The length of a simple pendulum is 0.55 m and the mass of the particle (the "bob") at the end of the cable is 0.32 kg. The pendulum is pulled away from its equilibrium position by an angle of 5.1 ° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing?
A stone has a mass of 3.41 g and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.972. When the tire surface is rotating at 16.6 m/s, the stone flies out of the tread. The magnitude FN of the normal force that each side of the tread channel exerts on the stone is 1.58 N. Assume that only static friction supplies the centripetal force, and determine the radius r of the tire (in terms of m).
Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 43.0 km/s and 62.9 km/s. The slower planet's orbital period is 6.87 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years?
A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to 2.22 times her weight as she goes through the dip. If r = 25.9 m, how fast is the roller coaster traveling at the bottom of the dip?