Calculate Amount of Weight Indicated by the Scale

Calculate the weight of an iron rod (D = 490.68 pounds per cubic foot), 5 feet long and 2 inches in diameter, as it hangs inside an empty vessel: (left side image)

Calculate Amount of Weight

Calculate Amount of Weight Indicated by the Scale

Right side image: Next, calculate the amount of weight indicated by the scale as the vessel fills with water until 3 feet of the rod is submerged.

Hint: the metal rod will be displacing a volume of water 3 feet in length and 2 inches in diameter.

Be sure to show all your mathematical work so that your instructor will be able to check the conceptual validity of your technique(s). A good way to check to see if you’re solving the problem correctly is to check that each and every one of your intermediate calculations (i.e. the results you get mid-way during the process to arrive at the final answer) has real physical meaning.

If you truly understand what you are doing, you will be able to identify the correct unit of measurement for every intermediate result and also be able to show where that number applies to the scenario at hand.

More Questions:

  1. Demonstrate how to estimate numerical answers for this problem without using a calculator.
  2. How would your weight calculations be affected if the rod were made of some material other than iron?
  3. How would your weight calculations be affected if the iron rod were a larger diameter but identical length?
  4. How would your weight calculations be affected if the liquid had a density different from water?

Answer:

Dry weight = 53.52 pounds

Submerged (by 3 feet) weight = 49.44 pounds

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Credits: Tony R. Kuphaldt

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Calculate Amount of Weight Indicated by the Scale

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