A forum set up for physics questions from students in the courses PHYS1121, 1131, 1221 and 1331 at the University of New South Wales. It is intended for questions that cannot readily be answered in class,
either because they fall outside the main syllabus and therefore would be distraction (however interesting) or for other reasons.

Here is one way of putting the question. For a falling object in an inertial frame, we write
Total force = m_i*a = m_g*g = gravitational force on the object.
where m_i is the inertial mass and m_g the gravitational mass.

The first equation is Newton's second law. m_i is the object's reluctance to accelerate under a given force.
The last equation indicates one or other gravitational law. m_g is the property of an object that interacts with a gravitational field.

To make the distinction clear, consider the analogy for an object in (only) an electric field, E
Total force = m_i*a = q*E = electrical force on object.

Compare this with a falling object in an inertial frame:
Total force = m_i*a = m_g*g = gravitational force on object.

We're not surprised that the ratio q/m_i is different for protons and neutrons. I was surprised that the ratio* m_g/m_i seems to be constant for all objects. (As was Newton.) Do a pendulum made of graphite (equal numbers of protons and neutrons) and a similar one made of plastic (many more protons than neutrons) have the same period? Why is the answer yes?

To oversimplify: Mach says it's not a coincidence, and that the two are related. Einstein says m_i and m_g are the same thing.

Joe
* And if they are proportional, we can make them equal with choice of units.