A string going over a massless frictionless pul- ley connects two blocks of masses 4.2 kg and
3.8 kg. As shown on the picture below, the
4.2 kg block lies on a 23° incline; the coefli-
cient of kinetic friction between the block and
the incline is u= 0.23. The 3.8 kg block is
hanging in the air.
The 3.8 kg block accelerates downward
while the 4.2 kg block goes up the incline
with the same acceleration.
If gravity is constant (g=9.8), what is the acceleration of the system?

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

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Arowboat passenger uses an oar to push the boat off the dock by exerting a force of 40n for 3.0s. what impulse acts on the boat.