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# Re: [Phys-l] Separating inertial mass and g mass. Was: Re: a different kind of math background quiz

--- On Tue, 1/5/10, Bernard Cleyet <bernardcleyet@redshift.com> wrote:

Speaking of:   You all know the mass of a simple pendulum's bob (a physical >also) serves both as an inertial mass, as in a spring oscillator, and also as a >gravitational mass (a non-linear spring).  Since Eötvös, they are the same.  >However, they are not the same if the pendulum is not so simple.  I mean when >the bob is immersed in a fluid.  A minor matter if the bob is in air (Horologists, >correctly disagree.), but always a serious matter if the fluid is water.  Pray tell, >how does one write the diff. eq. to make the correction.  I've done this, and its >solution disagrees w/ the horological lit.   Perhaps I've done it correctly and the >horological correction is an approximation or I'm too maths challenged to >convert.

Gravitational mass and inertial mass are the same only in the gravitational field alone. All forces other than gravity tend to mask this equivalence. One of the reasons of discrepancy with horological corrections for a physical pendulum might be the dependence of the forces involved on shape of moving object (a drag force on the swinging bob depends on its velocity AND on its size, and even on degree of smoothness of its surface if we go for high accuracy). An open parachute is a good illustration. For a class demo I used sometimes a box with chalk and a sheet of paper dropped together, and in the second trial did the same with the same sheet thoroughly crumpled so that now both items hit the floor simultaneously. By changing the shape of the sheet we could uncover the equivalence of the inertial and gravitational mass. My personal feeling is that the students were impressed by this simple demo.

Moses Fayngold,
NJIT

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