Answer the following questions below. The answer is provided you will need to show your solution.

\f1. A 60 kg woman walking through an alley accidentally broke the heel of her left high-heeled shoes. Now the woman tries to balance on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor? 2. A barrel contains a 0.120 m layer of oil floating on water that is 0.250 m deep. The density of the oil is 600 kg/m3. What is the gauge pressure at the oil- water interface and at the bottom of the barrel? 3. A 950-kg cylindrical can buoy floats vertically in salt water. The diameter of the buoy is 0.900m. Calculate the additional distance the buoy will sink when a 70.0-kg man stands on top of it. 4. A frog in a hemispherical pod, as shown in the figure on the right, just floats without sinking into a sea of blue-green ooze with density 1.35 g/cm3. If the pod has radius 6.00 cm and negligible mass, what is the mass of the frog? 5. A Ping-Pong ball has a diameter of 3.80 cm and average density of 0.084 0 g/cm3. What force is required to hold it completely submerged under water? 6. A piece of aluminum with mass 1.00 kg and density 2 700 kg/m is suspended from a string and then completely immersed in a container of water. Calculate the tension in the string (a) before and (b) after the metal is immersed. 7. Water runs into a fountain, filling all the pipes, at a steady rate of 0.750 m3/s. (a) How fast will it shoot out of a hole 4.50 cm in diameter? (b) At what speed will it shoot out if the diameter of the hole is three times as large? 8. You need to extend a 2.50-inch-diameter pipe, but you have only a 1.00-inch-diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 6.00 cm s in the wide pipe, how fast will it be flowing through the narrow one? 9. A sealed tank containing seawater to a height of 11.0 m also contains air above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a small hole. How fast is this water moving? 10. A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column Water is 15.0 cm as shown in the figure. (a) What is the gauge pressure 15.0 cm at the water-mercury interface? (b) Calculate the vertical distance h from the top of the mercury in the righthand arm of the tube to the top of the water in the left-hand arm