CHAPTER 2: MEASUREMENT

2-6: SI Measurement: Weight

Mass versus Weight

In daily life, the terms mass and weight are often used interchangeably. We associate mass and weight with the measurement of how heavy an object is. However, in the sciences, mass and weight are conceptually very different. Mass is defined as the amount of matter in an object with an SI basic unit of grams, while weight is the amount of gravitational force acting on that object, with an SI force unit of Newtons. While mass never changes, weight is dependent on location and the force of gravity at that location. The lower the force of gravity (e.g., on the moon or at the Earth’s poles), the lower the weight. So, technically we should be talking about mass rather than weight, but they are used so interchangeably in daily life that we won’t differentiate.

Explore Icon Measuring Mass

Prefixes multiply the basic unit of gram by powers of 10. For example, 1 kilogram = 1000 grams. Heavy weights are measured in metric tonnes, or just tonnes, where 1 tonne is equal to 1000 kilograms or 1 megagram or 106 grams. There is also 1 gigagram = 109 grams. When it comes to very small measurements (mostly scientific) we have microgram (µg), nanogram (ng) and picogram (pg) where 1µg = 10-6g, 1ng = 10-9g, and 1pg = 10-12g.

Units of Mass

1 gigagram = 109 grams (g)

1 megagram (1 tonne) = 106 grams (g)

1 kilogram (kg) = 1000 grams (g)

Base unit = 1 gram (g)

1 milligram (mg) = 0.001 grams (g)

1 microgram (µg) = 10-6 grams (g)

1 nanogram (ng) = 10-9 grams (g)

1 picogram (pg) = 10-12 grams (g)

Other prefixes of decigram (dg) = 0.1 grams or hectogram (hg) = 100 grams etc can be used, but are not commonly used in daily life.

 

Explore 1 – Appropriate measures

The weight of 4 pears is about 1 kilogram. A pen cap weighs about 1 gram. A tablet weighs around 1 to 5 milligrams.

Answer the following questions.

  1. What is an appropriate measure for the weight of a car?

Solution

kilogram or tonne

  1. What is an appropriate measure for the weight of an aspirin tablet?

Solution

milligram

  1. What is an appropriate measure for the weight of a small pebble?

Solution

gram

  1. What is an appropriate measure for your weight?

Solution

kilogram

 

Explore 2 – Basic weight unit conversion

Perform the following weight unit conversions.

  1. Kevin caught a 20kg steelhead trout. What is the weight in grams?

Solution

Since 1kg = 1000g, 20kg = 20 · 1kg = 20 · 1000g = 20,000g

  1. A dog weighs 15kg. What is this weight in grams?

Solution

Since 1kg = 1000g, 15kg = 15 · 1kg = 15 · 1000g = 15,000g

  1. A US banknote (a paper bill) weighs about 1 gram. What is the weight in kilograms of one million dollars in $100 notes?

Solution

$1,000,000 = 10,000 · $100 so weighs 10,000 · 1g = 10,000g. And since 1kg = 1000g, 10,000g = 10 · 1000g = 10 · 1kg = 10k

  1. Rated at 3.0 MegaWatts, a turbine’s blades are about 47m in length, weigh about 12,474kg and are valued at roughly $300,000 each.[1] a) Convert 12,474kg to tonnes. b) Calculate the weight per meter of a turbine blade. c) Calculate the cost per kilogram of a turbine blade.

Solution

a) Since 1 t = 1000kg, 12,474 kg = 12.474 (1000 kg) = 12.474 (1 t) = 12.474 t     b) weight per meter = 12,474 kg ÷ 47 m = 265.4 kg per meter    c) Cost per kilogram = $300,000 ÷ 12,474 kg = $24.05 per kg.

 

Examples

  1. A wind turbine blade weighs about 5200 kg. What is this weight in tonnes?
  2. A mountain bike weighs 12 kg. Convert this weight to grams.
  3. One cubic meter of concrete weighs about 2.4 tonnes. Convert 2.4 tonnes to kg.
  4. The weight of the Earth is about 5.972 × 1024 kg. Convert this weight to tonnes.
  5. A bottle of 1000 aspirin tablets weighs 462 g. If the empty bottle weighs 56 g, what is the weight of a single aspirin?
Show/Hide Answer
  1. 5.2t
  2. 12,000 g
  3. 2400 kg
  4. 5.972 × 1021
  5. 406 mg

 

Reflect Icon

  • What units are used to measure the weight of an object?
Show/Hide Answer

The basic unit is gram. Prefixes added to gram denote powers of 10 heavier or lighter than gram.

