2007-12-20

weight, gravity, and contact force

On the final exam, I asked the following:

Explain why the astronauts in the Space Shuttle are weightless.

I was lenient in grading. But my position is actually at odds with most of the textbooks. Here's why.

The standard textbook answer is something like Actually, the astronauts on the Shuttle still have weight, since there are still gravitational forces acting on them. However, they feel like they are weightless because they are in an accelerating reference frame that is accelerating at the acceleration that the gravitational force is providing. This will be followed with various things about equivalence and plummeting elevators and non-inertial forces and so on.

My explanation is that the gravitational force on an object is not the weight of the object, when the word weight is properly understood. The weight of an object is not the gravitational force but rather the contact force that holds the object up against gravity (and non-inertial forces). It is this contact force, after all, that a spring scale measures, because a spring scale does its job by providing a contact force. It is also this contact force, after all, that you perceive by having your feet pressed onto the floor or behind pressed into the seat of your chair. Indeed, gravitational forces can never be measured locally or internally (that's equivalence!), all you can measure is the stresses and strains required to oppose them in our non-inertial (by GR standards) frame.

My view makes the astronauts not misled but truly weightless. It also makes it true, not apparent, that one is lighter at the top of a hill and heavier at the bottom of a hill on a roller-coaster, and same for the related changes you experience in an elevator.

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