Rope (initially vertical) va flexible, uniform rope of mass m and length l is initially held motionless over frictionless ice, with one end just touching the ice. at the bottom of the rope is a very small, frictionless ramp that causes the rope to end up sliding horizontally on the ice with velocity v. what is the magnitude of v?

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?