Mass or Weight?

To determine the mass of an object, it is placed on a scale or laboratory balance and weighed. A “weight” is read from an analog scale or from a digital screen. An object's weight is a measure of the pull of the force of gravity on the object. Weight is an indication of the amount of matter that an object contains, but will vary with the pull of gravity.

Mass is the scientific term used to express the amount of material in an object independent of changes in gravity. It is standardized, and from 1889 until 2019, it was fixed relative to a platinum-iridium cylinder called “Le Gran Kilo”, an International Prototype that is stored in a vacuum near Paris, France. (See image.) However, the cylinder is an artifact, since the kilogram is now fixed relative to the energy of light and its relationship to mass (E =mc²) using a constant (Planck's constant), which provides a mathematical connection.

For our purposes the terms mass and weight are interchangeable since gravity is often nearly the same wherever weighing is generally done on earth. But technically, the two are different, and for accurate measurements they must be accounted for. On earth, under the influence of gravity, you have a certain body weight. Suppose after a long successful career you were to retire and take a once in a lifetime SpaceX vacation cruise to the moon. En route, in free space, you would become essentially weightless.

https://www.youtube.com/watch?v=WMK36dpHIkg

On the moon, where the pull of gravity is one-sixth that of earth, you would weigh one-sixth as much as you do on earth, that is about 85% less. Still, your “mass” will remain constant, the same as on earth. In space, your body consists of the same elements and molecules with the same masses as on earth. The mass of an object is independent of its location in the universe. But because gravitational force varies from one place to another, an object's weight is not the same in all locations. (The weight of an object even varies slightly from one location to another on the earth's surface!) Also, the mass of an object does not vary with temperature and pressure. Because an object's “mass” is constant wherever it is located, chemists and scientists use mass rather than weight for expressing the quantity of material in an object.

Questions:

1) A person discovers that their clothes fit too tightly and announces, "I'm going to have to lose some weight." From a scientific point of view, will a weight loss necessarily guarantee better- fitting clothes? Explain your answer and suggest how the statement should be changed to be more accurate.

2) Would one pound of uncooked hamburger weigh the same in a Safeway store in Pleasant Hill, CA, 26 feet above sea level versus a Safeway in Lake Tahoe, CA, elevation 5,901 feet? Would the mass differ? Would you pay the same amount if the listed price per pound were the same in both stores?

3) Gold is a precious metal that has been valued at over $1,000 per ounce or ~$35 per gram. An offer was made to sell a 24 carat 1.00 kilogram bar for $32,500 by a dealer in Denver, Colorado. The only proviso was that a scale, which she had calibrated in Washington, DC by the National Bureau of Standards and was un-tampered with, be used to weigh the bar in Denver. Do you recommend buying the bar on those terms? Explain why or why not.

4) An assayer is analyzing three samples of pure gold. The exact mass of the three samples were all recorded differently. One was recorded as 42.0 mg, another as 2.437 g, and the third 0.000458 kg. If gold is valued at $35.00 per gram, how much are the three samples worth in total?

5) A mixture of sand and sawdust contains 124 g of sand and 305 g of sawdust. Find the mass percent of each component in this mixture.

6) A 5.00-kg package of grass seed is composed of three types of grass seed—Kentucky bluegrass, red fescue, and colonial bent grass. Find the mass percent of all three types of grass seed in the mixture, if the package contains 2.80 kg of red fescue and 1.20 kg of colonial bent grass. (Hint: What mass of Kentucky bluegrass must be present?)