, we talked about the universe being intrinsically lazy just like people; well, here is just another natural law validating that. People, just like any inanimate object in the universe, always seem to need some motivating force to change course. Forces of circumstance need to arise for people to change course in life. In the absence of such forces, we simply continue unperturbed and uniformly along the trajectory of life that we happen to be on. Really, life is often simply a battle to overcome inertia.
Newton’s second law of motion is the centerpiece of the Newtonian view of the universe, which is captured by the simple relation
Mass × Acceleration = Force
It can also be written in another perhaps more revealing way:
Figure 11.1 Newton’s second law of motion states that acceleration is proportional to the applied force if the mass or weight of the object is unchanged. (a) A light spring exerts a weaker force and leads to smaller acceleration. (b) A heavy spring exerts a stronger force and leads to a higher acceleration so that the object moves farther in the same time.
or if the object is lighter (has less mass) as shown in . But we already know this from experience. That acceleration requires force should be pretty clear if you have ever driven a car. To make it go faster and faster, you need to apply a force, and that is exactly what you do when you press down on the gas pedal in a car; the engine is churning faster, applying a larger force, making the car speed up. The gas pedal controls the force by controlling the rate at which the gasoline burns. We often see the word “torque” when reading about performance of cars—well, torque is just a measure of the force that makes things rotate or spin, like the wheels of a moving car. A Porsche 911 can accelerate from 0 to 60 mph in close to four seconds because its powerful engines provide a much higher torque compared with the typical family minivan! Besides, the larger mass of the minivan also drags it down. Now, if you have any doubts about how mass affects acceleration, just ask yourself if you were to push a Mini Cooper and a tractor trailer in turn, which one do you think is more likely to start moving, or accelerate, from its state of rest?
Newton’s second law has a broader interpretation if we recall that for any physical object, its general position at any given time and/or how fast and which way it is moving are the basic characteristics that define its state in the quantum mechanical sense that we described in . Therefore, acceleration in Newtonian physics is really a measure of the change of state of an object. Well, people have many things that define their state, and so the analog of acceleration in human terms would be the change of state—mental, physical, financial, professional, emotional, familial, and everything else—that defines a person at any stage of life. Forces are literally acting on us all the time to change our state; we all know that. Physical motion requires physical force, but socioeconomic, emotional, professional, and other such changes relevant to us in life are wrought by corresponding nonphysical forces. That generalized definition of a force pervades our language already, and we talk about socioeconomic forces, emotional impulse, and familial dynamics, all of which conjure up imagery of people and society being accelerated along different life trajectories by external forces just like a physical force can accelerate a material object.
—the larger the mass, the greater the force necessary. As we generalize to human and social notions of force, we also have to broaden the concept of mass. We need to understand mass in its broader sense as a measure of inertia of an object. For individual humans, that measure of inertia is age and experience. It is well known that as we “amass” experience and the wisdom of the ages, we become less susceptible and less receptive to changes. Young people can, and often do, change their situation rapidly and are much more susceptible to external forces, but older people do not and cannot change course as easily. It would indeed require significant forces to alter the trajectory of a person in midlife—to change horses in midstream—but even small interpersonal forces can easily alter the life trajectory of people in their teens and twenties. For example, while peer pressure is always a significant force all through our lives, it is the most potent in our vulnerable formative years (when we have less mass of experience and constraints), and we yield to it more easily and more often. As we amass more experience and burden of various constraints in life, we get experience-heavy, and we become less susceptible to the forces of peer pressure and are less likely to start acting or moving on courses of action just because of what others around us say and do. Just as the weight or mass of a physical object is the measure of its inertia; in human terms inertial mass is measured by age and experience. It is borne out by the fact that we generally associate fickleness with youth and stability with age. But there is a strong positive side to the easy changeability of youth as well: Young minds are more flexible and open to new ideas and thoughts, and quite often in history great ideas and great changes came from relatively young people. In the light of all this, Newton’s second law provides the most important law of human dynamics:
, the action of ball 1 acts on ball 2, and vice versa, the reaction of ball 2 acts on ball 1, and because the action and the reaction forces are equal and act oppositely, the balls fly off in generally opposite directions. The action–reaction paradigm applies in every scenario where things move and accelerate. Suppose we are on a treadmill. Our feet push back on the treadmill, and that is the action that causes it to move backward; the treadmill pushes back on our feet with a reaction force and causes us to move forward. Obviously, we can accelerate on a treadmill—we are usually running fast shortly after starting from rest. But the treadmill belt accelerates, too, moving equally fast in the opposite direction as a reaction. With a treadmill, it is easy to visualize the effects of the action and the reaction, but the same thing happens when we walk on the ground; our feet are pushing back on the earth, but the earth being so massive cannot be moved by the puny force of our legs pushing back (recall Newton’s second law). This action and reaction thing is what makes it so tricky to operate things in space: If the astronauts push at anything, it pushes them back and they fly off because they are not held by Earth’s gravity or by the forces of friction that prevent us from floating and sliding around.
We often use the words “mass” and “weight” in a similar sense, and it is fine as long as we are close to the surface of the earth. Our weight is actually a measure of the gravitational pull of the earth on us, and if we go far enough out into space away from the earth, we can be “weightless” as that force diminishes. But we will never be “massless” because mass is just a measure of how much matter we are made of. Newton’s second law implies that the force of gravity or the weight of any object is proportional to its mass.
They would move in exactly opposite directions if the collision were head-on. But if as shown in , if the balls collide at an angle, they will bounce off at an angle still in generally opposite directions.