2.19 For a K+−Cl− ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to E A = − 1.436 r E R = 5.86 × 10 − 6 r 9 EA=−1.436rER=5.86×10−6r9 For these expressions, energies are expressed in electron volts per K+−Cl− pair, and r is the distance in nanometers. The net energy EN is just the sum of the preceding two expressions. (a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm. (b) On the basis of this plot, determine (i) the equilibrium spacing r0 between the K+ and Cl− ions, and (ii) the magnitude of the bonding energy E0 between the two ions.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.