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x c Sunny 3 Problem 3. A vector field F is termed "conservative" because it conserves the total energy of a mass m in motion within this field. The total energy is defined as: E K + U m I v 12 U where K represents kinetic energy, and U is the potential energy associated with F. a) Consider a scenario in which a mass m is following a smooth curve within a domain with a conservative force field F. Demonstrate that the total energy along the path, denoted as , remains constant if the following relation holds: F = md'(t). This is a manifestation of Newton's second law, f=ma, where a represents acceleration, a concept familiar from high school physics. b) Show that the work performed by a conservative vector field F to transport a mass from point po to P1 is equal to: W K (Pl) K(po), where K (p) denotes the kinetic energy of the mass at point p. _ 99+ Q Search o ENG US Relaunch to update 10:03 AM 2023-11-20