Self-Test C-1.13: Use Archimedes’ Principles of Displacement and Floatation
Complete Self-Test C-1.13 and check your answers.
- 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?
Answer:
- A 100-cm3 block of lead that weighs 11 N is submerged in water. One cm3 of water weighs 0.0098 N.
- What volume of water does the lead displace?
Answer: cm3
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- How much does that volume of water weigh?
Answer: N
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- What is the buoyant force on the lead?
Answer: N
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- Will the lead block sink or float in the water?
Answer:
- The same 100-cm3 lead block is submerged in a container of mercury. One cm3 of mercury weighs 0.13 N.
- What volume of mercury is displaced?
Answer: cm3
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- How much does that volume of displaced mercury weigh?
Answer: N
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- What is the buoyant force on the lead?
Answer: N
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- Will the lead block sink or float in the mercury?
Answer:
- 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?
Answer: lb.
- 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]
Answer: lb.
- What would be the relative density of steel if the density is 491 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
Answer:
- 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.
Answer: N or lb.
- If a substance has a density of 54.3 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex], what is its relative density?
Answer:
- If an object has a relative density of 3.1 and weighs 290 lb., how much volume will it occupy?
Answer: ft.3
- 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?
Answer: lb.
- If the specific weight of a substance is 4.9, what is its density in [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
Answer: [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
- A piece of iron alloy weighs 8.5 lb. in air and 7.2 lb. in water. What is its specific gravity?
Answer: SG =
- 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.
Answer:
- 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?
Answer:
- What is the weight of 3.4 cubic feet of iron with a density of 455 [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]?
Answer: lb.
- 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?
Answer: %
- Six pounds of argon occupy 43 ft.3. What is its density?
Answer: [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
- 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{in.}^3}[/latex]?
Answer: [latex]\frac{\text{lb.}}{\text{in.}^3}[/latex]
- 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.?
Answer: [latex]\frac{\text{lb.}}{\text{ft.}^3}[/latex]
- 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.
Answer: ft.3
Answer Key: Self-Test C-1.13 is on the other page.
