Fowles Cassiday 4.2.doc
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The document discusses conservative and non-conservative force fields. It states that a force field is conservative if its curl is zero everywhere, meaning the gradient of a scalar potential field can represent it. Option (a) represents a conservative field, while option (b) is not conservative because its curl is non-zero. Option (c) also represents a conservative field because its curl is equal to zero.
Fowles Cassiday 4.2.doc
- 1. 1 2 3 , det min : (a) (b) - (c) By finding the curl er e which of the following forces are conservative ix jy kz iy jx kz iy jx kz F F F Solution Conservative Field In summary, the curl of a conservative force field is zero everywhere because a field being conservative is equivalent to having zero curl, which can be derived in any basic text on vector analysis. Additionally, a conservative force field can be written as the gradient of a scalar field.
- 2. 2 2 3 4 ( ) ( 1) 0 ( 1) 0 ( 1) 0 0 Conservative a i j k X x y z x y z i X j X k X F
- 3. 3 2 2 3 4 ( ) ( 1) 0 ( 1) 0 ( 1) ( 1 1) 2 0 Not Conservative b i j k X x y z y x z i X j X k X F 3 2 3 4 ( ) ( 1) 0 ( 1) 0 ( 1) (1 1) 0 Conservative c i j k X x y z y x z i X j X k X F Analytical Mechanics Grant R. Fowles George L. Cassiday