Exam #2 Spring 2000

1. The bottom of a tank is filled with sea water to a depth of 94.0 cm with a density of 1030 kg/m ³. The top portion of the tank is filled with gasoline that has a density of 710 kg/m ³ to a depth of 68.0 cm above the sea water. The tank has a radius of 2.70 m and is open at the top to air at a pressure of 101 kPa. There is a plug in the bottom of the tank with a cross-sectional area of 3.60 mm ².

(A) How many kg of sea water are there in the tank?
Ans:{22,200 kg}

(B) What force (in N) does the liquids exert on the plug in the bottom of the tank?
Ans:{ .0512 N}

(C) If the plug is removed and the sea water flows out of the hole into the air, at what speed will the sea water flowing out of the tank?
Ans:{5.25 m/s}

2. A long tube with a radius of 3.20 cm is inserted in to a container of water in such a way that the bottom of the tube is 16.0 cm below the surface of the water. Oil with a density of 870 kg/m ³ is poured into the tube until all the water is displaced from the tube, i.e., the bottom of the oil is flush with the bottom of the tube. Use 1000 kg/m ³ as the density of water.

(A) What is the gauge pressure above atmospheric air pressure between the oil and the water at their interface at the bottom of the tube?
Ans:{1.57 kPa}

(B) How many grams of oil were poured into the tube?
Ans:{515 g}

(C) What is the height h of the oil above the surface of the water in the container?
Ans:{2.39 cm}

3. A balloon filled with helium has a volume of 4.50 l, a temperature of 21.0 ⁰C, and an inside pressure of 102 kPa. The balloon is lowered under water and allowed to come to equilibrium with the water that is at a temperature of 5.00 ⁰C. The outside air pressure above the lake is 101 kPa and the density of the water is 1000 kg/m ³.

(A) How many molecules of helium are there in the balloon?
Ans:{1.13x10 ²³ molecules}

(B) At what depth will the balloon have a buoyant force is equal to 16.5 N?
Ans:{16.0 m}

(C) What is the total kinetic energy of all the helium molecules in the balloon when it is under water? Did the total kinetic energy go up or down when the balloon is submerged under water?
Ans:{651 J, It has gone down.}

4. A glass 19.0 cm tall cylinder with a radius of 5.60 cm contains a gas trapped in its bottom by a massless piston. The top of the cylinder contains a liquid filled to the top of the cylinder with a density of 950 kg/m ³. Initially, the height of the gas is 14.0 cm high and is at a temperature of 67.0 ⁰C. The external air pressure is 101 kPa.

(A) What is the gauge pressure of the gas initially?
Ans:{466 Pa}

(B) How many moles of gas are there in the bottom of the cylinder?
Ans:{.0495 moles}

(C) If the gas is heated so that there is only 2.50 cm of liquid in the top of the cylinder, what will be the temperature of the gas? Assume no heat flows through the piston so that the density of the liquid remains constant at 950 kg/m ³.
Ans:{400 K}

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1. A closed tank has 2.80 moles of air trapped above oil that has a density of 870 kg/m ³. The bottom of the tank is connected to a vertical pipe that contains oil to a depth of 3.60 m and is open to the air that has a pressure of 101 kPa. The cross-sectional area of the tank with the trapped air 722.0 cm ² and height of the oil in this tank is 120 cm while the height of the trapped air is 85.0 cm.

(A) What is the pressure of the oil at the bottom of the tank with the trapped air?
Ans:{132 kPa}
(B) What is the pressure of the trapped air?
Ans:{121 kPa}
(C) What is the temperature of the air in ^oC?
Ans:{47.1 ⁰C}

2. A block of foam plastic with a density of 630 kg/m ³ is weighted with a steel bob that has a density of 7.80 g/cm ³. When the steel bob's mass is 2.10 kilograms, the top of the plastic foam block is level with the surface of the water in which it floats.

(A) What is the buoyant force of the water on the steel bob?
Ans:{2.64 N}
(B) What is the tension in the cord connecting the bob and the foam block?
Ans:{17.9 N}
(C) If the steel bob is placed on top of the foam block will the foam block float higher, lower or remain the same? Explain your answer .
Ans:{The foam block will float lower. Its distance below the surface will be equal to the height of bob. The will pus down on the foam block until they will both be under the surface of the water}.

3. A horizontal tube with a radius of 4.70 cm is joined to a second tube with a smaller radius. Gasoline with a density of 720 kg/m ³ is flowing through the two tubes. When the pressure difference between the gasoline in the two tubes is 7.40 kPa, the gasoline is flowing at 4.90 m/s in the second tube.

(A) Does the velocity of the gasoline in first tube have a higher or lower speed than the velocity of the gasoline in the second tube? Determine the velocity of the gas line in the first tube?
Ans:{Lower, 1.86 m/s}
(B) How long will it take for 42.0 kg of gasoline to flow through the second tube?
Ans:{4.52 s}
(C) What is the radius of the second tube?
Ans:{2.89 cm}

4. The pressure above the water in a large storage tank is 333 kPa and the tank is 3.80 m tall. An outlet pipe at the bottom of the tank narrows to a nozzle with a cross-sectional area of 110 mm ² which exit into the atmosphere at 101 kPa. The water flows through the outlet pipe at 150 liter per minute.

(A) What is the speed at which the water exits the outlet pipe?
Ans:{22.7 m/s}
(B) How far below the top of the water in the storage tank is the outlet pipe? You can neglect the height of the outlet pipe.
Ans:{2.68 m}
(C) What is the pressure of the air in the tank when the tank is half full of water if the temperature does not change?
Ans:{196 kPa}