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Weight, Force, Volume, Pressure

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1. A pirate in a movie is carrying a chest (0.30 m X 0.30 m X 0.20 m) that is supposed to be filled with gold. To see how ridiculous this is, determine the weight (in newtons) of the gold. To judge how large this weight is, remember that 1 N = 0.225 lb.

2. An airtight box has a removable lid of area 1.3 X 10^-2 m^2 and negligible weight. The box is taken up a mountain where the air pressure outside the box is 0.85 X 10^5 Pa. The inside of the box is completely evacuated. What is the magnitude of the force required to pull the lid off the box?

3. The Mariana trench is located in the Pacific Ocean at a depth of about 11000 m below the surface of the water. The density of seawater is 1025 kg/m^3.
(a) If an underwater vehicle were to explore such a depth, what force would the water exert on the vehicle's observation window (radius = 0.10 m)?
(b) For comparison, determine the weight of a jetliner whose mass is 1.2 X 10^5 kg.

4. A paperweight, when weighed in air, has a weight of W = 6.9 N. When completely immersed in water, however, it has a weight of W_in_water = 4.3 N. Find the volume of the paperweight.

5. A room has a volume of 120 m^3. An air-conditioning system is to replace the air in this room every twenty minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fluid, find the length of a side of the square if the air speed within the ducts is (a) 3.0 m/s and (b) 5.0 m/s.

6. The water tower in the drawing (in the attachment) is drained by a pipe that extends to the ground. The flow is non-viscous. The top surface of the water at point 2 is at atmospheric pressure. (a) What is the absolute pressure at point 1 if the valve is closed? (b) What is the absolute pressure at point 1 when the valve is opened and the water is flowing? Assume that the water speed at point 2 is negligible. (c) Assuming the effective cross-sectional area of the valve opening is 2.00 X 10^-2 m^2, find the volume flow rate at point 1.

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Mostly computations and calculations, with brief explanation as needed.

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