Please #3, 5, 9, 11, 15, 19, 21, 23, 25

1. How much work is done when a weight lifter lifts 200 kg from 1.5 m to 2.0 m above the ground? 2. Compute the work done in hoisting an 1 IOO-lb grand piano from the ground up to the third oor, 35 feet above the ground. 3. A variable force of 5x": pounds moves an object along a straight line when it is A feet from the origin. Calculate the work done in moving the object from .r = l ft to x = 10 ft. . A variable force of 4J; newtons moves a particle along a straight path when it is .r meters from the origin. Calculate the work done in moving the particle from .r = 4 to x = [6. . Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work is done by the force in moving an object a distance of 8 m? F IN) 0123456781\": 6. The table shows values of a force function x). where x is measured in meters and x) in newtons. Use the Midpoint Rule to estimate the Work done by the force in moving an object from x = 4 to x = 20. 7. A force of 10 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work is done in stretch- ing it from its natural length to 6 in. beyond its natural length? 8. A spring has a natural length of 40 cm. If a 60-N force is required to keep the spring compressed 10cm. how much work is done during this compression? How much work is required to compress the spring to a length of 25 cm? 9. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. (a) How much work is needed to stretch the spring from 35 cm to 40 cm? (b) How far beyond its natural length will a force of 30 N keep the spring stretched? 10. If the work required to stretch a spring I ft beyond its natural length is 12 ft-lb. how much work is needed to stretch it 9 in. beyond its natural length? 11. A spring has natural length 20 cm. Compare the work W: done in stretching the spring from 20 cm to 30 cm with the work W; done in stretching it from 30 cm to 40 cm. How are W1 and W1 related? 12. If6 I of work is needed to stretch a spring from 10 cm to 12 cm and another 10 .l is needed to stretch it from l2 cm to 14 cm. what is the natural length of the spring? 13-22 Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. 13. A heavy rope. 50 ft long. weighs 0.5 Ib/ft and hangs over the edge of a building 120 ft high. (a) How much work is done in pulling the rope to the top of the building? (b) How much work is done in pulling half the rope to the top of the building? 14. 15. 16. 17. 18. 19. 20. 21. A thick cable. 60 ft long and weighing ISO lb. hangs from a winch on a crane. Compute in two different ways the work done if the winch winds up 25 ft of the cable. (a) Follow the method of Example 4. (b) Write a function for the weight of the remaining cable after I feet has been wound up by the winch. Estimate the amount of work done when the winch pulls up Ax feet of cable. A cable that weighs 2 lb/ft is used to lift 800 lb of coal up a mine shaft 500 ft deep. Find the work done. A chain lying on the ground is 10 m long and its mass is 80 kg. How much work is required to raise one end of the chain to a height of6 m? A lOft chain weighs 25 lb and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end. A 0.4kg model rocket is loaded with 0.75 kg of rocket fuel. After launch. the rocket rises at a constant rate of 4 m/s but the rocket fuel is dissipated at a rate of 0, l5 kg /5. Find the work done in propelling the rocket 20 m above the ground. A lmky lOkg bucket is lifted from the ground to a height of l2 m at a constant speed with a rope that Weighs 0.8 kg/m. Initially the bucket contains 36 kg of water. but the water leaks at a constant rate and nishes draining just as the bucket reaches the 12-m level. How much work is done? A circular swimming pool has a diameter of 24 ft. the sides are 5 ft high. and the depth of the water is 4 ft. How much work is required to pump all of the water out over the side? (Use the fact that water weighs 62.5 lb/ftJ.) An aquarium 2 m long. 1 m wide. and l m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is [000 kg /m".) A spherical water tank. 24 ft in diameter. sits atop a 60-ft-tall tower. The tank is lled by a hose attached to the bottom of the sphere. If a 1.5-horsepower pump is used to deliver water up to the tank. how long will it take to ll the tank? (One horsepower = 550 ft-lb of work per second.) 23-26 A tank is full of water. Find the work required to pump the water out of the spout. ln Exercises 25 and 26 use the fact that water weighs 62.5 lb/ft'l. |-3m-l 24. \\ 'T V "a... t;+ gin\" 25. 6 ft 8 ft 3 ft frustum of a cone