Aforce in the + x-direction with magnitude f(x) = 18.0n -(0.530 n/m)x is applied to a 6.00-kg box that is sitting on the horizontal, frictionless surface of a frozen lake. f(x) is the only horizontal force on the box. if the box is initially at rest at x=0, use the work-energy theorem to determine its speed after it has travelled 14.0 m?

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

Afigure skater is rotating at a rate of 200 revolutions per minute. what is the angular speed, in units of rad/s? 20.9 12000 200 3.33

Assume that a person skiing high in the mountains at an altitude of h = 15100 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level. assume that the air composition (i.e. % of air that is oxygen) is the same at sea level as it is at 15100 ft.