Asolid sphere of radius r carries charge q distributed uniformly throughout its volume. find the potential difference from the sphere's surface to its center. express your answer in terms of the variables r, q and coulomb constant k.

Imagine you are riding on a yacht in the ocean and traveling at 20 mph. you then hit a golf ball at 100 mph from the deck of the yacht. you see the ball move away from you at 100mph, while a person standing on a near by beach would observe your golf ball traveling at 120 mph (20 mph + 100 mph). now imagine you are aboard the hermes spacecraft traveling at 0.1c (1/10 the speed of light) past mars and shine a laser from the front of the ship. you would see the light traveling at c (the speed of light) away from your ship. according to einstein’s special relativity, how fast will a person on mars observe the light to be traveling? a) 0.1c (1/10 the speed of light) b) c (the speed of light) c)1.1c (c+0.1c)

Light traveling in water, nwater = 1.33, strikes a plastic block at an angle of incidence of 51.4°; part of the beam is reflected and part is refracted. if the index of refraction of the plastic is 2.0, what is the angle made by the reflected and refracted beams?

An important dimensionless parameter concerned with very high-speed flow is the mach number, defined as v/c, where v is the speed of the object such as an airplane or projectile, and c is the speed of sound in the fluid surrounding the object. for a projectile traveling at 1170 mph through air at 50 ˚f and standard atmospheric pressure, what is the value of the mach number?