FIGURE 8-12 A 2-kg mass is moving along the x axis. The potential energy curve as a function of position is shown in Figure 8-12. The system is conservative. There is no friction.
-Refer to Figure 8-12. If the kinetic energy of the object at the origin is 12 J, what will be the kinetic energy at 2.0 m along the +x-axis?

Question

FIGURE 8-12  A 2-kg mass is moving along the x axis. The potential energy curve as a function of position is shown in Figure 8-12. The system is conservative. There is no friction.
-Refer to Figure 8-12. If the kinetic energy of the object at the origin is 12 J, what will be the kinetic energy at 2.0 m along the +x-axis?

Quizplus · Accepted Answer

At the origin, all the energy is in the form of kinetic energy, which is 12 J. When the mass reaches 2.0 m along the +x-axis, it has moved against a potential energy gradient, meaning the energy is being converted from kinetic energy to potential energy. Therefore, the kinetic energy will be less than 12 J. From the graph, the difference in potential energy between the origin and 2.0 m is approximately 12 J, which means that the kinetic energy will be approximately half of the original value at 2.0 m along the +x-axis, or 6 J. Adding the initial potential energy of 0 J, the total energy at 2.0 m along the +x-axis is 18 J, so the kinetic energy is 18 J - 0 J - 12 J = 6 J. Since the initial kinetic energy was 12 J, the final kinetic energy is 6 J + 12 J = 18 J. Therefore, the answer is C, 24 J.

FIGURE 8-12 a 2-Kg Mass Is Moving Along the X