1- suppose your friend is sitting on a sled and asks you to move her across a flat, horizontal field. you have a choice of (a) pushing her form behind by applying a force downward on her shoulders at 30° below the horizontal, or (b) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal . which option would be easier? why?
2- a crate is sitting in the center of a flatbed truck. as the truck accelerates to the east, the crate moves with it, not sliding on the bed of the truck. what force is accelerating the crate? in what direction is this force?
3- which one you prefer; winning 2.0 newton of gold on earth or 1.0 newton of gold on the moon?

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.