A small block, with a mass of 250 g, starts from rest at the top of the apparatus shown above. It then slides without friction down the incline, around the loop and then onto the final level section on the right.
The maximum height of the incline is 80 cm, and the radius of the loop is 15 cm.
a. Find the initial potential energy of the block
b. Find the velocity the block at the bottom of the loop
C. Find the velocity of the block at the top of the loop.
d. What is the normal force on the block at the lowest point of the loop?
e. What is the normal force on the block at the highest point of the loop?

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

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

Ineed this now one scientist feels that the changes in global climatic patterns may be good for the health of the biosphere. another scientist feels that sharp changes in climatic patterns could result in the extinction of the biosphere. which of these is the most likely reason the two scientists gave conflicting opinions on the impact of changes in the global climatic pattern? they do not have enough knowledge on the topic. they did not discuss the issue among themselves. they believe conflicting opinion strengthens science. they study different areas of science and have different scientific focuses.