Part One: Newton’s First Law
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
Newton’s First Law is sometimes referred to as the law of inertia. Inertia is the tendency of objects to resist changes in their states of motion. Thus, it is the natural tendency of objects in motion to remain in motion and for objects at rest to remain at rest.
example 1: Suppose Newton, 38, is an object in motion moving in the same direction and at the same speed every day of his damn life.
6 am wakeup. Shit, shower, shave. A 40 minute commute in suburban rush hour sandwiching 8 hours at the cube farm. Back at home, he pokes at a lumpy chicken breast while his wife relays her own 8 miserable hours at a different cube farm. After dinner, they watch the evening programs on the large television in the living room, then move into the bedroom and watch the late night programs on the small television. It’s Tuesday, which means they’ll fuck. They never fuck Monday because Mondays are depressing, or Wednesdays because they both work late, or Thursdays because they’re too tired, or Fridays because it’s the end of the week, or Saturdays because neither wants to work that hard on a Saturday, or Sundays although he has forgotten the reason why. So Tuesday it is. It’s become routine, clinical. They each strip off their own clothes because it’s easier and when it’s over, they lie on their backs, stare at the whirring ceiling fan. Tomorrow will be the same, minus the sex, and then the next day and the next and the next. According to Newton’s First Law, Newt continue on like this until he dies, or until an unbalanced force compels him to change his direction.
An object in motion will change its velocity only when acted upon by an unbalanced force.
example 2: Suppose Newt drives home early one day because of inclement weather. Due to a traffic accident on his usual route, he detours through a small residential area, where he notices his wife’s car parked in the driveway of a modest brick house. He grows curious, then unsettled, then enters the unlocked house. “Karen?” he calls, plodding across the wood grain in his rain-soaked loafers. “Karen?” He quiets. Through the steady rain pounding on the windows, he hears a faint human noise and follows it. Through the kitchen with its black granite countertops, three coffee cups soaking in the sink, and a circular wall clock whose batteries had ran out last week, stopping time. Through the home office, the laundry room, the main hallway. Until he’s standing in the doorway of the master bedroom, and she’s there, white and creamy and perfect, beneath some oaf, a redfaced neanderthal with a dull animal grunt, a sweat-soaked hairy back.
They see him, scream, and break apart.
And then Newt is outside himself. He’s jumping on the oaf man and punching his head, biting his oversized ears, digging his nails into the hairy back, the hairs thick and curly and repulsive, and he’s eating the hairs, ripping them out with his bare teeth, spitting them onto his wife’s pearly breasts, where they stain her skin like ashes on snow.
In the previous example, we saw what happens to an object in motion when acted on by unbalanced forces. We will now consider a more complex example involving both objects in motion and objects at rest.
example 3: Suppose Newt, in the midst of choking on back hairs, picks up an object at rest, a lamp sitting on the nightstand, and smashes it against the redfaced oaf man’s gargantuan monkey skull. And he does this again. And again. At first, the redfaced oaf man grunts and tries to buck Newt off. But Newt is overcome with an adrenaline that gives him an otherwise uncharacteristic strength and speed. And then the oaf slumps over, a pliant piece of clay molding to the bed.
Consider the case of an object at rest by itself, without the interference of unbalanced forces.
example 4: Suppose the redfaced oaf man is an object at rest. He lies still, motionless, spread-eagled on the bed, blood drying on the corners of his lips. In this case, the object at rest, weighing approximately 190 lbs, has much mass and thus much inertia; he will not become an object in motion again unless acted on by a large unbalanced force, such as a medic or the Grim Reaper.
Part Two: Newton’s Second Law
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Second Law describes the behavior of objects when acted on by unbalanced forces. To fully understand Newton’s Second Law, a thorough grasp of the terminology is necessary.
A force is a push or pull on an object that occurs only when there is an interaction between objects. Consider the case of two objects beginning their interaction:
example 5: Suppose Newt and Karen are two objects interacting. In fact, Newt and Karen have been interacting for the past fifteen years, since they met in college. The interaction began something like this: Newt, 20, was a lanky junior physics major who hadn’t been laid in over a year and who, upon mentioning these difficulties to a freshman year acquaintance, was encouraged, bribed, and eventually blackmailed into attending a frat party. Wearing some t-shirt from an obscure indie rock band no one else has ever heard of, he is standing in the corner, tapping his feet against a floor littered with empty beer cans and crushed plastic cups, when she approaches. “Cool obscure indie band t-shirt,” she says, running her fingers across the lettering on his chest before disappearing, like a dream, into a pool of piss and PBR and fraternity brothers vomiting into silo cups. Intrigued, he follows her.
