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A fluid is (a) a liquid. (b) a gas. (c) anything that flows. (d) anything that can be made to change shape. (e) All of the above In the drawing on the right, the dotted line represents the volume of fluid equal to the volume of the object on the right. Fluid Fbuoyant Volume of fluid equal to object at right. Displaced volume of fluid Suspended object 1. What is the buoyant force on the fluid inside the dotted line, if the fluid is stationary? (a) Equal to the weight of the object (b) Equal to the weight of the fluid inside the dotted line (c) Equal to (a) - (b) (d) Zero 2. What is the buoyant force on the object? 1 3 4 When blocks 2 and 5 are placed in the 2 liquid, they end up as shown. Which of the following best represents the positions of the other blocks if placed 5 in the liquid? All blocks have the same volume. m1 < m2 < m3 < m4 < m5 (b) (a) 1 1 2 2 3 4 3 5 (c) 4 5 (d) 1 1 2 2 3 4 3 4 5 5 An open cylinder of water of radius R has a circular hole of area A at a depth d below the surface. To determine the speed of the water stream as it leaves the hole we use p0 d (a) The continuity equation: v1 A1 v2 A2 1 2 (b) Bernoulli's equation: p0 v gd constant 2 (c) Archimedes' principle v p0 An open cylinder of water of radius R has a circular hole of area A at a depth d below the surface. We solve for v from 1 2 (a) p0 v gd 0 2 1 2 (b) gd v 2 1 2 (c) p0 gd v 2 1 2 (d) p0 2 v gd d v For which of the following is Bernoulli’s equation a conservation law? (Answer (a) for yes and (b) for no) 1. momentum 2. energy 3. mass 4. streamlines Liquid flows through a pipe. You can't see into the pipe, but there is transparent tubing feeding vertically off it at different positions, with the top end of the tubing open to the atmosphere. The height of the liquid in the is shown below. At which point in the tube is the flow speed the greatest? Liquid 1 2 (a) Point 1 (b) Point 2 (c) Point 3 (d) Not enough information to tell 3 Area A2 Area A1 p1 Flow x2 p2 y y2 y1 x1 In the figure above for an incompressible fluid, a volume of fluid of length )x1 enters on the left as an equal volume of length )x2 leaves on the right. Which of the following represents the net work done on the fluid in this flow tube in this time? (a) p1A1 (b) p2A2 (c) p1A1 - p2A2 .... Which situation can be described with Bernoulli’s equation? (Answer (a) for yes and (b) for no) 1. the flow of water out of a tank having a small hole near its bottom 2. the steady flow of water in a fire hose 3. the flow of air around an airfoil 4. fluid flow through a pump equipped with a piston Which of the following gives the correct definition of the bulk modulus B? V Bp a) V b) V BV V c) p B V V d) p B V e) F l B A l Aluminum has a bulk modulus of 100 GPa (giga = 109). Hydrostatic pressure of 100 atmospheres is applied to a cube of aluminum 2 cm to a side. What is the change in volume of the cube? (1 atmosphere ~ 100 kPa) (a) -8 x 10-4 cm3 (b) 8 x 10-4 cm3 (c) -2 x 10-9 cm3 (d) 2 x 10-9 cm3 (e) -8 x 10-1 cm3 The bodies A, B and C are held at the positions shown on the right. A 50 g Liquid B 40 g C 50 g 1. They have the same volume. Rank, from largest to smallest, the sizes of the buoyant forces FA, FB, FC on each of them. (a) FA = FB = FC (b) FC > FB > FA (d) FC = FA > FB (e) FA > FC > FB (c) FA > FB > FC 2. Now they have the same density but not necessarily the same volume. Rank, from largest to smallest, the sizes of the buoyant forces FA, FB, FC on each of them. (a) FA = FB = FC (c) FA > FB > FC (e) FA > FB > FC (b) FC > FB > FA (d) FC = FA > FB The buoyant force on an immersed body has the same magnitude as (Answer (a) for yes and (b) for no) 1. the weight of the body. 2. the weight of the fluid displaced by the body. 3. the difference between the weights of the body and the displaced fluid. 