Hydrostatics

  1. What is the approximate mass of air in a living room 5.0m x 4.0m x 2.8m?
  2. If you tried to nonchalantly smuggle gold bricks by filling your backpack, whose dimensions are 70cm x 30cm x 20cm, what would its mass be?
  3. A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 88.78 g. what is the density of this other fluid?
  4. Estimate the pressure exerted on a floor by (a) a 50-kg model standing momentarily on a single spiked heel (area = 0.05 cm2), and compare it (b) to the pressure exerted by a 1500-kg elephant standing on one foot (area = 800cm2).
  5. (a) Calculate the total force of the atmosphere acting on the top of a table that measures 1.6 m x 1.9 m.

(b) What is the total force acting upward on the underside of the table?

  1. The gauge pressure in each of the four tires of an automobile is 200 kPa. If each tire has a “footprint” of 200 cm2, estimate the mass of the car.
  2. What is the total force and the absolute pressure on the bottom of a swimming pool 18.0 m x 10.0 m whose uniform depth is 2.0 m? What will be the pressure against the side of the pool near the bottom?
  3. Water and then oil are poured into a U-shaped tube, open at both ends, and do not mix. They come to equilibrium as shown in fig. 10-41 below. What is the density of the oil? (Hint: Pressure at points a and b are equal. Why?)
  4. A geologist finds that a moon rock whose mass is 8.20 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?
  5. A 0.30 kg plastic block has dimensions of 2cm x 3cm x 3cm. What is its density?
  6. A circular window of 30 cm diameter in a submarine can withstand a force of 5.08 x 105 N. What is the maximum depth the submarine can go without damaging the window?
  7. A cylindrical rod of length 12 cm and diameter 2 cm will barely float in water. What is its mass?
  8. A crane lifts a submarine (density = 7.8 x 103 kg/m 3 of a mass 20,000 kg. What is the tension in the cable when

(a)The sub is completely out of the water? (b) The sub completely submerged?

Answers:

  1. 72.2 kg
  2. 811 kg
  3. 848 kg/m3
  4. Model 9.8 x 107 N/m2 ; Elephant 1.84 x 105 N/m2
  5. (a) 304,000 N (b) 304,000 N
  6. 1632 kg
  7. Pressure 119,600 N/m2 ; Force 21,528,000 N
  8. 654 kg/m3
  9. 4059 kg/m3
  10. 1.65 x 104 kg/m3
  11. 723 m
  12. 0.03768 kg
  13. Air 196,000 N; submerged in water 171,000 N

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