Optional Practical: Flying Pig
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)
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
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.