A teacher's guide to

Inertia

E. M. Purcell, Harvard Unversity

This film (together with the following one on Inertial Mass leads into the study of dynamics by proving some experimental basis for the generlaizations which comprise Newton's law of motion.

The film Inertia relates to Sections 20-1, 2, 3, 4 of the PSSC physics text (1st ed). Inertial Mass relates primarily to Sections 20-5,6. Both films relate to Laboratory III-2,3,4.

Summary

Professor Purcell begins with an experimental investigation of the simplest practicable situation--the motion of a body on a nearly frictionless surface with no applied force (dry ice pucks on a smooth table). Galileo's principle of inertia is suggested from the observations.

Next, a single constant force is applied to a body initially at rest. Analysis of the ensuing motion shows that such a force produces uniform acceleration of the body in a straight line.

A third experiment demonstrates the effect of twice the original force upon the motion of the same body. Twice the acceleration is observed.

Finally, an experiment is performed from which one could show that the accelration of a single body acted on by two forces of different directions is in the direction of their vector sum.

The question of te acceleration of different bodies acted on by the same force is deferred until the next film, Inertial Mass

Points for Discussion and Amplification

(a) These experiments were performed on a "horizontal" surface. But how do we know when the table is horizontal? If we adjust it so that the disc remains a rest are we assuming a principle which the experiment is designed to establish? One can not "prove" the Galilean principle by experiment, since no independent method is available to insure the fact that no net force acts on the body. The demonstrations serve, however, to show that observation is consistent with the Galilean principle.

(b) Stress the limited character of the first acceleration experiment. The body starts from rest, the motion is in a straight line and only one force, a constant force, acts on the body. Further experiments are needed to extend the range of phenomena to which the experimental "law" is applicable.

(c) Since no independent force-measuring instrument is available at this stage, Professor Purcell. uses a symmetry argument to get double the force, using as indicators two identical rubber rings in parallel. But how can we be sure that two rings exert twice the force of one? How do we know that the pull of one is not somehow affected by the presence of the other? We don't! The independence of forces is a basic assumption of Newtonian mechanics. It should be impressed upon students that the principles of physics are not obtained soley from experimental observation.

(d) It is important that the evidence supplied (in the film) for the vector nature of forces is dynamical evidence, different in kind from such evidence as is supplied by, say, a force table apparatus.

(e) It should be made clear to students that the particular method of finding the acceleration in the film is valid only for the case of constant acceleration. Since the velocity increases uniformly with time, the average velocity over a one-second interval is the instantaneous velocity at the center of this time interval. Consequently the difference of average velocities in successive one-second intervals is the change in intstantaneous velocity in a time interval of one second. The average acceleration thus obtained is also the instantaneous acceleration, in this special case of constant acceleration.

(f) To understand how Dr. Purcell's helper works, a student must be familiar with Newton's law in vector form and the experimentally established proportionality between inertial mass and gravitational mass. Since these concepts will not be studied until later in the course (Ch. 21), care should be taken to avoid a detailed discussion at this time.

(g)Stuents who wish to build their own low friction pucks can be referred to the yellow pages in the Part III Teacher's Guide. To assure a level table free from depressions, plate glass of at least 1/4 inch thickness on top of a good solid base is needed.

(h) Dr. Purcell performed four experiments in this film, and a strobe photograph of each is reproduced below. In each photograph the flash rate was one per second and the scale is graduated in centimeters. In Fig. 1, with no force acting, the puck is seen to be moving at a constant speed of 16 cm/s. Fig. 2 shows the same puck being pulled by a constant force. Measurements of the photograph give an acceleration of approximately 2.6 cm/s^2. In Fig. 3, twice the force produces an acceleration of about 5.1 cm/s^2, which is almost twice the earlier acceleration. Measurements of Fig. 4, with the double force acting at an angle of 60 degrees, yield an acceleration of 4.4 cm/s^2. The vector sum of these forces predicts, by calculation from the previous data, an acceleration of 4.5 cm/s^2.