A proton with mass m moves in one dimension. The potential-energy function is U(x) = alx2- B/x, where a and p are positive constants. The proton is released from rest at Xo = alp.
(a) Show that U(x) can be written as Graph U(x). Calculate U(xo) and thereby locate the point Xo 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 maximum? 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 Xl = 3al p. Locate the point Xl 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 = Xl), what are the maximum and minimum values of x reached during the motion?
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