Practice question · Sort into groups
Sort each property: does it hold for a conservative vector field or a non-conservative one?
Groups: Conservative · Non-conservative
- Friction-like: always drains energy along any real path
- A potential function with exists
- Work can differ along two paths with the same endpoints
- Work around every closed loop is zero
Hints
- Path-independence, zero circulation, and having a potential are one property in three costumes.
- Friction opposes every motion, so a round trip always costs energy, closed-loop work cannot be zero.
Show the answer
Conservative: Work around every closed loop is zero, A potential function with exists
Non-conservative: Work can differ along two paths with the same endpoints, Friction-like: always drains energy along any real path
Why
The three faces of conservativeness (potential exists ⇔ path-independent ⇔ zero loop integrals) stand or fall together. Friction fails all three at once, which is exactly why "potential energy of friction" is not a thing.
Practise Line Integrals
The app has 8 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
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