Weight

The popular press often talks about the astronauts in spacecraft orbiting the earth as being weightless. This is verified by watching them on television floating around inside the space capsule. You might jump to the conclusion that because the astronauts are floating around in the capsule, they do not feel the effects of gravity. This is true in the same sense that when you jump off a high diving board, you do not feel the effects of gravity—until you hit the water. While you are falling, you are weightless just like the astronauts.
The only significant difference between your fall from the high diving board, and the astronaut’s weightless experience in the space capsule, is that the astronaut’s experience lasts longer. As the space capsule orbits the earth, the capsule and the astronauts inside are in continuous free fall. They have not escaped the earth’s gravity, it is gravity that keeps them in orbit, accelerating toward the center of the earth. But because they are in free fall, they do not feel the acceleration, and are considered to be weightless.

If the astronaut in an orbiting space capsule is weightless, but still subject to the gravitational force of the earth, we cannot directly associate the word weight with the effects of gravity. In order to come up with a definition of the word weight that has some scientific value, and is reasonably consistent with the use of the word in the popular press, we can define the weight of an object as the magnitude of the force the object exerts on the bathroom scales. Here on earth, if you have an object of mass m and you set it on the bathroom scales, it will exert a downward gravitational force of magnitude
F_g = mg
Thus we say that the object has a weight W given by
W = mg...... (1)
For example, a 60 kg boy standing on the scales exerts a gravitational force W(60 kg boy) = 60kg× 9.8 m/sec² = 588 newtons We see that weight has the dimensions of a force, which in the MKS system is newtons. If the same boy stood on the same scales in an orbiting spacecraft, both the boy and the scales would be in free fall toward the center of the earth, the boy would exert no force on the scales, and he would therefore be weightless.

Although we try to make the definition of the word weight consistent with the popular use of the word, we do not actually succeed. In almost any country except the United States, when you buy a steak, the butcher will weigh it in grams. The grocer will tell you that a banana weighs 200 grams. You are not likely find a grocer who tells you the weight of an object in newtons. It is a universal convention to tell you the mass in grams or kilograms, and say that that is the weight. About the only place will you will find the word weight to mean a force, as measured in newtons, is in a physics course.

(In the English system of units, a pound is a force, so that it is correct to say that our 60 kg mass boy weighs 132 lbs. That, of course, leaves us with the question of what mass is in the English units. From the formula F = mg, we see that m = F/g, or an object that weighs 32 lbs has a mass 32 lbs/32ft/sec² = 1. As we mentioned earlier, this unit mass in the English units is called a slug. This is the last time we will mention slugs in this text.)