Optional Practical: Flying Pig

Introduction

In this practical the acceleration due to gravity will be found by measuring the time period of a pig flying in a circle. Note: this experiment can also be done with flying cows, dinosaurs and even planes. (With acknowledgement to Mark Headlee UWC USA)

Theory

The pig flies in a circle because there is a force acting perpendicular to its velocity (towards the centre of the circle). This force can be identified by drawing a free body diagram.

There is no vertical acceleration so Newton’s 1st implies that the vertical component of forces are balanced so

FTcosθ = mg

The pig is moving in a circle because there is an unbalanced force towards the centre, this force is provided by the horizontal component of tension

FTsinθ = mω2r

Dividing these equations gives:

FTsinθ/FTcosθ = ω2r/g = tanθ

But tanθ= r/h

So r/h = ω2r/g

And ω = 2π/T where T = time period

So 1/h = 4π2/gT2

h = gT2/4π2

Method

Devise a method to measure the time period and height h for at least 5 different lengths of string. Enter your values into a table not forgetting to estimate the uncertainties in both measurements.

From the equation it can be seen that T2 is proportional to h. Process your data so that you can plot a graph of T2 against h and use the gradient of the line to find a value for g.

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