Serway & Jewett — Conservation of Energy: Problem 11

At time \(t_i\), the kinetic energy of a particle is \(30.0 \text{ J}\) and the potential energy of the system to which it belongs is \(10.0 \text{ J}\). At some later time \(t_f\), the kinetic energy of the particle is \(18.0 \text{ J}\). (a) If only conservative forces act on the particle, what are the potential energy and the total energy of the system at time \(t_f\)? (b) If the potential energy of the system at time \(t_f\) is \(5.00 \text{ J}\), are any nonconservative forces acting on the particle? (c) Explain your answer to part (b).