Mass and weight are easy to confuse. The difference is more than something that plagues students doing homework -- it is at the forefront of science. You can help children understand this by going over units and by discussing gravity, where mass comes from and how mass and weight act in different situations.

## Mass Versus Weight

An important difference between mass and weight is that weight is a force while mass is not. Weight specifically refers to the force gravity applies to an object. Mass reflects the amount of matter (i.e., electrons, protons and neutrons) an object contains. We can place a scale on the moon and weigh an object there. The weight will be different because the strength of gravity is different. But the mass will be the same.

## Units for Mass and Weight

In the United States, household and commercial scales measure weight in pounds, a measure of force, while in almost every other country in the world, scales measure in metric units, such as grams or kilograms (1,000 grams). Even though you might say that something “weighs” 10 kilograms, you are actually speaking of its mass, not weight. In science, weight is measured in Newtons, the unit of force, but this is not used in everyday life.

## Weight: Force Due To Gravity

Weight is the force with which gravity acts on an object. To convert between mass and weight, you use the value for gravitational acceleration g = 9.81 meters per second squared. To calculate the weight, W, in Newtons, you multiply the mass, m, in kilograms times g: W = mg. To get mass from weight, you divide the weight by g: m = W/g. A metric scale uses that equation to give you a mass, although the inner workings of the scale respond to force.

With children, it is helpful to talk about weight on another planet, the moon or an asteroid.The value of g is different, but the principle is the same. However, the formulas only apply near the surface, where the gravitational acceleration does not change much with location. Far from the surface, you need to use Newton’s formula for the gravitational force between two distant objects. However, we don’t refer to this force as weight.

## Newton's Laws of Motion

Newton’s first law of motion states that objects at rest tend to stay at rest, while objects in motion tend to stay in motion. Newton’s second law says that the acceleration, a, of an object is equal to the net force on it, F, divided by its mass: a = F/m. An acceleration is a change in motion, so to change an object’s state of motion you apply a force. The inertia, or mass, of an object resists the change.

## Gravitational Versus Inertial Mass

Because acceleration is a property of motion, not matter, you can measure it without worrying about force or mass. Suppose you apply a known mechanical force on an object, measure its acceleration, and from that calculate its mass. This is the object’s inertial mass. You then arrange a situation in which the only force on the object is gravity, and again measure its acceleration and calculate its mass. This is called the object’s gravitational mass. Physicists have long wondered if gravitational and inertial mass are truly identical. The idea that they are identical is called the equivalence principle, and has important consequences for the laws of physics. For hundreds of years, physicists have performed sensitive experiments to test the equivalence principle. As of 2008, the best experiments had confirmed it to one part in 10 trillion.

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