By examining the effective potential energy find the radius at which a planet (or cornet) with angular momentum t can orbit the sun in a circular orbit with fixed radius. [look at du_eff/dr.] (b) show that this circular orbit is stable, in the sense that a small radial nudge will cause only small radial oscillations. [look at d^2u_eff/dr^2.] show that the period of these oscillations is equal to the planet's orbital period. u_eff(r) = - g m_1 m_2/r + l^2/2 mu r^2.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Does work output exceed work input when a machine is used? a) yes, it does, as machines create energy. b) it depends on the type of machine used. c) no, it doesn’t, as machines are inefficient. d) no, it doesn’t, as machines cannot create energy.

Abar magnet cut in half will form a total ofpoles.a)fourb)eightc)two