Recently, dr. goodenough and his team at the university of texas filed a patent for a new kind of battery that might revolutionize electric cars. (links to an external site.)a newspaper report described the battery as "blazingly creative" because of

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.

Oxygen undergoes an isentropic expansion from 120 degree c and 280 kpa absolute to 140 kpa absolute. determine the final temperature of the oxygen and the amount of work per kg of o_2 produced in the process if it is adiabatic.

The system is released from rest with the cable taut, and the homogeneous cylinder does not slip on the rough incline. determine the angular acceleration of the cylinder and the minimum coeffi cient s of friction for which the cylinder will not slip.