Free For the Love of Physics by Walter Lewin Page A

take the case of a bowling ball dropped from a tall building in Manhattan—why not from the observation deck of the Empire State Building? It is known that the acceleration of objects dropped on Earth is approximately 9.8 meters per second per second; it is called the gravitational acceleration, represented in physics by g. (Forsimplicity I am ignoring air drag for now; more about this later.) After the first second the bowling ball has a speed of 9.8 meters per second. By the end of the second second, it will pick up an additional 9.8 meters per second of speed, so it will be moving at 19.6 meters per second. And by the end of the third second it will be traveling 29.4 meters per second. It takes about 8 seconds for the ball to hit the ground. Its speed is then about 8 times 9.8, which is about 78 meters per second (about 175 miles per hour).
    What about the much repeated notion that if you threw a penny off the top of the Empire State Building it would kill someone? I’ll again exclude the role of air drag, which I emphasize would be considerable in this case. But even without that factored in, a penny hitting you with a speed of about 175 miles per hour will probably not kill you.
    This is a good place to grapple with an issue that will come up over and over in this book, mainly because it comes up over and over in physics: the difference between mass and weight. Note that Newton used mass in his equation rather than weight, and though you might think of the two as being the same, they’re actually fundamentally different. We commonly use the pound and the kilogram (the units we’ll use in this book) as units of weight, but the truth is that they are units of mass.
    The difference is actually simple. Your mass is the same no matter where you are in the universe. That’s right—on the Moon, in outer space, or on the surface of an asteroid. It’s your weight that varies. So what is weight, then? Here’s where things get a little tricky. Weight is the result of gravitational attraction. Weight is a force: it is mass times the gravitational acceleration ( F = mg ). So our weight varies depending upon the strength of gravity acting on us, which is why astronauts weigh less on the Moon. The Moon’s gravity is about a sixth as strong as Earth’s, so on the Moon astronauts weigh about one-sixth what they weigh on Earth.
    For a given mass, the gravitational attraction of the Earth is about the same no matter where you are on it. So we can get away with saying, “Sheweighs a hundred twenty pounds” * or “He weighs eighty kilograms,” * even though by doing so we are confusing these two categories (mass and weight). I thought long and hard about whether to use the technical physics unit for force (thus weight) in this book instead of kilos and pounds, and decided against it on the grounds that it would be too confusing—no one, not even a physicist whose mass is 80 kilograms would say, “I weigh seven hundred eighty-four newtons” (80 × 9.8 = 784). So instead I’ll ask you to remember the distinction—and we’ll come back to it in just a little while, when we return to the mystery of why a scale goes crazy when we stand on our tiptoes on it.
    The fact that gravitational acceleration is effectively the same everywhere on Earth is behind a mystery that you may well have heard of: that objects of different masses fall at the same speed. A famous story about Galileo, which was first told in an early biography, recounts that he performed an experiment from the top of the Leaning Tower of Pisa in which he threw a cannonball and a smaller wooden ball off the tower at the same time. His intent, reputedly, was to disprove an assertion attributed to Aristotle that heavier objects would fall faster than light ones. The account has long been doubted, and it seems pretty clear now that Galileo never did perform this experiment, but it still makes for a good story—such a good story that the commander of the Apollo 15 Moon