My Daughter,the Physicist

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by Stephen Cohen

Science in Life

My young daughter cannot form a sentence yet, but she totally gets Newtonian Mechanics. As a proud father, I am inclined to believe that she is a gifted 15-month-old, but I have observed other toddlers, and must admit that they too demonstrate a solid understanding of Mechanics, the oldest branch of Physics. To be clear, these thumb-sucking individuals would struggle mightily in my Mechanics course, let alone get through the three-hour final without wetting themselves. Without basic linguistic or mathematical skills, a baby cannot be expected to understand or express the laws studied in the course or solve computational problems (their unrefined motor skills lead to calculator errors). However, these diaper-clad kiddies perform experimental studies in classical physics on a daily basis. Every day, as they learn to exist within their environment, they make observations on the laws that govern it. Through experience, they discover how to thrive within these universal constraints.

Newtonian Mechanics is, in a way, the oldest branch of science. It deals with the most basic manipulation of our environment. In essence, Mechanics is the study of motion of matter, or mass. A primitive invention such as the wheel is a mechanical device man has used in a variety of ways for millennia. Although the nature of how a wheel works has been clear since its inception, the physical laws governing the motion of a rolling wheel were derived by Isaac Newton in the seventeenth century. The foundation of classical Physics, which Einstein later proved apply only to things moving much slower than the speed of light, was laid by Newton’s three laws of motion.

The first law says that a moving body will only change its velocity if an external force is applied to it. This is evident enough – it means that a puck would slide down the ice indefinitely if not for the contact force known as friction between it and the ice surface as well as the drag force that point opposite to the direction of motion. One interpretation of this law is that an object at rest remains at rest if the net force acting on it is zero.

Newton’s second law is indeed the cornerstone of Mechanics. An economics student must leave an introductory class with an understanding of “Supply and Demand” – I ask that if students retain just one thing from my Mechanics course, it be that F = ma. The bold notation signifies a vector quantity (an entity that has a direction). This simple equation means that the net force is equal to the mass multiplied by the acceleration. Otherwise stated, the magnitude and direction of the acceleration of a body is equal to the magnitude and direction of the net force acting on it divided by its mass (a = F/m). The acceleration of a body means its change in velocity, and net force means the sum of all external forces which come in many forms (gravitational, contact, electromagnetic, etc). Note that the first law is simply a result of the second law for the case when the net force is equal to zero.

The third law is perhaps the most confusing, but may be stated very simply: “For every force applied by body one on two, there is an equal and opposite force applied by body two on one,” so all forces come in pairs. When a fly hits the windshield of a car cruising down the highway, the windshield imparts the same contact force onto the fly as that of the fly onto the windshield (the windshield is not bothered by this magnitude of force, while the fly will need two Advil at best). Imposing these laws, particularly the second and third, allows one to solve a wide array of mechanical problems. An understanding of Newton’s laws allows for a deeper appreciation of Mechanics, but is not necessary for a basic appreciation. When my daughter was six months old, she already knew that letting things go caused them to drop to the ground. She had discovered the law of gravitation, which says that all mass is attracted to other mass, particularly the nearest, largest mass. On the surface of the Earth, the only large gravitational force is the one established between all objects and the Earth. Her understanding of gravity deepened as she learned to walk. Every time she fell down, and converted her gravitational potential energy into kinetic energy, she hit the ground with a thump. In the process, she learned about surface hardness, as the harder surfaces, like our wood floors, gave her rear end a larger impulse than the softer carpeted areas. The next physics lessons involved projectile motion. It turns out that the only thing more fun than dropping stuff is throwing it. The curved path followed by the objects she throws is due to the unchanging horizontal speed of the ball and its downward uniform acceleration. Greater initial velocities yield greater distances. The study of motion in space and time is a branch of mechanics known as kinematics, and she is becoming well versed in it.

There are endless mechanical conclusions to be gathered whenever we go to the park. An introductory physics class could bring a stop-watch to a park, and the setting would suffice for the majority of their experiments. As she accelerates down the slide, she is learning about motion along an inclined plane with friction, a topic that many students struggle with. As we take a break from the see-saw and sit in equilibrium, she learns about the principle of torque, like that used in levers – as I sit eight times closer to the pivot point than she, my weight, which is eight times greater than hers, causes an equal and opposite torque to counteract hers. Finally, she displays simple harmonic motion as she vibrates back and forth in the swing. When she is older, she will be able to swing herself by adding well-timed angular impulses about the pivot point, thereby increasing the kinetic energy of the system.

When she is older, I look forward to teaching her about electricity and magnetism (she had better not discover that one on her own first via electrical outlets in our home). Maybe I will teach her about Einstein’s theories of relativity. Some kids have normal parents, who buy their girls Barbie dolls – my poor daughter will be stuck with a mass and pulley system. She may end up a nerd, but she will be ready to face the universe by understanding the laws that appear to be governing it. The truth is that no matter how much I try to teach her about Physics, her real appreciation for it will come from pushing up against its boundaries herself, by throwing stuff and playing in the park. We tend to learn things best when we teach them to ourselves. People tend to excel at things they are naturally drawn to. I will try to let her decide for herself if Physics is interesting. It is common for a Physics student to express their lack of understanding of Physics principles. I sometimes wish that my students realized just how much they already understood about Physics before they entered my classroom.