Work by Variable Force

Integrate F dot dr.

Concept

Work by Variable Force is a foundational idea in this chapter. The defining relationship is:

$W = \int \vec F\cdot d\vec r$

Use this for springs, gravity at variable r, etc.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $W = \int \vec F\cdot d\vec r$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.