For a K+ –Cl– ion pair, attractive and repulsive energies EA and ER , respectively, depend on the distance between the ions r, according to 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 two expressions above. (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,

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.

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)

With increases in magnification, which of the following occur? a. the field of view decreases. b. the ambient illumination decreases. c. the larger parts can be measured. d. the eyepiece must be raised.