# Determining the acceleration due to gravity by using simple pendulum.

## INTRODUCTION

My investigation is on determining the acceleration due to gravity by using simple pendulum. Also the G apparatus (freely falling mass) can be used to determine the acceleration due to gravity.

What is acceleration due to gravity?  It is the force or pull of the gravity of the earth according to Newton’s first law a=F/m

Objects accelerate because spacetime moves past them. The surface of the earth accelerates upwards at the rate of about 10 m/s<sup>2</sup> with respect to spacetime.

We have been told that the acceleration due to gravity of earth is 9.81 m/s² or g= 9.81 m/s², however, due to myriad of factors, g in one place differs slightly to other, as u increase the altitude the g decreases.

## PLAN

My plan for this investigation is to perform various experiment the determine acceleration due to gravity such as the pendulum, free falling object which is the g apparatus and also by

## AIM

The aim of this investigation is to measure the earth’s gravitational field strength, which is also the acceleration due to gravity. This involves mass, which is the amount of matter an object contains and weight, which is the force of gravity pulling down on an object with a mass. Mass is measured in Kg (kilograms) and weight is measured in Newton’s. Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large-scale structure of galaxies, stars. Etc. the earth’s gravitational strength is calculated by weight (N) / mass (Kg) as stated above a =F/m therefore the earths gravitational field strength (g) is measured in N/Kg but for the pendulum, the periodic time and the length of the string is to be found to find the acceleration due to gravity which is given by

Where g= acceleration due to gravity

L= length of pendulum string

T= periodic time

## And for the free falling object experiment the formula to determine g is by

S = ut + ½ at^2  Initial velocity is zero so, S = 0 + ½ gt^2
Therefore g = 2S / t^2.

EXPERIMENT 1
BACKGROUND INFO.

A simple pendulum is defined to have a small mass, or bob, which is suspended from a light wire or string.

The displacement of the bob is the arc length, s through which it swings. According to Hooke’s law, the simple pendulum would be a simple harmonic oscillator if the net force, restoring force, is proportional to the displacement.  From a vector analysis of the force vector involved we see that the restoring force, F = -mg sinθ. This says that the force is proportional to the sinθ and not just θ.

So it is not a simple harmonic oscillator.  However, if we confine ourselves to small angles, mathematically we will find that the sinθ ~ θ. Small angles of less than 20 degrees are usually acceptable.  This is called a small angle approximation.  If we keep to small angles we find the period of the pendulum to be:

T = 2p (L/G).5

Where L is the length of the string or wire to the centre of mass of the bob and g is the acceleration due to gravity.

. Simple harmonic motion states that the restoring force is proportional to the displacement. In more simple terms this means the further the bob from the rest position, the more it wanving forces theory.

## A SIMPLE PENDULUM

AIM

The aim for this experiment is to determine the acceleration due to gravity using a pendulum bob.

Variables

Length

The length of the pendulum has a large effect on the time for a complete swing. As the pendulum gets longer the time increases.

size of swing

Surprisingly, the size of the swing does not have much effect on the time per swing.

Mass

The mass of the pendulum also does not affect the time.

air resistance

With a small pendulum bob there is very little air resistance. This can easily be seen because it takes a long time for the pendulum to stop swinging, so only a small amount of energy is lost on each swing. A large and light pendulum bob would be affected by a significant amount of air resistance. This might change the way the pendulum moves.

Gravity

The pendulum is moved by the force of gravity pulling on it. On the Moon, where the pull of gravity is less, I would expect the time for each swing to be longer.

## EQUIPMENT

The equipments needed for the pendulum are:

1. A pendulum bob
2. A string (more than 100 metres)
3. Retort stand
4. A stopwatch
5. And a clamp for the retort stand with cotton to make sure that the pendulum swings from a single fixed point.

## PROCEDURE

The procedure for the simple pendulum to find the

1. Construct a pendulum at least one metre long, attached at its top a support (such as a clamp connected to a retort stand) and with a small mass tied to its lower end to act as a the pendulum bob.
2. Measure the length (L) of the pendulum, from its point of attachment to the centre of the pendulum bob.
3. Pull the pendulum aside and release tit so that it starts swinging, using a stopwatch, begin timing at an extreme of the pendulums motion and time twenty full swings (one swing = back and forth movement of the pendulum bob) of pendulum. Divide this time by 20 to get a value for the average periodic time (T) of the motion. By using these averaging techniques it minimizes random errors.

The period of pendulum depends upon length (L) and the value of acceleration due to gravity (g), s described in the following equation

Rearranging this equation gives an expression that can determine g,

1. Substitute your values for L and T into this equation to get g, which is the acceleration due to gravity.

• The value of acceleration due to gravity at the ...