Understanding Mass and Weight
Fundamental Physics Concepts Related by Acceleration due to Gravity
Mass and weight are related but distinctly different properties of an object. Mass is an inherent property; weight is the gravitational force acting on an object.
Mass
Physicists use the concept of mass to measure the amount of matter.
An object's mass is a measure of its inertia. An object's inertia is its resistance to an acceleration when a force acts on it. Accelerating, or changing the velocity, of a more massive object requires a greater force. Hence a more massive object has more inertia.
Mass also enters in to Newton's law of gravity. The gravitational force, both acting on and exerted by, any object depends on the object's mass.
An object's mass is a fundamental unchanging property of the object. An object's mass will not change by moving the object to a different location or changing the object's environment in any way. For example, a 70 kg astronaut will have a mass of 70 kg on Earth, in the space shuttle, on Mars, or anyplace else in the universe. The astronaut will however have a different weight at all these locations.
Weight
Weight is the gravitational force acting on an object. On Earth's surface, an object's weight is the gravitational force of Earth pulling the object down. When we say that a person weighs 150 pounds (= 670 Newtons), that means that Earth's gravity is pulling down on that person with a force of 150 pounds.
Notice that weight is a force not a mass. Unlike mass, an objects weight depends on its location. The astronaut mentioned above will have a different weight, but the same mass, on the Moon, Mars, and other locations because the gravitational force varies.
Acceleration due to Gravity and Newton's Second Law
Under the influence of gravity, all objects, regardless of their mass, accelerate downward at the same rate. Near Earth's surface this acceleration due to gravity, denoted by g, is 9.8 meters per second squared. On the surface of the Moon or another planet the acceleration due to gravity will have different values.
Newton's second law provides a mathematical relationship between the force acting on an object, its mass, and its acceleration. It states that the force equals the mass multiplied by the acceleration.
In equation form: F = m a.
The force is F; m is the mass; and a is the acceleration.
We can apply Newton's second law to weight, which is the force of gravity. Doing so gives: weight equals mass multiplied by the acceleration due to gravity.
In equation form: w = m g.
The weight is w; the mass is m; and g is the acceleration due to gravity.
Units of Mass and Weight
The kilogram is the standard unit for measuring mass. Weight and other forces are measured in Newtons which are kilograms meters per second squared. In the British system, weight and other forces are measured in pounds and masses are measured in slugs.
Unit conversion tables may list a conversion from pounds to kilograms. This is technically incorrect because kilograms measure mass and pounds measure force. The conversion factors assume that the standard acceleration due to gravity on Earth's surface applies.
Mass and weight are two related but distinctly different quantities. Those studying physics need to understand the difference and to not interchange the two quantities.
Further Reading
Knight, R.D., Physics for Scientists and Engineers, Pearson, 2004.
Hecht, E., Physics: Algebra/Trig, Brooks/Cole, 1997.
