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IBDP PHYSICS Internal Assessment

Student: Pascal BLAISE – Date: 10 December 2009

Supervisor: Mr. FOUCAULT – International School of Pisa

“To what extent does the length of the string affect

the period of a simple pendulum?”

IBDP PHYSICS Internal Assessment – The Simple Pendulum

9

INTRODUCTION

The original aim for this invesigation was to “investigate the simple pendulum”. There are many variables one could look into, such as displacement, angle, damping, mass of the bob etc. The most interesting variable, however, is the length of the swinging pendulum. The relationship between the length and the time for one swing (the period) has been researched for many centuries, and has allowed famous physicists like Isaac Newton and Galileo Galilei to obtain an accurate value for the gravitational acceleration ‘g’. In this report, we will replicate their experiment, and we will try to find an accurate value for ‘g’ here in Pisa. We will then compare this value with the commonly accepted value of 9.806 m/s2 [NIST, 2009]

A CLOSER LOOK AT OUR VARIABLES

In this investigation, we varied the length of the pendulum (our independent variable) to observe a change in the period (our dependent variable). In order to reduce possible random errors in the time measurements, we repeated the measurement of the period three times for each of the ten lengths. We also measured the time for ten successive swings to further reduce the errors. The length of our original pendulum was set at 100 cm and for each of the following measurements, we reduced the length by 10 cm.

THEORY

A simple pendulum performs simple harmonic motion, i.e. its periodic motion is defined by an acceleration that is proportional to its displacement and directed towards the centre of motion. It can be shown that the period T of the swinging pendulum is proportional to the square root of the length l of the pendulum:

T = 4π 2

l

g

(Hyperphysics, 2009),

[1]

with T the period in seconds, l the length in metres and g the gravitational acceleration in m/s2. Our raw

€

data should give us a square-root relationship between the period and the length. Furthermore, to find an accurate value for ‘g’, we will also graph T2 versus the length of the pendulum. This way, we will be able to obtain a straight-line graph, with a gradient equal to 4π2g–1.

EQUIPMENT AND METHOD

For this investigation, we had access to limited resources; clamps, stands, a metre ruler, a stopwatch, a metal ball (a.k.a. bob), and some string. The experimental set-up was equal to the diagram, shown in figure 1 (Practical Physics, 2009).

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As stated earlier in the introduction, it was decided to measure the time for ten complete swings, in order to reduce the random errors.

Clamp

These measurements would be repeated two more times, and in total ten successive lengths were used, starting from one metre, and decreasing by 10 cm for each following measurement.

String

A metre ruler was used to determine the length of the string. One added difficulty in determining the length of the pendulum was the relative big uncertainty in finding the exact length, since the metal bob

Tripod Stand

added less than a centimeter to our string length, measured from the bob’s centre. This resulted in an uncertainty in length that was higher than one would normally expect.

Clamp

The table clamp was used to secure the position of the tripod stand, Metal bob

while the pendulum was swinging.

After the required measurements, one experiment was carried out to find the

Figure 1: Diagram of the

set-up for this experiment

degree of damping in our set-up. Damping always occurs when there is...