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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 density B) B has larger density C) A and B have the same density.
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Answer: Cube A has larger density. A = M/L^3 , B = (4M)/(2L)^3 = (1/2)M/L^3 so object A has twice the density of object B. CTFluids- 2 The air pressure inside the Space Station is p = 12 pounds per square inch = 12 psi. There are two square windows in the Space Station) a little one and a big one. The big window is 30 cm on a side. The little window is 15 cm on a side. How does the pressure on the big window compare to the pressure on the little window? A) same pressure on both windows B) 2 times more pressure on the big window C) 4 times more pressure on the big window D) 9 times more pressure on the big window E) None of these
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Answer: same pressure on both windows. Pressure p is force per area. The larger window has 4 times the area of the smaller, and it experiences 4 times the force of the smaller. The pressure (force/area) is the same: 12 psi. CTFluids- 3 What is the mass of the big rock? (1 kg mass weighs 2.2 lbs). A) less than 30 kg B) between 30 and 80 kg C) between 80 and 200 kg D) between 200 and 400 kg E) more than 400 kg Answer: The "rock" is made of Styrofoam. Its mass is about 3 kg. (Any answer gets full credit for this question.) CTFluids- 4 As 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.
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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 g What is the correct equation for the weight of the cargo mass Mg? A) (air – He )V g B) (air + He )V g C) He V g D) water V g E) None of these Answers: 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 g CTFluids- 8 A solid piece of plastic of volume V, and density plastic is floating in a cup of water. (The density of water is water.)What is the buoyant force on the plastic? A) Zero B) plastic V C) water V D) water V g E) plastic V g Answer: 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.
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CTFluids- 11 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 of the plastic ball is just equal to the weight of the displaced water (since the Buoyant force must equal the weight of the ball). CTFluids- 12 Mercury 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 height B) 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. vacuum air pressure
