A large crate with mass m rests on a horizontal floor. The coefficients of friction between the crate and the floor are μs and μk. A woman pushes downward with a force
→
F
on the crate at an angle θ below the horizontal. (a) What magnitude of force
→
F
is required to keep the crate moving at constant velocity? (b) If μs is greater than some critical value, the woman cannot start the crate moving no matter how hard she pushes. Calculate this critical value of μs.

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?