### Mass, Weight, and Acceleration due to Gravity

In technical terms, mass and weight can easily be confused, and in fact, many people might not even know – or have forgotten – the difference. With our physical world being governed by such laws as gravity, momentum, and energy-conservation, the principle of mass and weight, and the distinction between them, are extremely vital to understanding more complex physics.

A 100 gram apple feels a weight-force of roughly 1 newton directed toward the center of the Earth.

So what IS the Difference between Mass and Weight?

Well, first of all, mass and weight can be used interchangeably when technical definitions are not required. For example, a person can “weigh” 75 kilograms and also have a “mass” of 75 kilograms. The difference lies in the Earth’s gravitational force, which is equal to an acceleration of roughly 9.8 meters per second per second, or 9.8 m/s2.

What this means exactly, is that the mass of an object can be thought of as the amount of “matter”, whereas the weight of an object is equal to the force the object exerts due to the gravitational force acting on it. Mass is measured in kilograms, whereas weight, being a force, is measured in newtons. Let’s take the example of an average 75 kilogram man.

If this 75 kilogram man were standing on the surface of the Earth, he would exert a weight-force on whatever he was standing on, equal to his mass multiplied by the acceleration due to gravity, or FW = mg, with FW being the weight-force, m equal to mass, and g equal to the gravitational acceleration on the surface of the Earth. – About 735 newtons.

Now what would happen if this same man were standing on the surface of the Moon? His mass would remain the same, at 75 kilograms, but his weight would most certainly change. The acceleration due to gravity on the surface of the Moon is roughly one-sixth that of the Earth’s, at about 1.6 meters per second per second. This would make the man’s weight-force about 120 newtons.

So comparing the two weight-forces from the Earth and the Moon, we come to the conclusion that while the mass remains constant, the weight changes depending on the force of gravity acting on the object. The concept of differentiating mass from weight is important when performing calculations involving statics and weight-forces acting on given structural elements.

An easy way to tell the two apart is to remember that mass is measured in kilograms, and equals the weight most people are more familiar with, as in, “how much do you weigh?”, and weight in the technical sense – contrary to the logic that weight equals kilograms – is a unit of force and therefore measured in newtons.

As I mentioned above, weight is equal to mass times gravitational acceleration, FW = mg. If you can remember this basic formula, you should have no problem differentiating the two, as it relates them both clearly. The simpler version of this formula is F = ma, which is the standard equation for force – which equals the object’s mass times its acceleration.