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Mass is a measure of how much "stuff" is present. Based on our everyday experiences we have an intuitive feel for mass: we call relatively massive objects (such as a bowling ball) heavy and objects with relatively less mass (such as a ping-pong ball) light.

A formal definition of mass is that it is the proportionality constant in Newton's First Law,

F = m a,

(1)

which describes the acceleration a of an object of mass m when a force of magnitude F is applied to it. Thus the mass of an object is what gives it inertia, the resistance to acceleration (change in velocity). Starting with a bowling ball and a ping-pong ball both at rest on a level floor, you must push much harder on the bowling ball to start it rolling than you need to for the ping-pong ball. If the bowling ball is 200 times heavier than the ping-pong ball, you must push precisely 200 times as hard.

Einstein's famous equation

E = m c2

(2)

shows that the energy E of a stationary object is directly proportional to its mass m. (The speed of light in a vacuum c is a constant; therefore c² is also constant.) So at a fundamental level energy and mass are equivalent. Because c is a large constant (3 x 10⁸ m/s), c² is an even larger constant, meaning that even a small amount of mass is equivalent to a tremendous amount of energy. For instance, a mass of 1 gram is equivalent to an energy of 9 x 10¹³ Joules! If you filled your car's gas tank 63,000 times you would have used about this amount of chemical energy.

Even though mass is fundamentally a type of energy, we don't know of a routine way to take an arbitrary object and convert a significant part of its mass to a different type of energy. Just this has been observed in high-energy particle physics experiments, however: an electron (which has mass) has been observed to collide with an anti-electron (positron) to produce only a high-energy photon (which has only energy, no mass). In a more commonplace scenario, it has been verified that nuclear reactions, with their associated huge heat releases, are accompanied by changes in mass consistent with eqn. (2). Chemical reactions have heat releases much smaller than nuclear reactions, and thus the mass change of the reacting chemicals is insignificant.

Because mass changes are insignificant in all but a few specialized cases, we usually treat an object's mass and energy as independent quantities. Thus, we typically make use of conservation of mass and conservation of energy as if they were completely independent statements. For the specialized cases where mass change is significant this is no longer a valid approach.

Symbol List:

Symbol	Description
a	Acceleration
c	Speed of light in a vacuum, 2.99792458x108 m/s
E	Energy
F	Force
m	Mass

 

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