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. . O in Sectic X Lectu x | Lectu x | Lectu x 2025 x MA24 X MA24 X MA 2 X |Ceng x | Home x | C A ver x | sy integ x | it#1 x Goog X Searcy + C webassign.net/userimages/MA241_Chapter_1_spring20.pdf?id=531539db=v4net New Chrome available : MA241_Chapter_1_spring20.pdf 49 / 51 - 100% + CHAPTER 1. APPLICATIONS OF INTEGRATION 11. A cube shaped water tank having 5 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of 100 1b. How high can the water reach before the sides shatter? 12. The end of a rope hangs from a table. Initially 3 ft of rope is left hanging. In pulling the rope up to the level of the tabletop, an average force of 10 lb is exerted (with respect to the height of the bottom of the rope from the floor). How much work is done in the process 13. Particles with masses 10 kg, 3 kg, 4kg, 1kg, and 8 kg are located at A(-5, -2), B(3, 7), C(0, -3), D(-8, -3), and E(0, 0). Find the moments My and My of this system. Then find the system's center of mass. 47 14. Find the center of mass of the homogenous lamina in the first quadrant bounded by y = 0, x = 0, f ( y) = -y2 +9. 15. Find the center of mass of the homogeneous lamina bounded by x = 0, x = 1, y = 0, f(x)=ex. 16. Find the center of mass of the homogeneous lamina enclosed by the graphs of y = 1, y = 1, and x = 1. 17. Find the center of mass of the homogeneous lamina enclosed by the graphs of y = x2 + 1, y =0, x = -2 and x = 2. Do you notice anything unusual about this center of mass? 18. A spring whose equilibrium length is 4 ft, extends to a length of 8 ft when a force of 2 1b is applied. If 9 ft-lb of work is applied in extending this spring from its equilibrium position, what is the extended length of the spring? 19. A gasoline storage tank in the shape of a right circular cylinder, with a height of 12 m and a radius of 10 m, is full of gasoline. How much work is required to pump all the gasoline over the top of the tank. (density of gasoline: p # 720 kg/m3). 20. The ends of a trough are isosceles trapezoids. The top of the trough is 5 m across and the bottom is 1 m; it is 2 m deep. If the trough is filled to 1m with water, what is the hydrostatic force due to the water pressurerom one end of the trough