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Union University Department of Physics

The Science Guys

Science Guys > May 2004

May 2004

A package at a store is labeled "One pound" but it is also labeled "454 grams." But, pounds is force and grams is mass - they are different things! How do they compare?

If there were more perceptive folks like Mr. Hageman around, shifty politicians wouldn’t have a chance. Indeed, pounds and grams measure two different physical quantities, and in general, you shouldn’t equate the two. So, why does the public often interchange these quantities?

Let’s delineate the difference between force and mass.

Mass is a basic property of matter and measures something called inertia. The inertia of an object is its resistance to changes in its motion. Suppose you have three identical lead bricks, and you throw one of those as hard as you can. The brick would resist being thrown; it would take effort to give the lead brick velocity. Two bricks glued together would resist your efforts twice as effectively. More mass means more inertia or more resistance to change.

The amount of mass (matter) is measured in units of kilograms (kg) or grams (g) in the metric system, and in the British system measured in units of slugs (sl) - an odd unit not used much today.

Now, weigh the bricks on a scale, and you find that each brick weighs 10 pounds. The scales are measuring weight, that is, the force of the Earth’s gravity pulling down on the mass. Weight is the force gravity exerts on something. If you determine the mass of each brick on a balance, you find that each brick has a mass of 4.54 kg. (Balances work by canceling out the effects of gravity.)

If you go to the Moon, the mass is the same but the weight is six times less because the gravity is six times weaker there. Mass and weight are related, but different. Mass refers to the amount of matter, weight to the force of gravity pulling on that matter. (In British units, a mass of one slug placed on your bathroom scale would weigh 32 pounds!)

Thus, if you place 1000g of mass on your bathroom scale, your scale would read a weight of 2.2 pounds. So, you often see written, 1000g = 2.2 pounds. This equation will irritate science purists, since we’ve equated apples and oranges here by setting mass equal to force. What we have just written is really an equivalence. A 1000g mass on Earth has an equivalent weight of 2.2 pounds. With a little arithmetic, you find that 454 grams has a weight of 1.0 pound (1000 / 2.2)!

Grams are different from pounds - one is mass and one is force, two different physical quantities. Yet 454 grams is equivalent to 1.0 pound here on Earth. That is, an object weighing 1.0 pounds contains 454 grams of mass.

A web site that allows one to convert units of all kinds can be found at http://www.megaconverter.com/Mega2/.