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The Relationship between the Acceleration of an Object and the Angle Produced using an Improvised Mechanical Accelerometer

J.C. Elmaguin*, J. Laurente, B.D. San Diego
Department of Physical Sciences, College of Science,
Polytechnic University of the Philippines Sta. Mesa, Manila 1016 *elmaguin55@gmail.com

Abstract. Accelerometer is a device which is used to measure the acceleration of an object. Its simplest form is the pendulum mechanical accelerometer. This study used an improvised mechanical accelerometer to determine the relationship of the acceleration of the object to the angle produced by the pendulum. Data and observation shows that the acceleration of the object is directly proportional to the angle produced by the pendulum accelerometer.

Keywords: Pendulum, Acceleration, Accelerometer.

Introduction
Accelerometer is a device which measures the acceleration of an object. There are two kinds of accelerometer, the electronic accelerometer and the mechanical accelerometer. The simplest form of mechanical accelerometer is a pendulum, a bob is supported by a light rod or string from a solid support attached to the accelerating vehicle supposed moving forward. The angular displacement of the rod or string form vertical is the measure of the acceleration [1].

Figure1.Mechanical Accelerometer [2]

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

a= Fm (1)

As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased [2].

Rearranging the variables form equation (1), gives the net force is equal to the mass of the object times the acceleration.
F=ma (2)

where: F = net force
m = mass of the body at motion
a = acceleration of the body

Figure 2. Free-body diagram of (a) pendulum and (b) wood and (c) weights.[2]

The free-body diagrams for the pendulum, wood and weights are given in figures 2. All three objects have same magnitude of acceleration. In each case take the direction of a to be the positive coordinate direction. Equation (2) applied to the ball gives Tcosθ=mg. F=ma applied to the ball gives Tsinθ=ma. Combining these two equations to eliminate T gives:

tanθ=ag (3)

Where: a is the acceleration
g is the acceleration due to gravity

This study considers only the use of a mechanical accelerometer which involved the use of a pendulum, furthermore, this study is ought to determine the relationship of the acceleration of an object to the angle produced by the pendulum.

Methodology
Materials used on the experiment of the study were two slab of wood, set of weights, pulley, strings, and an improvised mechanical accelerometer. The mass of the two slabs was measured, and then the improvised accelerometer was attached on the slab. The slab was then attached to a string, and the string was hang on a pulley, and was then attached to the weights.

Shadow displacement method was used to measure the angle produced by the slab. It was performed by flashing a light on the top of the accelerometer, thus the bob of the accelerometer casted a shadow, the initial point of the shadow when the pendulum was on its equilibrium state was recorded, then took note the displacement of the shadow after it was accelerated, to obtain the angle of displacement. In determining the static friction of the system, a weight was attached on the string which passed over a pulley and was then attached on the slab of wood. A weight was...
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