Wednesday, 19 April 2017

classical mechanics - 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 as


$$W=\int_\gamma \mathbf{F} = \int_I \langle \mathbf{F}\circ \gamma, \gamma'\rangle$$


Now usually I see the term "work done against a force" and I don't really understand what it means. The reason is that in my understanding, work is always done by a force upon a particle or system of particles. If we talk about work done against a force, it is work done by which force on which particle or system?


Also, mathematically, how it is obtained? If we want to know not the work done by a force, but against it how we obtain it? I imagine is just the opposite, just changing the sign, but I'm unsure, and if it is really that I can't grasp why it should be.





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