Two clastic strings. ab and a'b', have the same natural length / and the same modulus of elasticity. the ends a and a' are attached to two fixed points in the same vertical line, with 4 a distance i above a'. the ends b and b' are both attached to a particle p of mass m. when phangs freely, both strings are extended. show that mig > .. the particle is pulled down a distance d below its equilibrium position and then released from rest. given that in the subsequent motion both strings remain taut, show that 2d2 < img - 2). given also that 2 = mg/3, find the potential energy stored in cach string when p is at its lowest position in the above motion.

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.