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Suppose we have block of some mass. We apply a force on it and it moves. This means that work is done on the particle resulting in a gain of energy. But the very same force is applied by the particle. Hence, negative work is done by the particle. So it loses the same amount of energy. Where am I wrong?

Qmechanic
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user64348
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2 Answers2

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Hence, negative work is done by the particle.So it loses the same amount of energy.Where am I wrong?

Everything you've said is correct, except the last conclusion. If a particle or any entity performs positive work, it spends energy. If it performs negative work, it gains energy.

Saying that an entity performs negative work is equivalent to saying that a positive work is performed on the entity.

V.F.
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The work energy theorem in its differential form states that, if you form the dot product between the net force that acts on a particle and its velocity, this will be equal to the time rate of change of its kinetic energy. if you just do it with one of many forces acting on that particle, then just as a force is a mass times a disposition to accelerate, you get a disposition to change kinetic energy, which can be called “power exerted” on the particle and then we could talk about “net power” for the net force.

You are correct that by Newton's third law, forces always come in pairs. But powers exerted, don't. And that's for a really simple reason, which is that two things can be exerting forces on each other, even when they're not moving at the same velocity. So, like, a car can accelerate or decelerate against a stationary road. The road is connected to the Earth, and so whatever motion it gets is tiny, nearly zero—and that's the power exerted on it is tiny. But the power exerted on the car is potentially very large.

Now in the broader sense we do expect energy to be conserved. That means that if the car accelerates, then it must have burned some gas in order to get that power. And if the car decelerates, the brakes must have heated up in order to dissipate that power. But what I'm trying to get you to see is that that is not a property of the road, it's something that just has to be somewhere else in the system, albeit logically connected to it.

CR Drost
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