4. the average pressure of the fluid times the surface area of the body. For which cube is the buoyant force the greatest? (a) A (b) B (c) the forces are the same A liquid is (a) more compressible than a gas (b) highly compressible, but less than a gas (c) almost incompressible The equation of continuity says that the velocity of fluid flow in a pipe is inversely proportional to the cross-sectional area (a) only for an incompressible fluid. (b) only for a horizontal pipe. (c) both (a) and (b) (d) always In the figure on the right, an incompressible fluid flows Area from left to right. The A1 volume shown at the left entering this region of flow is the same as that leaving at the right over the same time interval. Area A2 Flow v1 Which of the following statements is true? (a) v1 = v2 (b) A1v1 = A2v2 (c) A1/v1 = A2/v2 (d) None of these v2 Compared to its solid form, a liquid usually (a) has a higher density (b) has a lower density (c) Has the same density Rank, in order from largest to smallest, the densities of A, B, and C. (a) A>B>C (b) A>C>B (d) B>C>A (e) C>A>B A B (c) B>A>C Because: (a) the heaviest object displaces the most water (b) the buoyant force on the object is equal to the weight of the water it displaces (c) the least dense object displaces the least amount of water C A floating object displaces a volume of fluid (a) whose weight is equal to the product of the pressure in the fluid and the surface area submerged (b) whose weight is equal to the weight of the floating object (c) whose mass is equal to the density of the object multiplied by the volume submerged (d) equal to the volume of the object A floating wooden block sinks until (a) the weight of fluid displaced equals the weight of the block (b) the product of the surface area of the bottom of the block, and the gauge pressure there, equals the weight of the block (c) the submerged volume of the block, times the density of water, is equal to the weight of the block (d) both (a) and (c) (e) all of (a), (b), (c) The diagram on the right is the free body diagram of an object sitting on a table. Which of the following is the most appropriate free body diagram for the object when floating (ignoring forces on the sides)? (a) (b) (c) A and B are rectangular tanks full of water. Their y and z dimensions are the same, but their x dimensions are different z y x A B The total force on the bottom of tank A is (a) greater than the force on the bottom of B (b) the same as the force on the bottom of B (c) smaller than the force on the bottom of B A and B are rectangular tanks full of water. Their y and z dimensions are the same, but their x dimensions are different z y x A B The total force of the liquid on the front wall of tank A is (a) greater than the force on the front wall of B (b) the same as the force on the front wall of B (c) smaller than the force on the front wall of B Air enclosed in a cylinder has density 1.4 kg/m3. What will be the density of the air if the length of the cylinder is doubled while the radius is unchanged? (a) 1.4 kg/m3 (b) 2.8 kg/m3 (c) 0.7 kg/m3 What will be the density of the air if the length of the cylinder is doubled while the radius is halved? (a) 1.4 kg/m3 (b) 2.8 kg/m3 (c) 0.7 kg/m3 The gauge pressure is the pressure in a fluid in excess of atmospheric pressure. The gauge pressure a the bottom of a cylinder of liquid reads pg = 0.4 atm. The liquid is poured into another cylinder with twice the radius of the first cylinder. What is the gauge pressure at the bottom of the second cylinder? (a) 0.1 atm (b) 0.2 atm (c) 0.4 atm (d) 0.8 atm (e) none of the above Wind Wind flows over the house above. A window on the ground floor is open. Does air flow (a) in the window and out the chimney or (b) down the chimney and out the window? Rank in order, from largest to smallest, the magnitudes of the forces required to balance the masses. The masses are in kilograms. 1. F2 > F1 > F3 2. F2 > F1 = F3 3. F3 > F2 > F1 4. F3 > F1 > F2 5. F1 = F2 = F3 from Knight An inflated balloon does not collapse under the atmosphere's pressure because (a) there are more collisions of air molecules against the inside of the balloon wall than against the outside (b) so much extra air is put inside that the air molecules start to push against each other, making the air almost incompressible (c) the air inside warms under the pressure, so the molecules inside are moving faster than outside A small wooden block is placed in a bowl of water initially full to the brim. The block has a volume of 15 cm3 and a density 2/3 that of water. What volume of water overflows from the bowl? (a) 5 cm3 (b) 10 cm3 (c) 15 cm3 A blood platelet drifts along with the flow of blood through an artery that is partially blocked by deposits. As the platelet moves from the narrow region to the wider region, it experiences (a) an increase in pressure. (b) no change in pressure (c) a decrease in pressure PI A blood platelet drifts along with the flow of blood through an artery that is partially blocked by deposits. As the platelet moves from the narrow region to the wider region, its speed (a) increases (b) decreases (c) remains the same PI In the figure on the right, a tensile stress is applied to the rod. Force l transverse Poisson's ratio is defined as: longitudinal Where represents strain. 