The figure below shows a plot of potential energy U versus position x of a 1.30 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are U1 = 10 J, U2 = 35 J, and U3 = 50 J.

Sorry, but I'm unable to see the figure you mentioned. However, I can still provide you with an explanation based on the information you have provided.

The plot you described represents the potential energy versus position for a 1.30 kg particle moving along the x-axis. The potential energy is denoted as U, and the positions are represented by x.

From the information given, there are three specific positions identified, and their corresponding potential energies are U1 = 10 J, U2 = 35 J, and U3 = 50 J.

This plot provides valuable information about the system's potential energy as the particle moves along the x-axis. Specifically, it tells us how the potential energy of the particle changes at different positions.

To determine how the potential energy changes as the particle moves, you can analyze the slope of the plot. The slope of the potential energy versus position graph gives us the force acting on the particle.

If we take the derivative of the potential energy function U with respect to position x, we get the force F acting on the particle:

F = dU/dx

By examining the graph, you can determine the force acting on the particle at different positions. A positive slope indicates a positive force, while a negative slope indicates a negative force.

Additionally, you can also determine the total mechanical energy of the particle, which is the sum of its kinetic energy and potential energy. The total energy is conserved if no non-conservative forces are present. In this case, the only forces being considered are conservative forces.

To determine the kinetic energy of the particle at each position, you can subtract the potential energy from the total mechanical energy at that position:

K = E - U

where K is the kinetic energy, E is the total mechanical energy, and U is the potential energy.

Overall, analyzing the potential energy versus position plot provides valuable insights into the forces acting on the particle as well as the energy conservation in the system.