displacement?

My textbook reports the following definition of Work: where ds is the infinitesimal displacement. I know that an infinitesimal displacement is usually denoted by dr and I also know that the ...
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4answers
216 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 ...
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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 ...
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123 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 ...
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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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215 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 ...
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320 views

Work done by frictional force on a sliding block

A block slides across a table horizontally with an initial velocity $V$. The frictional force $F$ brings it to rest after its Centre of Mass covers distance $S$. What is the work done by the ...
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92 views

Lack of rigour in usual derivation of Work-Energy Theorem

The derivation of the Work-Energy theorem usually goes as follows: You define the work done on a particle under net force $\vec{F}$ as $$W=\int\limits_C \vec{F}\cdot\mathrm{d}\vec{r}$$ And then you ...
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when an object is lifted (at a constant velocity) shouldn't the work done on the object be zero? [duplicate]

When I lift an object from the ground (at a constant velocity) I'm applying force on the object equal to its weight and the earth is also pulling it downwards with equal amounts of force. So if the ...
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3answers
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Is work done = change in KE, or change in mechanical energy?

Starting from $F = ma$ we get: $$ F=m\frac{dv}{dt} = m\frac{ds}{dt}\frac{dv}{ds} = mv\frac{dv}{ds} $$ which leads to the work done: $$ W = \int Fds = \int mvdv = m\frac{v^2}{2} - m\frac{u^2}{2} ...
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2answers
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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 ...
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67 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
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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. ...
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3answers
58 views

Using thermal expansion for mechanical work

Assume I could heat up a bar with zero heat loss to the environment. I could then use the thermal expansion to do some work, for example compress a gas. Where does the energy needed for the ...
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1answer
45 views

Is the integral of $dK$ equal the work done?

$$\frac{dK}{dt} = \frac{d}{dt} (1/2 mv^2) = mv \frac{dv}{dt} = F\frac{dx}{dt}$$ $$\implies dK = F. dr$$ Also, work is defined as $W = \int F. dr$. So does this imply integral $dK = W$?
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201 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, ...
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981 views

Factors on which Coefficient of restitution depend

What are the factors on which coefficient of restitution depend? What is the reason for more coefficient of restitution of two glass balls (0.95) than for two lead balls (0.20)?
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1answer
189 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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1answer
198 views

Confusion with curl of Lorentz magnetic force

Since the magnetic force is a no work force, $dW=\vec F\cdot d\vec r=0$ for $\vec F(\vec r)=q(\vec v(\vec r) \times \vec B(\vec r))$, therefore $\oint \vec F \cdot d\vec r=0$ by Stoke's theorem. ...
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2answers
2k views

Why do two equal-and-opposing forces each do work on a moving object but not on a stationary object?

Consider a point-mass $m$ having constant velocity but undergoing influence from two forces, $F_1$, $F_2$, having equal magnitude but opposite directions. Because the forces' magnitudes are equal, I ...
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648 views

Measuring energy when no work is done — comparing push-ups to planks

tl;dr Is there any meaningful (physical) way to compare the energy expended in the exercise of doing $x$ pushups in $t_1$ seconds, vs the exercise of doing the plank for $t_2$ seconds? I'm ...
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2answers
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Does a force do work on an object with constant velocity?

I know that a force does no work on an object if the object's displacement is zero, but if an object is moving at a constant velocity $\bar{v}$, and a force $\bar f$ (let's say that $\bar f$ and $\bar ...
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1answer
505 views

Why work to change velocity from 0 to 20 km/h is less then from 20 to 40? [duplicate]

Imagine spaceship in vacuum with mass = 1. At beginning, it has velocity 0, and kinetic energy 0. $$W_1 = 0$$ Then, it turns on its engine, and changes velocity from 0 to 20 (delta v = 20). It's ...
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3answers
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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 ...
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1answer
27 views

What information does kinetic energy and work give us about a body?

When I studied momentum I learned that momentum says about a body how hard is it to stop it. In addition, I learned that impulse tells us in some way how much time would I need to stop the object. If ...
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2answers
57 views

Why dont you take derivative of force in definition of power ? P=F.v

The derivative of work is $\bf F\cdot v .$ $$P(t)= \frac{\mathrm dW}{\mathrm dt}= \mathbf{F\cdot v}=-\frac{\mathrm dU}{\mathrm dt}\;.$$ But why not $$(\mathrm d(\mathbf F)/\mathrm dx)\cdot \mathbf x ...
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165 views

The float on a frozen lake

We have a bit of a debate going on at work. If a basketball (or any round float - let's assume one firm enough to not change size with temperature) was floating on a lake, and overnight the lake ...