1. transverse is (a) w / l (b) l / w (c) w / w (d) l / l 2. Poisson's ratio is (a) Negative (b) positive w Force A cylindrical metal wire is 10-m long and has a Poisson's ratio of 0.4. It is extended 10 mm by applying a tensile stress. What is the fractional change in its radius? (a) -4 x 10-4 m (b) 4 x 10-4 m (c) -16 x 10-8 m (d) 16 x 10-8 m (e) -4 x 10-6 m The pressure exerted by each of your feet on the floor is closest to (a) 10 Pa (b) 100 Pa (c) 1000 Pa (d) 10,000 Pa A graduated cylinder holds a column of liquid of height h, area A and mass density D as Liquid sketched below. What is the downwards pressure on the bottom of the container? (a) patm (b) patm + DAhg (c) patm + Dhg (d) DAhg (e) Dgh A patm = atmospheric pressure h A static fluid in a container is subject to both atmospheric pressure at its surface and Earth’s gravitation. The pressure at the bottom of the container (a) depends on the height of the fluid column. (b) depends on the shape of the container. (c) is equal to the atmospheric pressure. Rank in order, from smallest to largest, the pressure at each point shown below. The top of the tank is open to the atmosphere. (a) C, D, E, A, B (b) C, D=E, A=B (c) C, E, D, A, B (d) D, C, E, A=B (e) C, D, E, A=B Which statement does not apply? In the steady flow of an incompressible fluid, (a) the flow velocity at a point is tangent to the streamline through that point. (b) the density of the fluid is proportional to the density of streamlines. (c) the wider the streamline spacing, the lower the velocity of the flow. (d) streamlines cannot cross each other. Ceiling Suction cup m In the figure above, the suction cup is held to the ceiling by (a) the suction of the vacuum formed between it and the wall. (b) the unbalanced force of the air molecules bouncing off the bottom of it. (c) the molecular attraction between the suction cup and the ceiling, where they are in contact. (d) the centrifugal force of the Earth's rotation. Compare the gas pressure inside the cylinder to the pressure of the surrounding air. The gas pressure inside the cylinder is (a) equal to the gas pressure outside the cylinder (b) equal to the gas pressure outside the cylinder plus the mg/A where m is the mass of the block and A is the area of the piston (c) equal to the gas pressure outside the cylinder plus the mg/A where m is the mass of the block and A is the area of the block Fan A vacuum cleaner is constructed as on the right. A fan forces air out of the canister, creating a partial vacuum in the hose. Ejected air Hose Paper A vacuum-cleaner hose is placed near a piece of a paper lying on the floor. The paper enters the vacuum-cleaner hose because the partial vacuum in the hose (a) removes air molecules from above the paper, leaving an excess of molecules below the paper to push it into the hose. (b) makes the pressure above the paper lower than below it, so the paper is forced up (c) sucks the paper inside. (d) does both (a) and (b) (e) does both (b) and (c) A wire of length l and cross-section A has a tensile force F applied to it. The extension )l is proportional to which of the following? (Answer (a) for yes and (b) for no) 1. l 2. A 3. F 4. 1/l 5. 1/A 6. 1/F A force stretches a wire by 1 mm. 1. A second wire of the same material has the same cross section and twice the length. How far will it be stretched by the same force? (a) 1/4 mm (b) 1/2 mm (c) 1 mm (d) 2 mm (e) 4 mm 2. Another wire of the same material has the same length and twice the diameter of the of the first wire. How far will it be stretched by the same force? (a) 1/4 mm (b) 1/2 mm (d) 2 mm (e) 4 mm (c) 1 mm A wire of square cross-section has a side of 0.1 mm and is 10-m long. The wire is suspended from a high ceiling and a mass of 10 kg is hung on the bottom end. The wire stretches 10 mm. What is the Young's modulus of the wire, roughly? (a) 1 x 106 N/m2 (b) 1 x 108 N/m2 (c) 1 x 1010 N/m2 (d) 1 x 1011 N/m2 (e) 1 x 1013 N/m2