Calculus 2 :

Section 7 6: Problem 3 [1 point) Suppose that 2 J of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. How much work (in J} is needed to stetd'u it from 35 cm to 4|] cm? Work done = E] J Section 7 6: Problem 4 (1 point) A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. (a) How much work is done (in ft-lb) in pulling the rope to the top of the building? Work done = ft - lb (b) How much work is done (in ft-lb) in pulling half the rope to the top of the building? Work done = ft-lbSection 7 6: Problem 5 (1 point) An aquarium 2 m long, 1m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. Use the fact that the density of water is 1000 kg/m3. Work done =Section 7 6: Problem 6 (1 point) A circular swimming pool has a diameter of 14 m. The circular side of the pool is 4 m high, and the depth of the water is 2.5 m. (The acceleration due to gravity is 9.8 m/s' and the density of water is 1000 kg/m3.) How much work (in Joules) is required to: (a) pump all of the water over the side? (b) pump all of the water out of an outlet 1 m over the side?Section 7 6: Problem 7 (1 point) A tank in the shape of an inverted right circular cone has height 6 meters and radius 2 meters. It is filled with 4 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is $ = 1070 kg/m". Your answer must include the correct units. Work =Section 7 6: Problem 8 [1 point) Atrough is TI" feet long and 1 foot high. The verlical crosssection of the trough parallel to an end is shaped like the graph of y = :I:2 from :I: = 1 to z = 1 .The trough is full of water. Find the amount of work in footpounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot. C] Section 7 6: Problem 9 (1 point) The tank shown below is full of water. Using the fact that the weight of water is 62.5 1b/ fts, find the work (in ft-lbs) required to pump the water out of the outlet. Make sure your answer is correct to within ten ft-lbs. 5 ft hemisphere Work = ft-lbs