Consider next what happens when those same objects stop their interaction:
Types of Forces
Forces can be subdivided into two main types: contact forces and action-at-a-distance forces. Contact forces result when the interacting objects are physically in contact with one another:
friction: He has been seeing her for several weeks now. He lifts the shirt over her head with just two fingers, as if it will tear if he’s not careful. It glides across her form effortlessly, like water. The tiny hairs on her arm sticking straight up, and he smoothes them down. Her body pushes against his open palm.
air resistance force: Next his shirt. They stumble out of their shoes, kicking them across the room. She unbuckles his belt, lets his pants drop to the floor. Cool air, bare legs.
gravity: And there they are, dropping to the floor too. Their faces flush, their clothes crumpled beneath them. The room spins and spins, and all he can taste is the vanilla coffee creamer on her tongue.
applied force: His nails digging at her waist.
tension: His fingers tugging gently at her hair.
normal force: The floor cool and hard against his back.
spring force: The creaking of a dorm-issued mattress. She puts a finger to her lips, smiles. Quiet, quiet. They rock together slowly. Their breaths hushed, the room fading to a faint murmur.
With the exception of gravity, the aforementioned forces are all contact forces. Action-at-a-distance forces result when the interacting objects are not in physical contact with one another and include gravity, electrical forces, and magnetic forces. In the context of our previous example, we might consider a fourth at-a-distance force, a highly controversial one which has not been recognized by the majority of scientists:
example 6: It has only been a few months, but he cannot remember a time before her. All objects seem to exert a force in her absence. He feels her fingers tiptoeing across his spine in the patter of rain on his dorm window, tastes her breath in the breeze. He has trouble concentrating in his classes because he is in love and this love exerts a powerful force, even in her absence.
Determining Mass, Acceleration, and Force
A simple way to think about Newton’s Second Law is to realize that, as the force acting on an object increases, so too does that object’s acceleration. Conversely, if the mass of an object increases, the object’s acceleration decreases:
example 7: Suppose several years pass. They are both physics graduate students, each working long hours in different research labs, and have been living together for the past year. In the evenings, he thinks of her. He runs equations through a computer and pictures her sprawled across the bed, head casually tilted on her forearm. He makes little notations on charts and wonders what she will be wearing. He sifts through data and imagines how they will make love when he gets home, writes equations on a whiteboard and feels her small, cool hands. But when he gets home, he finds her pacing the room, running her hands through her hair. He hears the words before she says them. He will watch her slight figure grow round, and he will feel this heaviness in him too, this weight. He will drop to one knee. He will take her hand and say, “I do,” feeling the weight of those words tickling his lips. They will get boring jobs. They will buy a house in the suburbs with red bricks and white shutters. They will feel themselves growing old in it, will feel the accumulation of years fixing them to this place, this future, and they will feel heavy.
Two Body Problems, Free Fall, and Air Resistance
Thus far, we have restricted our analysis to single objects operating under Newton’s laws. We might also consider what is called a two body problem, when two objects are connected together. In these types of problems, one approach is to consider the two objects as a system before isolating the objects and determining the value of the force between them. Consider the following:
“What are we going to do?” Karen asks, nodding at the still man on the floor.
“I have an idea,” Newt says, covering the redfaced oaf man with a towel.
It takes both of them together to lift him into the car’s backseat, where she sits with his head on her lap, staring out the window. He watches her from the rearview mirror, his eyes trained to her slight movements, her half-hearted fidgetings.
“Do you love him?” he whispers softly. She looks down at the head cradled in her lap, strokes the tufts of hair. Their eyes meet in the mirror. “No.”
“What are we going to do?” Karen asks, lifting her head from Newt’s three years into their marriage. It feels like a lifetime but was only this morning when the aging rescue dog they’ve cared for like a child collapsed in the backyard, his eyes rolling to the back of his head, his body trembling all over. A classic seizure. They lay him in the backseat of the car, rushed right over to the vet. Now they wait for news.
