Assignment  – Pulling G's

Assigned: Friday, Sept. 11, 2009 
Due:  Monday, Sept.21, 2009
30 points

I want you to determine the maximum G's your insect can pull for two minutes, and survive. I will provide the experimental subjects, you provide the experimental apparatus. Basically, put the larva in something, spin it around very quickly, and then see if it survives. You can work in groups of up to four for ("four for" ? a very awkward construction) this assignment, and you need turn in only one report (but with the names of everyone involved please). As you will note at the bottom of this page, how you do and describe your experiment is more important than what you find. Similarly, how you explain what you find is also more important than what you find.

How to Convert Centripetal Force (Spinning) into a Measure of Gravitational (G) Force

Based on a brief review of my old Halliday and Resnick physics text (and a phone call to my engineer buddy Malcolm Eveans), the centripetal force for an object in uniform circular motion is given by:

(velocity)²/radius of circle

The velocity is 2*pi*radius/revolution, so for one revolution per second, this is:

2*pi*radius/sec = 4*pi²*radius² = 39.48 * radius²

Because the force is divided by the radius, the force can be simplified as:

39.48 * radius/sec²

To find out how many G's this is, just divide by the force of gravity (9.81 meters/sec² or 32.2 ft/sec² for those of you not with the metric system). So, spinning an insect around a one meter length of string for 1 sec per revolution would give:

(39.48 * 1)/9.81 = about 4 G's

Remember, if you have more than one revolution per second, the formula changes slightly, so the most general formula for the G calculation is:

(rev. per second * 2 pi)² * radius/gravitation =
((rev)² * 39.48 * radius)/gravitation

If you measure the radius in ft, divide by 32.3 ft/sec² (gravitational acceleration on earth for those mired in the English measurement system).
If you measure the radius in meters, divide by 9.81 m/sec² (gravitational acceleration on earth for those sufficiently enlightened to use the metric system).

Clear as mud, right?

You can use the calculator below to determine your G forces.  Alternatively, you can download an Excel spreadsheet of this here, or do it the old fashioned way, with the equations listed above.

Using a Car Tire as a Centrifuge

For those of you planning to tape insects to the side of a car tire (in an effort to produce higher G's), you will need to determine the revolutions per second of your tire. You can do this by (1) determining the distance traveled in one minute, (2) determining the circumference of the tire, (2) dividing distance traveled by tire circumference (make sure the units are the same), which gives the revolutions per minute, and (4) divide revolutions per minute by 60 to get revolutions per second. With this information and the radius (the distance from the hub of the tire to where you taped the insect), you can use the formula above to calculate G forces. For example:

1. At 60 mph, you go 1 mile in a minute (mph divided by 60 minutes per hour).
2. 1 mile is 5280 feet or 5280 feet * 12 inches per foot = 63,360 inches
3. I don't know what a real tire circumference is, but as a guess, if a tire has a 15 inch radius, the circumference is 2 * pi *r = 94.25 inches
4. For revolutions per minute, the distance traveled in one minute (63360 inches) divided by circumference (94.25 inches) = 672.3 (roughly) revolutions per minute
5. 672.3 revolutions per minute divided by 60 seconds per minute = 11.2 revolutions per second
6. If we tape the insect at 14 inches from the hub, the radius (in feet) is 14/12 or 1.17 ft
7. Finally, the G force (from the equation above) is ((rev)² * 39.48 * radius)/gravitation or ((rev)² * 39.48 * radius)/32.3  (because we are doing calculations in feet), 
   which in this example is ((11.2)² * 39.48 * 1.17)/32.3 = 179.4 Gs
8. Whew!

What I Want in Your Assignment

Write a brief paragraph on what you did (be specific), your final answer (including your calculations), and why you think your larvae could/couldn't handle the G forces. If you have trouble with the math, just give me a call. You can work in teams of up to four on this assignment (you only need to turn in one page for each team, but include all names). I'll award some prize to the team showing the greatest high G survival and/or the best explanation for what is going on.

Back to class assignments and examinations
	Home, home on the range