Experiment 7
Inertial and Gravitational Mass

Objectives

In this experiment we will attempt to show the equivalence of gravitational and inertial mass.

Introduction

A net force applied to an object causes the object to accelerate.  The ratio of the magnitude of the net force to the magnitude of the acceleration is the "inertial mass' of the object.

A mobile body near a fixed body experiences a gravitational force proportional to the masses of the bodies.  These masses are "gravitational" masses.  The mobile body, as before, will be accelerated in inverse proportion to its inertial mass.  Although inertial and gravitational mass are not logically the same, we know that they are indistinguishable in experience.  The General Theory of Relativity is an attempt to explain this situation.

Procedure

 1)       Weigh your unknown mass.  This measures gravitational mass because weight is used in the measurement.

 2)       Clamp an inertia balance to the table and place your unknown mass in the hole in the balance.  Set the balance into gentle oscillation and time 100 oscillations.  Calculate the period of an oscillation.  Repeat.

 3)       Place a support arm over the balance and tie the mass to a string.  Tie the string to the support so that the mass will still oscillate with the balance but the weight of the mass is supported by the string.  Time 100 oscillations and calculate the period.  If no change in the period occurs, the period of the balance must be responding to inertial mass.

 4)       Remove the unknown mass and put 700 gm on the balance.  Set the balance into gentle oscillation and, once the mass has stopped slipping, measure the period of oscillation as before.  Repeat.

 5)       Repeat 4 for 600, 500, 400, 300, and 200 gm.

 6)       The oscillation is simple harmonic motion so the period squared is proportional to the inertial mass.  Plot period squared vs. mass and fit the data with a least squares fit.

 7)       Square the period from 2 and find the corresponding mass from the least squares line.  This is the inertial mass of your unknown mass.  What percent deviation from the weighed mass do you find?