Newton's 2nd Law
Boats occasionally hit rocks. When they do, things sometimes break. That river you see flowing between the tall red cliffs is too lazy to throw boats into rocks, but a hundred miles downstream, it will awaken and drop much faster, in real haste to get to the ocean. There, boats hit rocks.
What happens when a boat hits a rock? What happens that might break things?
Newton's first law says that force produces a change in motion, not the motion itself. Newton's second law tells how much change.
Newton's first law tells us that our notion that force and velocity go hand in hand is wrong. Newton's second law tells us that force and acceleration go hand in hand. The net force on an object is proportional to its acceleration.
Acceleration is speed of the change in velocity. And it is something that is precisely defined, a quantity which can be used in calculations.
Probably no more than 5% (again!) of college students who learn about acceleration understand it well enough to "see" it as a useable concept in the world about them. Handball, anyone?
Forces break things.
Acceleration, not velocity, is the measure of forces.
Acceleration is rate of change of velocity.
Can you see?
A boat thrown into a rock must accelerate in the direction the rock pushes on the boat, because the rock isn't going to accelerate. There's not much "give" in the boat. (Even less in the rock.) So the change in velocity must occur in a very short time. The acceleration is, therefore, high because accelertion is the ratio of change in velocity divided by the time the change takes. Short time means high ratio. That makes the force that the rock puts on the boat high. The boat is weaker than the rock. The boat may break. "The loud cracking sound you hear when the hero punches the villain in the jaw is the sound of finger bones breaking. Jaw bones are stronger than finger bones."
said by a movie critic
A case history
An Oregon jury was once presented with this case:
A large log loader collided with the rear of a parked log truck at a speed of approximately 5 miles per hour. The log loader weighed in at several times the weight of the log truck, which was unloaded. The boom attached to the tractor of the log truck was crumpled by the collision. The driver who was sitting at the wheel of the log truck sued the lumber company for a little under one million dollars claiming total loss of ability to continue working due to spinal injury.
The "science expert" for the plaintiff—a doctor who had treated the plaintiff—claimed that the plaintiff had been initially thrown violently forward into the steering wheel and then was thrown back into the seat by recoil. The weight of the log loader was, the jury was assured, the critical factor assuring severe damage to the body of the driver. The crumpled boom was cited as additional evidence for the violence of the collision. (The speed of the log loader was not considered significant by this expert.) Severe nerve damage to the spine had made the plaintiff an invalid, claimed his doctor. He was now even unable to engage in wrestling with his son as he had so greatly enjoyed in the past.
The "science expert" for the defendant—a neurologist at the Oregon Health Sciences University—testified that, in his opinion, the low speed of the collision was crucial to the case, and it was not likely to produce serious injury. Furthermore, the crumpling of the boom absorbed much of the energy of the impact. The initial reaction of the plaintiff's body was to be thrust into the padded back of the seat, after which recoil from the seat thrust the plaintiff into the steering wheel. He also testified that an extensive medical examination of the plaintiff could find no damage to the spine or its nerves. However, psychological examination indicated hysterical reaction. (And in the courtroom, the plaintiff froze up when asked to state the name of that neurologist, and he got up and left the courtroom whenever the neurologist was present.)
The jury was shown movies, taken surreptitiously by a detective, of the defendant engaged in vigorous activities around his home.
Newton's laws of motion clearly identify one expert as correct and the other as incorrect. One comprehended Newton's laws; the other retained the prescientific misconceptions.
The jury of twelve went against the opinions of the one physicist and the one aircraft mechanic on the jury and found, ten to two, in favor of the plaintiff and in opposition to Newton. In their deliberations, they expressed disgust with the defendant for hiring the sneaky detective and a wish to punish anyone who would stoop so low.
The elementary physics was apparently not within the reach of comprehension of those ten jurors--as it is not for about 95% of the students of elementary college physics courses (including the one of that ten who had taken a course given by that physicist). Conceptual science is unlike so many human discoveries—such as the existence of a Western Hemisphere of continents and moons orbiting Jupiter. Those things are easy to understand and once they are discovered they become a part of society's general knowledge.
Conceptual science requires new, unfamiliar ways of looking, unfamiliar ways of reasoning, and those discoveries do not become part of society's general knowledge. Instead, society continues to accept as "truth" the pre-scientific misconceptions that have been corrected by the new concepts.
Our system of laws and legislatures, of attorneys and juries and judges, can incorporate flaws if it doesn't effectively reject such misconceptions and the inadequate reasoning that underlies them.
Motion implies a force: that's wrong.
Newton's laws of motion.