At time t_1, the kinetic energy of a particle is 34.0 J and the potential energy

Question

At time t_1, the kinetic energy of a particle is 34.0 J and the potential energy of the system to which it belongs is 11.0 J. At some later time t_f, the kinetic energy of the particle is 19.0 J. (a) If only conservative forces act on the particle, what are the potential energy and the total energy at time t_f? potential energy total energy (b) If the potential energy of the system at time t_f is 23.0 J, are there any nonconservative forces acting on the particle? Yes. The loss in potential energy and the gain in kinetic energy of the system are not equal. Yes. The gain in potential energy and the loss in kinetic energy of the system are not equal. No. The gain in potential energy and the loss in kinetic energy of the system are equal. No. The loss in potential energy and the gain in kinetic energy of the system are equal. c) Explain your answer to part (b).

Explanation / Answer

For conservative forces, the total energy of the system remains constant.
The initial total energy of the system is
Ei = Ki  + PEi
Ei  = 34 J + 11 J = 45 J
The final total energy of the system
Ef = Kf + PEf
The final kinetic energy of the system is
Kf = 19 J
The conservation of the energy
Ef  = Ei
19 J + PEf  = 45 J
PEf = 26 J
The total energy Ef = 45 J
b) yes, the gain in potential energy and the loss in kinetic energy of the system are not equal
If the potential energy of the system at the time tf is 23 J,then the total energy of the system is
Ef  = K + PE = 19 J + 23 J =   42 J
The total energy of the system is reduced, this means that there must be some non conservative forces acting on the system
The gain in potential energy and the gain in kinetic energy of the system is not equal

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