Asatellite is in a circular orbit around mars, which has a mass m = 6.40 × 1023 kg and radius r = 3.40 ×106 m.

a) derive an expression for the orbital speed assuming that the orbital radius is r.

b) derive an expression for the orbital period assuming that the orbital radius is r.

c) the orbital period of the satellite can be synchronized with mars’ rotation, whose period is 24.6 hours. determine the required orbital radius for this to occur.

d) determine the escape speed from the surface of mars.

Apulley system is used to lift a 2,000 newton engine up a distance of 3 meters. the operator must apply a force of 250 newtons to the chain of the pulley system to lift the motor. to lift the engine 3 meters, the operator must pull a total of 30 meters of chain through the pulley system. what is the value of di?

Athin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. a) what is the magnitude of the electric field due to the rod at z = 0? n/c (b) what is the magnitude of the electric field due to the rod at z = infinity? n/c (c) in terms of r, at what positive value of z is that magnitude maximum? r (d) if r = 4.00 cm and q = 9.00 µc, what is the maximum magnitude? n/c

16. a brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 n on him. the mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1.20m/s2 size 12{1 "." "20"" m/s" rsup { size 8{2} } } {} backward. (a) what is the force of friction between the losing player’s feet and the grass? (b) what force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) draw a sketch of the situation showing the system of interest used to solve each part. for this situation, draw a free-body diagram and write the net force equation.