An ideal spring obeys hooke's law: f = −bikx. a mass of m = 0.3 kg hung vertically from this spring stretches the spring 0.13 m. the acceleration of gravity is 9.8 m/s 2 . calculate the value of the force constant k for the spring. answer in units of n/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

An charge with mass m and charge q is emitted from the origin, (x, y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.

Rank the six combinations of electric charges on the basis of the electric force acting on q1. define forces pointing to the right as positive and forces pointing to the left as negative. rank positive forces as larger than negative forces. q1,q2,q3 = positive(+) q1 = + q2 = + q3 = - q1 = + q2= - q3= + q1= - q2= + q3= + q1= + q2= - q3= - q1,q2,q3 = negative