Determination of G by Bar Pendulum

                                          Bangabandhu Sheikh Mujibur Rahman Maritime University [pic 1]

LAB  REPORT

Course  no. : OCN 1108                Group no.: 09

Experiment  number: 05

Experiment name: To determine the value of g, acceleration due to gravity, by means of a compound pendulum

Submitted by:

Name: Mohd. Mahdiuzzaman

Roll no: 16311025

Registration No: 2301121600025

Semester 1

Department of Oceanography

Abstract

There are many way of measuring this gravity acceleration, but the experiment of compound pendulum is the easiest and effective among them. This involved timing small oscillations of a compound pendulum, and taking moments of inertia about the axis of rotation of the pendulum. In the experiment the acceleration due to gravity was measured using the rigid pendulum method.  From this experiment the acceleration due to gravity (g) is obtained and it is 986.96cm/s2 with 0.608% error which is slightly higher from the accurate gravity acceleration 981cm/ s2 that the error is negotiable.

Introduction

Of all the forces that act on us each day, gravity is the one force that we are all aware of. Newton was the first to underline the principles of gravity; each particle with a mass attracts all other particles with mass, with a gravitational force that is directly proportional to the product of their masses and inversely proportional to their distance of separation squared. This leads to show that on Earth a mass will have an acceleration due to the gravitational force of the earth, g, because from Newton’s second law force is proportional to acceleration [1]. This value g is of course dependant on the distance to the centre of the Earth and there therefore will be minor differences in its precise value in different areas of the world.

Due to these fluctuations in the Earth’s gravity, the local value for g is very useful for various reasons: from predicting the underlying geology of the rocks in the Earth’s crust [2], to the oscillations of a pendulum. There have been a number of different methods used previously to calculate the value for gravity, some of which are as follows. We can measure gravity by timing how long it takes for a body to drop a certain distance, as the distance a body falls is proportional to the time it takes squared, and the constant of proportionality is the gravitational acceleration [3]. Unfortunately it is difficult to precisely measure the exact distance the body has travelled and the time it takes to give g to a precise enough value. Another method widely used in “gravimeters” is suspending a mass on a spring and measuring the amount that the spring is stretched by, due to the force of gravity, and knowing the value for the spring constant [4].