A Hooke's law force -Toe and a constant conservative force F in the +x-direction act on an atomic ion
(a) Show that a possible potential-energy function for this combination of forces is U(x) = Toe - Fx - F2/2k. Is this the only possible function? Explain.
(b) Find the stable equilibrium position.
(c) Graph U(x) (in units of F2/k) versus x (in units of F/k) for values of x between -5Flk and 5Flk.
(d) Ate there any unstable equilibrium positions?
(e) If the total energy is E = F2/k, what are the maximum and minimum values of x that the ion reaches in its motion? If the ion has mass m, find its maximum speed if the total energy is E = F21k. For what value of x is the speed maximum?