Fig Newtons

Newton's Laws of Motion (or The Three Laws of Motion) are liberally quoted. Here are some of the things one hears from time to time.

From people in general:

"That object is in equilibrium, so by Newton's First Law, there must be no forces acting on it."

From a project manager, remarking on someone else's project:

"That project is definitely in free fall."

From a manager in response to observing a backlash to a recent business initiative:

"We should have known that would happen. Newton's Third Law predicts that for every action, there is an equal and opposite reaction."

Let's look at these one by one.

Misapplication of the First Law

Newton's First Law of Motion says:

A body at rest or in a state of uniform motion (constant velocity) will stay that way unless acted upon by an external force.

Note that this means there are no net external forces acting on the body unless precisely stated. Or, to put it another way, there may be external forces acting on the body, but they (the multiple external forces) cancel exactly. When these external forces balance each other, the object is in equilibrium: static equilibrium if the body is at rest, or else equilibrium in uniform motionthat is, in a straight line at constant velocity. So remember: Equilibrium does not mean "no forces acting." Equilibrium means "all external forces balance exactly." Of course, internal forces have no effect, as they cancel in pairs by Newton's Third Law, as we shall soon see.

Let us assume that a lump of coal is moving at constant velocity along the surface of a level table. Ignore for a moment how it came to be in motion, but let's assume it is moving at one inch per hour toward the west. Newton's first law tells us that unless we impose some other horizontal force on the lump, it will continue to move at one inch per hour toward the west forever.

Now, as I pointed out earlier, this defies common sense. In our real world, we would expect the lump of coal to slow down and eventually stop for at least two reasons. One, there is air resistance; and two, there is friction with the table's surface. Both of these will tend to retard the uniform westward motion. But of course, there is no violation of Newton's First Law here at all: Both air resistance and friction are external forces acting on the lump of coal, and the first law states very precisely that the rule does not apply if external (net) forces are acting on the body in question. Now a physicist, used to thinking about and stating conditions precisely, would understand that a force is a force and you can't neglect any of them. To describe the case precisely, you would have to state: "The lump of coal will continue to move at one inch per hour to the west in a perfect vacuum on a perfectly level, frictionless table." The problem is, most of us are not so precise in describing daily phenomena, so it's easy to understand how ordinary folks might misapply Newton's First Law.

A member of the younger generation of physicists recently pointed out to me that, these days, students use deep space as a theoretical framework for working out problems, so that they can quickly dispense with the effects of air resistance, friction, "tables," and the gravitational pull of nearby massive bodies. Although this idealized context simplifies the requirements for understanding mechanics, one wonders what will happen when these students are called on to solve real problems "back on Earth."

Misapplication of the Second Law

The Second Law says:

A body will be accelerated by an external force in direct proportion to the force and inversely proportionally to its mass.

This one is often quoted as simply "F = ma," which is just a formulaic restatement.^[1] It is an unbelievably simple and elegant result that applies over an incredible range of phenomena.

^[1] While "F = ma" is the commonly quoted formula, the more general equation is "F = dp/dt," which says that the force is proportional to the rate of change of momentum. This only matters if the mass of the system does not remain constant, as in the problem of a rocket becoming lighter as it burns its fuel and thus loses mass during its flight. "F = dp/dt" is more general than "F = ma," but the latter formulation is the one you hear the most. Just remember when you hear it that it contains the assumption that the mass doesn't change.

But what does it mean to talk about a project "in free fall?" I think managers mean that it is accelerating under the influence of gravity, which means that it is gaining speed and will inevitably collide, inelastically and catastrophically, with Mother Earth. Splat! I understand the notion that there are no parachutes and no brakes, thus a sense of rapidly impending doom. Yet I see here a misuse of the physics analogy. Projects are subject to constraints just as surely as they have mass (inertia); the notion that management is so absent that we have effectively yanked the table out from under the lump of coal is certainly disheartening, to say the least.

Misapplication of the Third Law

The Third Law says:

Whenever two bodies interact, the force on the second body due to the first is equal and opposite to the force on the first due to the second.

When something happens in the business world in reaction to an event, someone is sure to bleat out, "For every action there is an equal and opposite reaction." In fact, it is that person who is having a knee-jerk "reaction." Rather than applying any thought to the situation, he quotes Newton to justify or validate whatever backlash has taken place. The reaction is postulated as something that had to happen according to the laws of physics. In truth, however, what goes on has nothing to do with physics. Not only is the typical reaction unequal to the effect that produced it; often it is not even delivered in the opposite direction but is rather off at some tangent. Moreover, it may not have been a result of the original action at all.

Once again, Newton's Law is correct, but we must be precise about the force and the body. Often the "equal and opposite" forces people cite in business situations are really an internal force pair that does not exert any external net force on the body. So whenever you hear someone intone, "For every action there is an equal and opposite reaction," my advice is to check to see what the forces are and what bodies these forces are being applied to.