“Do you think he’ll be ok?” she whispers softly. He looks down at her, squeezes her hand. Their eyes meet. “Of course.”
These previous examples logically follow from Newton’s Second Law. However, let us turn our attention to several less intuitive examples. In free fall, all objects fall with the same acceleration, no matter their mass:
example 10: Suppose we have have two objects, Karen and the redfaced oaf man, of varying existential mass. Married with a mortgage, Karen has more existential mass than the redfaced oaf man, a bachelor. Thus, Karen rejected the redfaced oaf man’s advances, initially. She would think back to her early days with Newt. To summer evenings lying spread-eagled on a creaky student housing fire escape, speaking of lives that had yet to unfold. To his breath fogging a cool summer ale, his palm warm and sweaty against her thigh. Then she would think of the last few years, how something had changed between them. Sometimes, she would catch him looking right through her like he was noticing a crooked picture frame, a door slightly ajar. Neither could quite explain this rift but both felt it, a gradual wearing away.
So when the redfaced oaf man suggested drinks one day after work, she accepted. But then she drank too much and started saying things that weren’t true. How Newt didn’t love her, hadn’t loved her in years. How unhappy she was, how lonely. And the refaced oaf man nodded sympathetically. He wiped a loose strand of hair from her face, ran his finger down her cheek, told her she was never alone, kissed her long and slow. And then they were free falling back to his apartment and onto the bed at the same acceleration because this was a vacuum an aberration a one-time thing a dream a nowhere a somewhere wonderful and hypothetical that didn’t count and would only happen once and had no friction or air resistance. Because the first indiscretion always feels as though it were in a vacuum, isolated from the rest of our actions.
Free fall is the great equalizer. But we rarely encounter free fall in the real world because of air resistance. Consider what happens then to a falling object that encounters air resistance. When falling objects encounter air resistance, the heavier object will fall faster:
example 11: Karen is not in a vacuum. She is not in free fall. She is in this real car, and the redfaced oaf man is probably really dead. She is really falling, falling fast.
Part Three: Newton’s Third Law
For every action there is an equal and opposite reaction.
Forces always occur in pairs as action and reaction forces. We can apply this law to collisions between two objects:
example 12: Suppose Newt and Karen have driven to a small lake where you can rent paddle boats and kayaks. The rental facility is all out of paddle boats and kayaks so they are instead in a swan boat only their swan boat was in a fight with another swan boat and is therefore missing its head, and in the course of explaining the swan boat’s decapitation to Karen, the boat attendant does not notice Newt dragging the redfaced oaf man’s body into the boat.
They paddle to the middle of the lake. Newt lifts the body, dangling the feet into the murky water.
Karen taps him on the shoulder. “Should we say a few words?”
They look at each other, shrug. Then Newt heaves the body overboard.
When the splash dissipates, the lake turns from murky to clear, the clearest water they’ve ever seen, clear enough for them to see the redfaced oaf man is not really dead. Instead, he thrashes and bobs just beneath the lake’s surface, clawing at the decapitated swan boat. “I’m alive, help, I’m alive!” he sputters, in case there’s any confusion.
They pull the man aboard. His face is purple from lack of oxygen, and he lies on his back gasping for air, water dribbling from his mouth.
“I think we need to do CPR,” says Newt. “That’s how they do it on TV.”
He bends down and pries open the man’s mouth. Then he gives him chest compressions and air, savoring the man’s delicious lips.
“I almost don’t blame you at all,” says Newt, turning now to his wife as the redfaced oaf man regains consciousness. “He really is a good kisser.”
And then Karen does something she never thought she’d do. She rips off what remains of the decapitated swan’s neck and beats her husband’s lover again and again, until he slumps over again, once more an object at rest.
example 13: Suppose money is tight (again). The roof is leaking (again). And so they are fighting (again). They have been together ten years.
“I thought you said you had this fixed,” she yells, running for a bucket before there’s further damage to the furniture.
“I was going to have it fixed,” he said. “Next paycheck.”
“And you didn’t think to tell me that?” She returns, slams the bucket on the ground, crosses her arms.
He sighs. Then he picks up the bucket and turns it on his head. Water drips down his neck, leaving dark spots on his shoulders.
“What are you doing?”
Without answering, he flips the bucket over, catches more raindrops, and turns them on her head. Before she can think to yell, he has lifted the bucket off and pulled her close.
