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16 votes
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Areas with anti-parallel gravity in classical physics

If we let the $y$-axis point upwards then OP's 2D gravitational field is $$\vec{g}~=~ \begin{pmatrix} 0 \cr g~{\rm sgn}(x)\end{pmatrix}.$$ It has a non-zero curl $$(\vec{\nabla}\times \vec{g})_z~=~2g\...
Qmechanic's user avatar
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10 votes
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Is the work I do on the object always equal in magnitude but opposite in sign to the work the object does on me?

I think there is a difficulty in answering this question because it is not always possible to locate energy in one body or the other when they are interacting. Some of the energy (and it might even be ...
Andrew Steane's user avatar
7 votes

Is the work I do on the object always equal in magnitude but opposite in sign to the work the object does on me?

A mass $m$ which starts from rest has constant force $F$ acting on it for a time $\Delta t$. The change in position of the mass is $\frac 12 \frac F m (\Delta t)^2$ and this can be used to determine ...
Farcher's user avatar
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5 votes

Areas with anti-parallel gravity in classical physics

The potential that yields your provided force field is discontinuous. One possible choice would be $$V(x,y) = \begin{cases} gy & x\leq 0 \\ -gy & x>0 \end{cases},$$ which has a dicontinuity ...
Refik Mansuroglu's user avatar
5 votes

Is the work I do on the object always equal in magnitude but opposite in sign to the work the object does on me?

Newton's third law holds If we deal with a system that can be described by the laws of classical mechanics, third law is a principle of such a theory and thus it holds. So, to answer your question ...
basics's user avatar
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4 votes

Is the work I do on the object always equal in magnitude but opposite in sign to the work the object does on me?

In other words, are the 'work I do on the object' and the 'work the object does on me' equal in magnitude but opposite in sign? Sometimes yes, sometimes no. For the work to be equal and opposite the ...
Bob D's user avatar
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4 votes

Strange calculus involved in work and power

The correct formula for work is $$ \Delta W = \int P d t = \int \vec{F} \cdot \vec{v} \,dt $$ Now, if $\vec{F}$ is constant, then we can take it out of the integral and write $$ \Delta W = \vec{F} \...
Prahar's user avatar
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2 votes

Where am I wrong in proving that force perpendicular to motion increases speed and kinetic energy?

First, I am using $z$ for the vertical direction. The eq. of motion are: $$ \frac{d^2\vec r}{dt^2} = \frac 1 m \vec F = -g\hat z $$ or: $$ \ddot x = 0 $$ $$ \ddot y = 0 $$ $$ \ddot z = -g $$ which is ...
JEB's user avatar
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2 votes
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Work Done by kinetic friction in Circular Motion

In circular motion, your total displacement $$\oint \mathrm{d}\vec{s}$$ is zero, correct. But for work, you are not integrating just the displacement $\mathrm{d}\vec{s}$, but the quantity $\vec{F}\...
CompassBearer's user avatar
1 vote

Can siphons improve the efficiency of hydroelectric dams?

No, you cannot gain any efficiency. Remember the bernoulli equation: $P_1 + \frac12\rho v_1^2 + \rho gh_1 = P_2 + \frac12\rho v_2^2 + \rho gh_2$ If you have water at rest at $P_{atm}$ on the top, and ...
Pato Galmarini's user avatar
1 vote

Is the work I do on the object always equal in magnitude but opposite in sign to the work the object does on me?

Does Newton's third law also hold in the work-energy theorem? In other words, are the 'work I do on the object' and the 'work the object does on me' equal in magnitude but opposite in sign? Sometimes ...
Ján Lalinský's user avatar
1 vote

Energy Transfer and Work in Action-Reaction Forces

Because doing work on something doesn't make you gain kinetic energy. Now I have said this multiple times on this site, and will continue: Bringing the human body into physics never, ever, helps. It ...
JEB's user avatar
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1 vote

Voltage: work to move a charge, or difference of electric potential?

In the diagram below the red dashed circle with the negative charge at its centre is an equipotential with the electric field lines produced by the negative charge at right angles to the circle. As ...
Farcher's user avatar
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1 vote
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Voltage: work to move a charge, or difference of electric potential?

it will take work to move the positive charge from point A to point B, as I must counteract the vertical component of the electric force and so on. You are quite correct that the distance to the ...
John Rennie's user avatar
1 vote

Why is work done by force $+mgh$ in the situation of throwing something up?

You are right, the work applied is not necessarily equal to $mgh$. To see this, let's look at energy conservation: $$K_0+U_0+W_{\text{n.c.}}=K_f+U_f$$ where $K_0$ and $K_f$ are the initial and final ...
BioPhysicist's user avatar
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1 vote
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Work performed by hydrostatic pressure

With a little less math, the power of a stress distribution $\mathbf{t}_n$ over the boundary of a volume $V$ is $$P(t) = \oint_{\partial V} \mathbf{t}_n \cdot \mathbf{u} \ ,$$ being $\mathbf{u}$ the ...
basics's user avatar
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1 vote

The conservative force

While @basics has the math right, I understand your question is about the physical interptetation. To answer this, we must understand what a force field is, since the definition of the rotation ...
paulina's user avatar
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1 vote

The conservative force

An example might be the best way to see it. Set up some electrodes that create a horizontal electric field. Make it so the field strength is proportional to height. This is a non-conservative field. ...
mmesser314's user avatar
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1 vote

The conservative force

Remark the curl it's the measure of the rotation of the vector field around a specific point Before answering your question, I'd replace (local) "rotation" with (local, or elementary) &...
basics's user avatar
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1 vote

What are the forces that do work when a spring between two masses pulls inwards?

There is no kinetic energy change in the second system (1,2, spring). So there is no net work done, so no need to ask which external forces that do the work. The constituent particles of the system do ...
Steeven's user avatar
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