Suppose you are myopic (nearsighted). you can clearly focus on objects that are as far away as 52.5 cm away. you can clearly focus on objects which are as close as 17.2 cm from your eyes, but no closer. the purpose of glasses would be to make objects that are far away appear to be at your far point. what would be the refractive power (in diopters - do not enter units) for your prescription? if your glasses make distant objects appear to be at your far point, then any object that is closer to you will appear even closer than it really is. what is the closest distance from your face at which you could hold a book and still be able to see it clearly while wearing your glasses?

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

(**i would really appreciate if this was answered soon** ) which pair of quantities includes one quantity that increases as the other decreases during simple harmonic motion?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.