 

Practice Exercises

  1. The Earth has a mass of 5.972 × 1024 kg. Write this mass in gigagram.
  2. The heaviest person ever recorded weighed 635 kg. Write this weight in tonnes.
  3. A heavy-weight punching bag typically weighs about 50 kg. Write this weight in grams.
  4. A lightweight golf bag weighs about 1300 g. Write this weight in kg.
  5. The average weight for a set of golf clubs is 13.6 kg. Write this weight in grams.
  6. The average feather weighs 0.0082 grams. Write this weight in mg.
Show/Hide Answer
  1. 5.972 × 1018 gigagrams
  2. 0.635 t
  3. 50,000 g
  4. 1.3 kg
  5. 13,600 g
  6. 8.2 mg

 

 

In this section, we will take what we have learned and apply the concepts to new situations.

Perspectives

  1. Tankers that carry gas in Europe have a capacity of 16,000 liters across four equal capacity chambers. How many liters are in each chamber?
  2. The world’s largest gold bar weighs 250 kg, measuring at the base 455mm by 225mm and 170mm high (equal to 15,730 cm3). It was manufactured by the Mitsubishi Materials Corporation. As of January 2023, it is worth approximately $15.1 million.   a) Convert 250kg to grams.     b) Calculate the volume of the gold bar, assuming it is a rectangular solid.     c) Calculate the worth of the gold per gram.     d) Calculate the worth of the gold per cubic centimeter.
  3. Pennies minted after 1983 weigh 2.50 g. What is the weight in kilograms of $50 in pennies?
  4. A quarter weighs 5.670 g. Jenny has a jar full of quarters she has been saving. The jar of quarters weighs 3.2 kg. Jenny figures the jar weighs no more than 500 g. How much money is in the jar?
  5. Water weighs 1 kg per liter. A hot tub that weighs 220 kg has a capacity of 1.135 kiloliters. What will be the total weight of the filled hot tub? 
  6. A liter of gasoline weighs about 750 grams. Many cars have a gas tank with a capacity of 60 liters. How much weight does a full tank of gas add to a car? 
  7. A liter of jet fuel weighs about 840 grams. A jet flying from London to New York burns approximately 82,853 liters of jet fuel. How much weight does the fuel add to the plane? 

 

Show/Hide Answers
  1. 4000 l
  2. a) 250 kg = 250,000 g     b) Volume = 17,403.75 cm3     c) $60.40 per gram     d) $867.63 per cm3
  3. 12.5 kg
  4. 476 coins totalling $119
  5. 1355 kg = 1.355 t
  6. 45 kg
  7. 69.6 t

 

 

 

 

Skills IconIn this section we will use what we have learned so far to practice skill problems.

Skill Exercises

  1. How many milligrams are in one gram?
  2. How many grams are in one kilogram?
  3. Convert 5 kg to g
  4. Convert 6.3 kg to mg
  5. Convert 5,000,000 mg to kg
  6. Convert 4,500 kg to tonnes
  7. Convert 65.3 t to kg
  8. Convert 3,400 µg to mg
  9. Convert 74,200,000 t to gigagrams
  10. Convert 3.5 gigagrams to tonnes
Show/Hide Answers
  1. 1 g = 1000 mg
  2. 1 kg = 1000 g
  3. 5 kg = 5000 g
  4. 6.3 kg = 6,300,000 mg
  5. 5,000,000 mg = 5,5 kg
  6. 4,500 kg = 4.5 t
  7. 65.3 t = 65,300 kg
  8. 3,400 µg = 3.4 mg
  9. 74,200,000 t = 74,200 gigagrams
  10. 3.5 gigagrams = 3,500 tonnes

 

  1. https://www.compositesworld.com/articles/wind-turbine-blades-big-and-getting-bigger ↵
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