Physics, Astronomy & Cosmology / Re: what would happen if gravitational mass were different than inertial mass?« on: Yesterday at 10:15:05 »
Quote from: Colin2B
similarly with the pendulum having different masses, you would get different periodsI think most models of unequal gravitational & inertial mass would still assume that they were proportional to each other.
- Otherwise you could end up with a situation where a zero gravitational mass had a non-zero inertial mass (or vice-versa)
- Or (more extreme), a positive gravitational mass had a negative inertial mass (or vice-versa)
A pendulum works by the periodic interchange of gravitational potential energy (calculated from gravitational mass) & kinetic energy (calculated from inertial mass).
- The key being that the mass of the pendulum cancels out in the calculation
- so two pendulums with different masses (but same length & gravity field) have the same period.
Lets say mi = k mg
- mi is inertial mass
- mg is gravitational mass
- And k is some constant, close to 1
From the "Energy" method of calculating the period of a pendulum:
mggh = 1/2 miv2
or kmigh = 1/2 miv2
- Where g is the acceleration due to gravity (assumed uniform)
- h is the height of the pendulum
- v is the velocity of the pendulum
Change in velocity due to a change in height is:
v=SQRT(2kgh) (note that mi still cancels out)
So the period would be slightly different than if mi = mg...
- But the period is still independent of the mass of the pendulum.
..and expand the section on the "Energy derivation".
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