I am investigating the relationship between the fall time of a paper tray and its projected area.
In this investigation I have been using the following variables:
- Controlled Variable: The air density, the height from which we drop the tray, the shape of the tray, its mass and the material it is made from (paper).
- Independent Variable: The cross-sectional area of the paper tray.
- Dependent Variable: The time it takes for the tray to fall on the ground
I found the relationship for when the paper tray is traveling at terminal velocity. This relationship I devised by using the formula for the speed of a object traveling at terminal velocity:
Terminal velocity can be considered uniform motion (acceleration = 0) and so the above formula can be rewritten in the following way:
But all this excludes the acceleration period before a object reaches terminal velocity. I suppose that because the paper tray is only 0.016 kg and the paper tray has a fairly high drag coefficient 1.31 that the acceleration period can be ignored since the tray reaches terminal velocity quite soon, but then again the trays are being dropped from only 2 meters.
Can I ignore the acceleration period? Is there a better equation for the relationship? Can you suggest further reading?