Problem NASA is testing a new propulsion system for interstellar travel. The system uses a unique fuel whose denssitj.r varies with the amount remaining in the fuel tank. The cylindrical fuel tank is 15 meters. high 'with a radius of 5 meters. The density of the fuel at a height h from the base of the tank in given by pfh] = 3m + am? 1(3me '11) simulate space condition-a. NASA uses a vacuum Chamber where the force mquired to expel the fuel at a height h is Flhl = PU!) X 9 where g is the acceleration due to gravity on Earth (9.3! mfszj. Objective Determine the total work done by the propulsinn system to expel all the fuel from the tank in the vacuum chamber. [5 mi . Hints 1. Start by determining the differential volume of a thin slice of the fuel tank. 2. Use the given densit}r flmetion to determine the differential mass ofthis slice. 3. Calculate the force exerted by this differential mass. 4. Integrate this force over the height of the ten]: to determine the total work done. r151