Kramer goes bowling and decides to employ the force of gravity to "pick up a spare." He rolls the 5.00 kg bowling ball very slowly so that it comes to rest a center-to-center distance of 0.140 m from the one remaining 1.25 kg bowling pin. Treat both the ball and the pin as point objects, and determine the magnitude of the force of gravity Fgrav between them.

Ten students stand in a circle and are told to make a transverse wave. what best describes the motion of the students? each student bumps the shoulder of his or her neighbor. at the exact time, all students take a step to the right. the students skip clockwise, going in a circular motion. one at a time, each student lifts his or her hands up and then down.

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.

1. a net force of 100 newton’s is applied to a wagon for 5 seconds. this causes the wagon to undergo a change in momentum of