Terminal velocity

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Introduction

The terminal velocity of an object is the velocity at which any accelerating force is equal to any decelerating force. Usually this relates to an object falling in air or through a viscous liquid such as glycerol or oil.
The mathematics behind the falling object is covered by Stokes' law. The Wikipedia article Stokes'Law has the details, however it is in cgs units.


Liquid filled tube and ball bearings

Apparatus required: Glass tube, ball bearings, strong magnet, stopwatch, paper towels (for cleaning spills), screw guage micrometer, viscous liquid
In order to gain useful experimental values from dropping ball bearings, the size of the bearings should be small and the diameter of the tube should be at least TEN TIMES that of the largest bearing. These precautions ensure that a streamline flow is achieved. The length of tube is also important to get a good data set Ideally the tube should be at or around eye level of the students taking readings. The tube should be marked at 10cm intervals (using rubber bands is an easy method). The student should then take the time the various bearings pass the bands. This will give many values and allows for the results to show a terminal velocity has been reached. The relationship between radius or diameter and terminal velocity can be found and compared to the predicted values from Stoke’s law. A Strong magnet can be used to retrieve the ball bearings for multiple runs. The tube should be covered with cling film when not in use. Ball bearings should not be left in glycerol as they will rust.


Paper cups/ filter papers.

Aparatus required: Paper cake cases or coffee filters, stopwatch ruler. These are dropped from a height and their time to fall measured. A digital video camera set to sports mode can act as a timer for class display. A clear length datum is required in the field of view.
The mass is changed by nesting other cups/ papers so that the area presenting drag is kept constant. This is more GCSE than "A" level.


Bernoulli’s blower and ball

Apparatus required: Blower (linear air track blower, card tube and tape, held with boss clamp and stand to point vertical) and weighted Table tennis balls, rule.
Blower.JPG This is suggested as an alternative for more able classes. The relative motion idea may be hard to convince less able classes. But it is, as a demo, quite fun!
The hose is taken from a linear air track and a length of 10inch or so poster card tube inserted into the end. Table tennis balls are dropped into the flow and the height they rise in the air stream measured. The table tennis balls can have their masses changed by the addition of water via a hypodermic needle and syringe. This method allows several masses to be acurately set. The hole will need sealing with a dab of epoxy adhesive.
Height against mass can be plotted. Note there are many variables in this experiment(for example) the flow is not streamline.
It is suggested that a more powerful air blower, such as a leaf blower, be used with water filled squash balls. Larger Bernoulli blowers can be made and beach balls used.
A web search for sites such as:Blowers from around the world - will give some idea of the potential for entertainment here. There are a few suggestions on how to make a blower.
An anemometer can be a useful adition so as to calibrate force vs height.


Other ideas

Ostwald viscosimeter
CLEAPSS has a pipette viscosity meter in their PS67 for members.
Oil drops or air bubbles rising in water (note air will expand)

This apparatus could be used for open days especially if a good quality blower has been made. --D.B.Ferguson 20:53, 18 April 2007 (BST)

External links

Wikipedia entry for Stoke's Law

Back to Physics Theory


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