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Physics · 术语表

什么是 Work along a path?

又称: work (of a force) along a path

Definition 29.1 High School Physics · 第 29 章 — Work and Mechanical Energy

Let a force F→\vect F act on a body moving along any path from AA to BB: cut the path into displacements  ⁣dℓ→\vect{\dd\ell} so short that each is straight and F→\vect F barely changes along it. Each step earns the small work F→⋅ ⁣dℓ→=F  ⁣dℓcos⁡θ\scal{F}{\dd\ell} = F\,\dd\ell\cos\theta (Chapter 17), and the work along the path is their sum, WAB(F→)=∑F→⋅ ⁣dℓ→W_{AB}(\vect F) = \sum \scal{F}{\dd\ell} — which on a straight path with constant force collapses to last year’s F×AB×cos⁡θF \times AB \times \cos\theta.

A curved path is a broken line of many short steps: each  earns F\,; the work is the sum.
A curved path is a broken line of many short steps: each  ⁣dℓ→\vect{\dd\ell} earns F  ⁣dℓcos⁡θF\,\dd\ell\cos\theta; the work is the sum.
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