8.8 calculate the propellant mass required to launch a 2000-kg spacecraft from a 180-km-altitude circular earth orbit on a hohmann transfer trajectory to the orbit of saturn. calculate the time required for the mission and compare it with that of cassini. assume the propulsion system has a specific impulse of 300 s. {ans.: 6.03 yr; 21,810 kg}

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

A1-lb collar is attached to a spring and slides without friction along a circular rod in a vertical plane. the spring has an undeformed length of 5 in. and a constant k =25 lb/ft. knowing that the collar is released from being held at a determine, the speed of the collar and the normal force between the collar and the rod as the collar passes through b.

During the experiment if you could triple the breakaway magnetic force with all other quantities left unchanged, what is the new value for the critical velocity if it was v0 (initial velocity), initially? (b) now if you halved the radius with all other quantities left unchanged, what is the new critical velocity if it was v0 (initial velocity), initially? (c) if during the experiment, critical velocity quadrupled with all other quantities left unchanged, what is the new breakaway force if its magnitude was initially f0,?