Two Mathematical statements If F is a conservative force, we have A rab/+Wb 0 Fig 12-4 a Fds+|.Fds=0(121) Path1 Path2 F·ds=0 Statement 1 (b) b Fds=F·ds(123) Path 1 Path2 Path2 F·ds=|F· d Statement2 Path 1 Path2 Ch 12 Energy II: Potential energyCh.12 Energy II: Potential energy Two Mathematical statements: a a b 1 b 2 2 1 Fig 12-4 (a) (b) If is a conservative force, we have: → F W W 0 ab.1 + ba.2 = F d s F d s 0 a b b a  +  = → → → →   (12-1) Path1 Path2 Statement 1 → → → → → →  = −  =     F d s F d s F d s b a a b b a Path1 Path2 Path2 (12-3) 0  F  ds =   Statement 2 → → → →  =    F d s F d s b a b a Path1 Path2