Donnie Smith Assignment Section 7 6 due 04/17/2017 at 11:59pm MST Sharma MAT 266 ONLINE B Spring 2017 5. (1 point) An aquarium 2 m long, 1 m 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 . J Work done = 1. (1 point) When a particle is located a distance x meters from the origin, a force of cos(x/9) newtons acts on it. Find the work done in moving the particle from x = 4 to x = 4.5. Find the work done in moving the particle from x = 4.5 to x = 5. Answer(s) submitted: 2450 Find the work done in moving the particle from x = 4 to x = 5. (correct) Answer(s) submitted: 6. (1 point) A circular swimming pool has a diameter of 10 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/s2 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 2 m over the side? (9/pi)[1-sin((4pi)/(9))] (9/pi)[sin((5pi)/(9))-sin((4.5pi)/(9))] sin((4pi)/(9))-sin((5pi)/(9)) (correct) 2. (1 point) A force of 5 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? Answer(s) submitted: Answer(s) submitted: 6.125 (incorrect) (correct) 7. (1 point) A tank in the shape of an inverted right circular cone has height 7 meters and radius 4 meters. It is filled with 5 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 = 1010 kg/m3 . Your answer must include the correct units. 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 stretch it from 35 cm to 40 cm? Work done = J Answer(s) submitted: 25/24 Work = (correct) Answer(s) submitted: 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-lb (incorrect) 8. (1 point) A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x2 from x = 1 to x = 1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot. Answer(s) submitted: 625 468.75 Answer(s) submitted: 66.1334 (correct) (correct) 1 9. (1 point) The tank shown below is full of water. Using the fact that the weight of water is 62.5 lb/ f t 3 , 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. Work = Answer(s) submitted: 30679 (correct) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 2 ft-lbs