7.86 - A particle moves along the x-axis while acted on by a Figure P7.86 single conservative force paral- U() lel to the x-axis. The force corre- sponds to the potential-energy 4.0 A C function graphed in Fig. P7.86. 2.0 The particle is released from rest Lr (m) at point A. (a) What is the direc- 05 -2.0 1.5 2.0 2.5 B tion of the force on the particle when it is at point A? (b) At point B? (c) At what value of x is the kinetic energy of the particle a maximum? (d) What is the force on the particle when it is at point C? (e) What is the largest value of x reached by the particle during its motion? (f) What value or values of x correspond to points of stable equilibrium? (g) Of unstable equilibrium? CHALLENGE PROBLEM 7.87 ... CALC A proton with mass m moves in one dimension. The potential-energy function is U(x) = a/x - B/x, where a and B are positive constants. The proton is released from rest at to = a B. (a) Show that U(x ) can be written as U(x) = Graph U(x). Calculate U(xo) and thereby locate the point to on the graph. (b) Calculate v(x), the speed of the proton as a function of position. Graph v(x) and give a qualitative description of the motion. (c) For what value of x is the speed of the proton a maxi- mum? What is the value of that maximum speed? (d) What is the force on the proton at the point in part (c)? (e) Let the proton be released instead at x 1 = 30/ B. Locate the point x ] on the graph of U(x). Calculate v(x) and give a qualitative description of the motion. (f) For each release point (x = xo and x = x1), what are the maximum and minimum values of x reached during the motion