A uniform rod of length l and mass m rests on supports at its ends. The right support (white triangle) is quickly removed. a) What is the force from the left support immediately thereafter? A uniform rod of length 2r and moment of inertia rests on top of two supports, each of which is a distance d away from the center where is a constant. The right support (white triangle) is quickly removed. b) What is the force from the left support immediately thereafter?

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

Two polarizers are oriented at 24.0∘ to one another. light polarized at a 12.0-degree angle to each polarizer passes through both. what is the transmitted intensity (%)?

Estimate the kinetic energy of the neptune with respect to the sun as the sum of the terms, that due to its daily rotation about its axis, and that due to its yearly revolution about the sun. [assume the neptune is a uniform sphere with mass = 1.0×1026 kg , radius = 2.5×1010 m , rotation period 16.1 h , orbital period 6.01×104 d and is 4.6×109 km from the sun.]