Assuming that two 1 kg balls have equal magnitude charges, how much net charge would each need to have in order for the electric force between the balls to have the same magnitude as the gravitational force betwee n the balls? if you want the balls to remain fixed in place without moving, should they have the same sign of charge or opposite signs?

Aball bearing at 220.0 °c is dropped into a cup containing 250.0 g of water at 20.0 °c. the water and ball bearing come to a temperature of 30.0 °c. what is the heat capacity of the ball bearing in j/°c? (hint: how are the algebraic signs of q related for the ball bearing and the water? )

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

J. j. thomson’s experiment disproved the theory that an atom