I am having troubles with these: If you could answer any 1 of these, thank you :) This is due by Midnight (tonight) 12/15/05 (*sigh*) (1) The coefficient of static friction between the person and the wall is 0.64. The radius of the cylinder is 5.48 m. The acceleration of gravity is 9.8 m/s squared. An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away. What is the minimum angular velocity wmin needed to keep the person from slipping downward? Answer in units of rad/s. (2) To prepare for the g-forces of space launch, an astronaut is training on a centrifuge where his apparent weight is 4.2 times his normal weight mg. The centrifuge spins the astronaut in a horizontal circle of radius R = 4.17 m at constant speed v while the Earth's gravity pulls him down at g = 9.8 m/s squared. The astronaut's seat is inclined to stay perpendicular to his apparent weight. Calculate the centrifuge's rotational speed v. Answer in units of m/s. (3) On the way from a planet to a moon astronauts reach a point where that moon's gravitational pull is stronger than that of the planet. The masses of the planet and the moon are, respectively, 5.37E24 kg and 7.36E22 kg. The distance from the center of the planet to the center of the moon is 3.45E8 m. Determine the distance of this point from the center of the planet. Answer in units of m. (4) Given: G = 6.67259E-11 N m^2 / kg^2 (^2 means to the power of 2). A distant star has a single planet circling it in a circular orbit of radius 3.67E11 m. The period of the planet's motion about the star is 722 days. What is the mass of the star? Answer in units of kg. (5) Given: G = 6.67E-11 N m^2 / kg^2 (^2 means to the power of 2). Mearth = 5.98E24 kg. An earth satellite remains in orbit at a distance of r = 12010 km from the center of the earth. What speed would it have to maintain? Answer in units of m/s. (6) The planet Mars has a mass 6E23 kg and radius 3.5E6 m. The gravitational constant is 6.67259E-11 N m^2 / kg^2. What is the acceleration of an object in free-fall near the surface of Mars? Answer in units of m/s squared. (7a) Given: G = 6.67259E-11 N m^2 / kg^2. The asteroid Ceres has a mass 7.384E20 kg and a radius of 536.7 km. What is g on the surface? Answer in units of m/s squared. (7b) How much would a(n) 83.7 kg astronaut weigh on this asteroid? Answer in units of N. Thank you very much for your time and help!