“No,” she says, trying to push him off. “Stop it.” But he is laughing, and soon she is laughing too. There is nothing to do but laugh.
Newton’s Third Law of Motion implies the law of conservation of momentum. In an isolated system, momentum is always conserved after a collision. The total momentum of the system remains constant despite – and perhaps because of – the complexity of the collision between two objects:
example 14: Suppose Newt and Karen have driven the redfaced oaf man to the hospital and are now sitting in the waiting room, clipboards spread on their laps. “What’s his name?” Newt asks his wife. Her words echo in the empty plastic room. He writes the name in neat block letters and asks her the man’s date of birth, his occupation. With each answer, a sharper image forms in his mind.
Looking up, he notices an elderly couple in the corner. They both wear dull, maroon shirts, the same color as the chairs, and the woman rests her hands on the man’s thigh. He wonders how long they’ve been married. Too long, in any case. They are starting to look alike, as if they’ve molded together after so many years. The woman rests her hand on the man’s thigh. A cane stretches across his small, round stomach.
Suddenly, he feels the need for physical movement. “I’ll be right back,” he tells his wife, and slips out of the waiting room. He finds himself staring down miles and miles of hallway bitter with the smell of antiseptics. The walls are white, the floors shiny. Nurses squeak down the corridors in absorbent white clogs. Doctors rush back and forth with clipboards, whispering strange words and numbers Newt cannot comprehend.
A door opens, and he narrowly avoids bumping into a nurse.
“So sorry,” he mutters, but she brushes his apologies away. She asks him, instead, if he “would be a dear” and hold the door open for her. She will be right back.
Newt nods. He props the door open with his foot, waiting for her to return, and peers inside, where a middle-aged man is hooked up to all kinds of little tubes and bags. Asleep? Or dead? Newt cannot tell. Then the man opens his eyes and blinks. It happens so fast that Newt wonders if he imagined it.
The nurse returns with a bowl, some shaving cream, and a razor.
“Well, I’ll just be leaving,” Newt says, and turns towards the door.
He pauses and turns back. The nurse is lathering the man’s face.
“You know, I think he blinked at me. It was only for a second, but I swear, he did. Maybe he’s coming to.”
The man’s face is completely lathered in shaving cream.
“Oh, he does that from time to time,” the nurse says, picking up the razor.
“So he’s not going to wake up then?”
“Actually, he’s already awake. He’s in a vegetative state, not a coma. He even experiences sleep-wake cycles, we think. And he’ll respond to us every now and then. Sometimes, he’ll swallow or grind his teeth. All these things,” she motions to the tubes and wires, “are just so he gets fed.”
She puts down the shaving cream bottle, wipes her fingers on a towel, and picks up the plastic razor. “He’s awake,” she says, the razor poised above the man’s left cheek, “just not aware. He’s a pretty young guy, too. He can keep going for a long time still.”
The razor glides across the man’s face in short, swift strokes. Newt stands, transfixed. He closes his eyes and pictures his own face in recent years, the bags beneath his eyes, the wrinkled forehead. He pictures himself growing older but never changing, his body continuing to go through the motions like a hamster on its wheel whose past is its present is its future.
“Isn’t it strange,” the nurse says to him, wiping the last bits of shaving cream from the man’s lips with a towel, “that you can live out the remainder of your life unconscious?”
The man blinks again, and Newt leaves.
Outside the waiting room, he pauses. Through the window pane of the door, he sees his wife seated in the waiting room beneath a circular clock whose batteries ran out last week, stopping time. He can’t know yet that the redfaced oaf man will wake up and file charges or that he will be sent to a prison whose pitiful excuse for a library is stocked with outdated textbooks. He can’t know yet the countless hours he’ll spend revising these books, lingering over equations he once found eloquent but which now, in the harsh reality of his irrational steel world, fail him miserably. He can’t know yet the long lonely nights on a hard cot, the fluorescent lights bright on his face and the air damp and stale over the many miles of hard crusted earth.
He knows only that he feels conscious for the first time in years, that he is no longer an object moving uniformly straightforward. He is accelerating and falling all at once, his future–their future–wide open, no equation to chart the way. They lock eyes. Her forehead is wrinkled just like his but more elegant so that he cannot tell whether he has grown to look more like her or she like him, only that there is something still between them, a force he feels after all these years.