TALLER DE HIDROSTÁTICA 1) Substance A has a density of 3 g/cm 3 and substance B has a density of 4 g/cm 3. In order to obtain equal masses of these two substances, what must be the ratio of the volume of A to the volume of B? A) V A VB = 1 3 B) V A VB = 4 3 C) V A VB = 3 4 D) V A VB = 3 1 E) V A VB = 3 4 1) 2) A styrofoam sphere of radius R has a density. You now carefully compress the sphere so its radius is R/2. What is the density of the compressed sphere? A) 8 B) 8 C) 2 D) 2 E) 4 2) 3) As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest? 3) A) A B) B C) C D) D E) The pressure is the same at each of the labeled points. 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 4) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the gauge pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s? 4) 5) A plastic block of dimensions 2.00 cm 3.00 cm 4.00 cm has a mass of 30.0 g. What is its density? 5) A) 1.20 g/cm3 B) 0.80 g/cm3 C) 1.60 g/cm3 D) 1.25 g/cm3 6) A compressed gas with a total mass of 107 kg is stored in a spherical container having a radius of 0.521 m. What is the density of the compressed gas? A) 110 kg/m3 B) 181 kg/m3 C) 134 kg/m3 D) 161 kg/m3 6) 7) The density of material at the center of a neutron star is approximately 1.00 1018 kg/m3. What is the mass of a cube of this material that is 1.76 microns on each side. (One micron is equal to 1.00 10-6 m.) A) 5.45 kg B) 6.16 kg C) 4.74 kg D) 6.70 kg 7)
8) A round coin has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.50 g. What is its density? A) 5.37 10 3 kg/m 3 B) 1.34 10 3 kg/m 3 C) 2.68 10 3 kg/m 3 D) 21.5 10 3 kg/m 3 E) 1.86 10-4 kg/m 3 9) The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam? The density of water is 1000 kg/m 3. A) 1.11 10 2 Pa B) 1.09 10 6 Pa C) 1.09 10 3 Pa D) 1.16 10 6 Pa E) 1.11 10 5 Pa 10) The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the gauge pressure in the water at that point? The density of seawater is 1025 kg/m 3. A) 8.88 10 7 Pa B) 1.11 10 8 Pa C) 2.22 10 8 Pa D) 3.33 10 8 Pa E) 5.55 10 7 Pa 11) A circular window 30 cm in diameter in a submarine can withstand a net maximum force of 5.20 10 5 N without damage. What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is 1000 kg/m 3. A) 680 m B) 750 m C) 740 m D) 1200 m 12) A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is 570 kg/m3. The mass of the oil is closest to 8) 9) 10) 11) 12) A) 410 B) 820 C) 210 D) 620 E) 1000
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) As shown in the figure, a large open tank contains a layer of oil ( density 450 kg/m3) floating on top of a layer of water (density 1000 kg/m3) that is 3.0 m thick, as shown in the sketch. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 8.5 x 104 Pa? 13) 14) A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density 0.820 g/cm 3. If a 125-kg object is placed on the larger plate at A, how much mass should be placed on the smaller plate at B to balance it? 14) 15) In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight. A) 6.7 10 3 N B) 5.0 10 3 N C) 2.2 10 3 N D) 2.9 10 3 N 16) If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is 1000 kg/m 3. A) 10 10 m 3 B) 10 4 m 3 C) 10 7 m 3 D) 10 12 m 3 E) 10 8 m 3 15) 16) 17) A 1.00-m 3 object floats in water with 20.0% of its volume above the waterline. What does the object weigh out of the water? The density of water is 1000 kg/m 3. A) 9,800 N B) 11,800 N C) 1,960 N D) 7,840 N 18) A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? ( Fe = 7.87 g/cm 3, water = 1.00 g/cm 3 ) A) 37 cm B) 6.6 cm C) 131 cm D) 79 cm 17) 18)
19) A rectangular wooden block measures 10.0 cm 4.00 cm 2.00 cm. When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is 1.00 g/cm3. A) 1.65 g/cm3 B) 0.825 g/cm3 C) 1.21 g/cm3 D) 0.350 g/cm3 E) 0.606 g/cm3 20) A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m3. How much deeper into the water does the barge sink when 3.0 x 10 5 kg of coal are loaded on the barge? A) 50 cm B) 25 cm C) 1.0 m D) 75 cm E) 1.5 m 19) 20)