In 1913 niels bohr formulated a method of calculating the different energy levels of the hydrogen atom. he did this by combining both classical and quantum ideas. in this problem, we go through the steps needed to understand the bohr model of the atom. consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus(a single proton) with charge +e . in the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. when the electron is in a circular orbit, it must meet the condition for circular motion: the magnitude of the net force toward the center, fc, is equal to mv2 / r. given these two pieces of information, deduce the velocity v of the electron as it orbits around the nucleus. express your answer in terms of e, m, r, and epsilon 0, the permittivity of free space.

Apulley with a mechanical advantage of 5 will require you to pull times the amount of rope. a. 1/5 b. 5 c. 10 d. 15

Classify the following soils according to the uscs classification system. provide appropriate uscs designations. a) this sample of well-graded gravel with sand was obtained from a large earthen dam in vancouver, canada. the sample has 73% fine to coarse sub-angular gravel, 25% fine to coarse sub-angular sand and 2% fines. the maximum size of the particles is 75 mm. the coefficient of curvature is 2.7, while the uniformity coefficient is 12.4. b) this dark brown and wet soil with a “strong organic odor” has 100% passing the no. 200 sieve. the liquid limit of the material is 32% when not dried and is 21% when oven-dried. the plastic index is 21% when not dried. c) this sand has 61% predominantly fine sand, 23% silty fines, and 16% fine sub-rounded gravel size. the maximum size is 20 mm. the liquid limit is 33% and the plastic limit is 27%. d) this soil has 74% fine to coarse sub-angular reddish sand and 26% organic and silty dark brown fines. the liquid limit is 37% when not dried and is 26% when oven dried. the plastic index is 6% when not dried.

The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. find the period when the length is 144 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 7pi seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.