A 0.40-kg particle moves under the influence of a single conservative force. At point A where the particle has a speed of 10 m/s, the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 J of work on the particle. What is the value of the potential energy at point B?
A) +65 J
B) +15 J
C) +35 J
D) +45 J
E) −40 J

Question

Quizplus · Accepted Answer

The work done by the force on the particle is equal to the change in the particle's kinetic energy. The initial kinetic energy at point A is (1/2)mv^2 = (1/2)(0.40 kg)(10 m/s)^2 = 20 J. The work done on the particle increases its kinetic energy to 20 J + 25 J = 45 J. The total mechanical energy at point A is the sum of kinetic and potential energies, which is 20 J + 40 J = 60 J. Since mechanical energy is conserved in a system with only conservative forces, the total mechanical energy at point B is also 60 J. The kinetic energy at point B is 45 J, so the potential energy at point B must be 60 J - 45 J = 15 J to conserve the total mechanical energy.

A 040-Kg Particle Moves Under the Influence of a Single Conservative