ACCELERATION

Film Loop: Inertial Forces - Translational Acceleration

Length: 2:05 min., Black and White, No sound

A 156-lb student riding in an elevator experiences an increase in weight when the elevator starts up and a decrease when it accelerates downward. When moving at constant speed (between floors) his weight is normal.

The elevator in the Buckeye Federal Savings and Loan building in Columbus, Ohio, was selected for its large acceleration and relatively smooth stop. The safety interlock is disabled so that the elevator can be operated with its doors open. In this way the direction of motion can be seen as the floors go by. The indicator of the spring scale overshoots the mark; the actual increase and decrease of weight is somewhat less than the maximum readings of the indicator.

There are two equivalent ways of analyzing the forces. To an outside observer the acceleration is known to exist (relative to an inertial frame). The push of the floor on the student is P. The resultant force is P-mg, and Newton's 2nd law says P-mg=ma, whence P = m (g+a). For an upward acceleration a>0, P>mg, and the floor pushes upward with a force greater than the student's normal weight. According to Newton's 3rd law, the student pushes downward on the floor with a force of magnitude P, and therefore the scale registers the force Pwhich is greater than mg. Similarly when a is negative, the apparent weight is less than mg.

If the student does not know the elevator is accelerating, he considers himself to be in equilibrium under the action of two forces: the push of the scale platform P, and a "gravitational" force -m (g+a). The inertial force -ma which has arisen because of the (unknown to him) acceleration of his frame of reference is in every respect equivalent to a gravitational force. He is at liberty to say either "someone accelerated the elevator upward" or "someone turned on an extra downward gravitational force."