Create a bucket by rotating around the y axis the curve y = 5 In(5) from y=0 toy 9. If this bucket contains a liquid with density 780 kg/m³ filled to a height of 8 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s² for gravity. Work 108828728.1 # Preview Joules

When a person sits erect, increasing the vertical position of their brain by 36.0 cm, the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 mL of blood raised 36.0 cm? (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.

(a) Estimate the time it would take to fill a private swimming pool with a capacity of 80,000 L using a garden hose delivering 60 L/min. (b) How long would it take to fill if you could divert a moderate size river, flowing at 5000 m3/s, into it?

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A water tank, shown to the right, is shaped like an inverted cone with height 4 m and base radius 1 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. 1 m 4 m

3. For the hydraulic lift shown; A, Az The small piston area is 5 cm? and the large piston area is 50 cm?. The system is used to lift up a block of mass m = 300 Kg. Find the magnitude of the force F sufficient to do the work and find the work done on the block when it is lifted 120 cm.

10 Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.22 g/cm³. The area of each base is 3.36 cm2, but in one vessel the liquid height is 0.740 m and in the other it is 1.38 m. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected. Number i Units

A log splitter uses a pump with hydraulic oil to push a piston, attached to which is a chisel. The pump can generate a pressure of 2.4x107 Pa in the hydraulic oil, and the piston has a radius of 0.035 m. In a stroke lasting 15 s, the piston moves 0.69 m. What is the power needed to operate the log splitter's pump? Number i Units

Cords are loop around a small spacer separating two cylinders each weighing 400 lb and pass, as shown in the figure over frictionless pulleys to weights of 200 lb and 400 Ib. a. Draw the FBD and set up the equations to solve the problem. b. Solve the angle e and normal pressure N between the cylinders and the smooth horizontal surface. Total W = 800 lb 400 lb 200 lb

A conical water tank has its top at ground level (consider this to be the x-axis) and its base 12 ft below ground. The radius of the cone at ground level is 4 ft. It is filled with water weighing 62.4 lb/cu.ft. and is to be emptied by pumping the water to a spigot 3 ft above ground level. Find the total amount of work performed in emptying the tank? A 3456 ft-lbs B 23961.6 ft-lbs c) 8985.6 ft-lbs с D 1296 ft-lbs