Eric Murray, Spring 2006
Newton's Second Law states that an object's acceleration is proportional to the net force on it
∑F ∝ a
The proportionality constant is the mass, or inertia, of the object
∑F = ma ⇒ m = ∑F/a
A mass determined in this manner, by measuring an object's resistance to acceleration, is called
an inertial mass.
You might be more familiar with gravitational mass, which is determined
by measuring an object's attraction to other objects (such as the Earth). As far as anyone has
been able to measure, these two kinds
of mass are the same. If you take PHYS 2213,
Introduction to Modern Physics, you will see that the Equivalence Principle
in General Relativity states, in effect, that inertial and gravitational mass are actually identical.
By making multiple measurements of ∑F and a, you will be able to find an object's inertial mass, m ± Δm. If you find a inertial mass that does not agree with the gravitational mass (determined using a balance) within your measure of experimental error, then you will have to consider systematic errors. Two likely sources of systematic error are a frictional force acting on the object, and the inertia of a pulley that is part of the experimental apparatus. Note that as greater forces are applied to the object, a frictional force will be of decreasing significance, while the significance of the pulley's inertia would not change.