In an early attempt to understand atomic structure, Niels Bohr modeled the hydrogen atom as an electron in uniform circular motion about a proton with the centripetal force caused by Coulomb attraction. He predicted the radius of the electron's orbit to be 5.29 ✕ 10−11 m. Calculate the speed of the electron and the frequency of its circular motion.

Aspecial electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. the sensor measures the magnitude of the normal force that the seat exerts on a rider. the loop-the-loop ride is in the vertical plane and its radius is 23 m. sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 740 n. at the top of the loop, the rider is upside down and moving, and the sensor reads 370 n. what is the speed of the rider at the top of the loop?

A23 kg log of wood begins from rest, 300 m up a sluice (a water track used to transport logs, think of it as an inclined plane with negligible friction) inclined at 20° to the horizontal. after it reaches the flat waterway at the bottom it collides elastically with a 100 kg block of wood initially at rest near the base of the incline. (a) how long does it take the 23 kg log to travel down the incline? (b) what is the speed of the 23 kg log at the bottom of the incline? (c) what are the velocities of both blocks of wood after the collision? (d) what is the total kinetic energy before the collision? (e) what is the kinetic energy of the 23 kg log after the collision? (f) what is the kinetic energy of the 100 kg block of wood after the collision? (g) what is the total kinetic energy after the collision? (h) compare the total initial and total final kinetic energies. is this consistent with what you would expect for elastic collisions? explain!

Awoman stands a distance d from a loud motor that emits sound uniformly in all directions. the sound intensity at her position is an uncomfortable 2.0×10-3 w/m2. at a distance 2.6 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?