CTFluids-1 Cube A has edge length L and mass M. Cube B has edge length 2L and mass 4M. Which has greater density?A) A has larger densityB) B has larger densityC) A and B have the same density.L 2L Mass M Mass 4 M A B Answer: Cube A has larger density. A = M/L3 , B = (4M)/(2L)3 = (1/2)M/L3 so object Ahas twice the density of object B.CTFluids-2 What is the mass of the big rock? (1 kg mass weighs 2.2 lbs).A) less than 30 kgB) between 30 and 80 kgC) between 80 and 200 kgD) between 200 and 400 kgE) more than 400 kgAnswer: The "rock" is made of Styrofoam. Its mass is about 3 kg.CTFluids-3As shown, two containers are connected by a hose and are filled with water. Which picture correctly depicts the water levels? Answer: The levels must be equal. The pressures at the bottom must be equal (otherwise water would be pushed through the connecting tube). Pressure p is related to depth h by p = g h. Since the pressures must be the same, the depths are the same. If the levels were unequal, you could build a perpetual motion machine and violate conservation of energy. With unequal water levels, you could set up a water fall to turn a turbine and generate electricity, for free.ABCCTFluids-4 Two bricks are held under water in a bucket. One of the bricks is lower in the bucket than the other. The upward buoyant force on the lower brick is...A) greaterB) smallerC) the same as the buoyant force on the higher brick.Answer: The same. Archimedes Principle says that the buoyant force is equal to the weight of the displaced fluid. Both bricks have the same volume, so they displace the same amount of water. It true that the pressure on the bottom side of the lower brick is greater than the pressure on the bottom side of the upper brick. But the same is true of the upper sides as well. The difference in the pressure on top and bottom sides is the same for both bricks.CTFluids-5 A solid piece of plastic of volume V, and density plasticwould ordinarily float in water, but it is held under water by a stringtied to the bottom of bucket as shown. (The density of water is water.)What is the buoyant force on the plastic?A) ZeroB) plastic VC) water VD) water V gE) plastic V gAnswer: water V g , which is the weight of the displaced fluid.CTFluids-6 A solid piece of plastic of volume V, and density plasticis floating in a cup of water. (The density of water is water.)What isthe buoyant force on the plastic?A) ZeroB) plastic VC) water VD) water V gE) plastic V gAnswer: plastic V g ! The answer is NOT water V g, because V is not the volume of the displaced fluid. Note that some of the plastic is above the water. Since the plastic is stationary, the upward buoyant force FB must be equal to the downward weight of the plastic, which is plastic V g.CTFluids-7 A helium-filled balloon of volume V can carry a total mass M (M includes the mass of the rubber balloon but not the mass of the air inside). What is the correct expression for the buoyant force FB on the balloon ?A) air V g B) helium V g C) Mg D) (air–helium) V gWhat is the correct equation for the weight of the cargo mass Mg?A) (air – He )V g B) (air + He )V gC) He V g D) water V g E) None of theseAnswers: air V g The buoyant force is the weight of the displaced fluid, which is the air.The weight of the cargo is Mg = FB – mHeg = (air – He )V gFBmplastic gMgFBmHe gHeairCTFluids-8 An ice cube is floating in a glass of water. As the ice cube melts, the level of the water...A) rises.B) falls.C) stays the same.Answer: stays the same. According to Archimedes' Principle, the buoyant force on the icecube is the weight of the displaced water. But in this case, the buoyantforce is also equal the weight of the ice cube, since the cube is not moving. Therefore, (mass of ice cube) g = (mass of displaced water) g. When the cube melts, itwill become an equal weight of water, which will just fill the displaced volume.CTFluids-9A rock of mass m sits at the bottom of a bucket. How does the magnitude of the upward buoyant force FB compare to the weight mg of the rock?A) FB = mgB) FB > mgC) FB < mgA carefully-made sphere, when placed under water, remains at rest, in equilibrium as shown above. How does the magnitude of the upward buoyant force FB compare to the weight mg of the rock? (Same choices)Answers: When the rock is at the bottom, it must have sunk, so FB < mg.If the rock is in equilibrium, not at the surface or at the bottom ("neutral buoyancy"), thenit must be that FB = mgCTFluids-10 Two identical cups are filled with water to the same level. One of the cups has a plastic ball floating in it. The plastic ball has a lower density than water.Which cup weighs more?A) The cup with the ball.B) The cup without the ball.C) The two cups weigh the same.Answer: the two cups weigh the same! According to Archimedes' Principle, the weight ofthe plastic ball is just equal to the weight of the displaced water (since the Buoyant force must equal the weight of the ball).CTFluids-11Mercury is 14 times as dense as water. If we measured the air pressure with a water barometer instead of a mercury barometer, how high would the column of water be, compared to the height of the mercury column?A) the same heightB) 14 times higher.C) 14 times shorter.Answer: 14 times higher. The height h of the column is given by patm =  g h where  is the density of the fluid. So height h = patm/(  g). If  is smaller, then h is larger.vacuumair