Aheavy rope, 50 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 140 ft high. approximate the required work by a riemann sum, then express the work as an integral and evaluate it. how much work w is done in pulling the rope to the top of the building?

Water is siphoned from a large tank and discharges into the atmosphere through a 50-mm diameter tube. the end of the tube is b = 2.6 m below the tank bottom which is a = 6.7 m deep, and viscous effects are negligible. determine the maximum height h over which the water can be siphoned without cavitation occurring. atmospheric pressure is 101.4 kpa, and the water vapor pressure is 1.79 kpa (absolute). report your answer in meters to two decimal places.