Answer Key: Self-Test C-1.13

  1. A block of gold and a block of wood both have the same volume. If they are both submerged in water, which has the higher buoyant force?
    1. They are equal
  2. A 100-cm3 block of lead that weighs 11 N is submerged in water. One cm3 of water weighs 0.0098 N.
    1. What volume of water does the lead displace?
      1. 100 cm3
    2. How much does that volume of water weigh?
      1. 0.98 N
    3. What is the buoyant force on the lead?
      1. 0.98 N
    4. Will the lead block sink or float in the water?
      1. sink
  3. The same 100-cm3 lead block is submerged in a container of mercury. One cm3 of mercury weighs 0.13 N.
    1. What volume of mercury is displaced?
      1. 85 cm3
    2. How much does that volume of displaced mercury weigh?
      1. 11 N
    3. What is the buoyant force on the lead?
      1. 11 N
    4. Will the lead block sink or float in the mercury?
      1. float
  4. An iron anchor weighs 250 pounds in air and has a density of 480 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex] If it is immersed in seawater that has a density of 64 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], how much force would be required to lift it while it is immersed?
    1. 216.67 lb.
  5. An aluminum bar weighs 82 pounds in air. How much force is required to lift the bar while it is immersed in gasoline? The density of aluminum is 170 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], and the density of gasoline is 42 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
    1. 61.7 lb.
  6. What would be the relative density of steel if the density is 491 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
    1. 7.87
  7. What would be the buoyant force on an object under water, whose volume is 0.35 m3 (12.36 ft.3)? Show you answer in both unit classifications.
    1. 3,430 N or 771 lb.
  8. If a substance has a density of 54.3 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], what is its relative density?
    1. 0.87
  9. If an object has a relative density of 3.1 and weighs 290 lb., how much volume will it occupy?
    1. 1.5 ft.3
  10. A rock has a specific weight of 2.6. On dry land it weighs 77 pounds. How much will its apparent weight be when it is submerged in water?
    1. 47.38 lb.
  11. If the specific weight of a substance is 4.9, what is its density in [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
    1. 305.76 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
  12. A piece of iron alloy weighs 8.5 lb. in air and 7.2 lb. in water. What is its specific gravity?
    1. SG = 6.54
  13. The most common method of finding the specific gravity of liquids is with the use of a hydrometer. Explain the principle of operation of the hydrometer.
    1. A solid suspended in a fluid will be buoyed up by a force equal to the weight of the fluid displaced by thesubmerged part of the suspended solid. Thus, the lower the density of the substance, the farther the hydrometer will sink.
  14. What is the reason that density is always expressed in units such as [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], while specific gravity has no units?
    1. Specific gravity is a ratio of the densities, compared to water.
  15. What is the weight of 3.4 cubic feet of iron with a density of 455 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
    1. 1,547 lb.
  16. If a square object with an SG of 0.58 is placed in a vessel of fresh water, what percentage of the object will be showing above the water line?
    1. 42%
  17. Six pounds of argon occupy 43 ft.3 What is its density?
    1. 0.1395 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
  18. The density of a certain material is 406 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex] What would the density be in [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
    1. 0.235 [latex]\frac{\text{lb.}}{\text{in.}^3}[/latex]
  19. What would be the density of a piece of steel in [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], if 5.46 cubic inches weighs 1 lb.?
    1. 316.48 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
  20. The density of brass is 0.283 [latex]\frac{\text{lb.}}{\text{in.}^3}[/latex] Find the volume of a piece of brass that weighs 475 lb.
    1. 0.97 ft.3

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