# Determining Acceleration Due to Gravity Essay

3990 Words 16 Pages
Determining Acceleration Due to Gravity The Determination of the acceleration due to gravity at the surface of the earth, g, using a simple pendulum.

Aim: The determination of the acceleration due to gravity at the surface of the earth, g, using a simple pendulum

Background ==========

All bodies exert gravitational forces on one another. A large mass, such as the earth produces a gravitational field.

Gravity acts between any two objects, causing a force of attraction which tries to pull the two objects together. An example is if you release an object above the ground it
If the maximum displacement of the string from the vertical equilibrium is less than 15Ëš, the pendulum is found to execute simple harmonic oscillations along the arc of a circle as shown. Simple harmonic motion is defined as oscillation motion of an object about a fixed point.

The time (in seconds) the bob takes to pass once, back and forth over this arc, is called its period. (T)

The period (T) of a pendulum can be related to the acceleration due to gravity and the length of the pendulum (L) by:

T represents period (in seconds)

L is the length of the string from the fixed point to the middle of the bob (in meters)

g is acceleration due to gravity

This tells us that, assuming g is constant at a given place on the earth, the period depends on only the length of the pendulum. The period is also said to remain constant, even when the amplitude of the oscillation decrease (probably due to air resistance). This result was first obtained by Galileo, who noticed a swinging lantern and timed the oscillations by his pulse (clocks had not been invented). He found the period remained constant even though the swing gradually diminished in amplitude.

The equation I will use to determine the acceleration due to gravity at the earth's surface is:

This means that I will need to find the period

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