Roman Ya. Kezerashvili

New York City College of Technology, The City University of New York

Alexander Sapozhnikov

Brooklyn College, The City University of New York

New York City College of Technology, CUNY

300 Jay Street

Brooklyn, NY 11201

718-260-5277

rkezerashvili@citytech.cuny.edu

Pendulum with Variable Acceleration

Abstract

The demonstration shows the relationship between the acceleration and a period of a simple pendulum. The steel ball is suspended on string attached to a dynamometer. A permanent ceramic magnetic disk is placed below the ball. The ball is oscillating in the effective field, which is a superposition of the magnetic field and gravitational field of the Earth. By varying the distance between the ball and the disk we can change the magnetic force and as a result the effective acceleration of the pendulum, therefore, the period of oscillation will change. The demonstration shows that with increasing of the dynamometer's reading the period of the pendulum decreases.

Construction and Use of Apparatus:

A simple pendulum is one of the most commonly used demonstrations and laboratory experiments in a course of college physics. It is a good instrument for the measurement of the acceleration due to gravity. A period of a simple pendulum in the small angle approximation is given by very well know expression

.

Thus, the period of vibrations of the simple pendulum is directly proportional to the square root of the length of the string, and inversely proportional to the square root of the acceleration.

In a laboratory it is difficult to change acceleration in order to confirm the relationship between the period and acceleration. We can explore the effect of altering acceleration by letting a steel pendulum swing in a magnetic field. This can be accomplished either way by suspending a steel ball in a magnetic field or by suspending a magnetic ball above the steel surface. The magnetic field can be produced by the permanent magnet or by a current coil. The presented experiment allows you to qualitatively model the relationship between the period of the pendulum and effective acceleration by the means of creating additional magnetic forces.

The steel or permanent magnet ball is suspended on a dynamometer. Under the ball a permanent ceramic magnetic disc is placed. This magnetic field acts on the steel ball and stretches the string as shown in Fig. 1. The dynamometer’s reading shows the magnitude of the net force of the magnetic field and force of gravity. By changing the distance between the ball and the magnetic disk we can change the magnitude of magnetic force and as a result the net force acting on the ball. Dividing the magnitude of the net force by the mass of the ball we can find the effective acceleration.

In other words the steel ball is placed in the effective field, which is a superposition of the magnetic field and gravitational field of the Earth. When a simple pendulum oscillating in this effective field, the oscillation period will depend on the effective acceleration. When an additional magnetic force acts on the oscillated ball it increases ball’s acceleration because the restoring force is increased. By varying the magnetic force we can change the effective acceleration of the pendulum, therefore, the period of oscillation will change.

Equipment and costs required to construct apparatus:

Item	Source	Part number	Cost
Spring Scale	Sargent-Welch	WLS-3774-16A	$13.00
Ceramic Disk Magnet	Sargent-Welch	WLS-44377-05	$5.50 set/2
Steel Ball	Sargent-Welch	WLS-4481-D	$1.50
Total Cost			$20.00