"The Mechanics Of Hamsters In Freefall" - Discussion

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"The Mechanics Of Hamsters In Freefall" - Discussion

Postby paddyohale on Mon Jan 25, 2010 10:10 pm

Following the inadvertant hijacking of Safire's hamster thread, I've decided to start a new thread here for us all to discuss the mechanics of a frefalling hamster. This discussion will be open to all contributors, and while it may appear to be an amusing joke and fun, I will ask that all contributions be meaningful and ontopic. Comments such as "hamsters r cute!!! LOL!" don't really help in this discussion, so please don't leave them here! Even if you can't directly contribute to the problem solving because you can't see how we worked out a previous stage, you can always ask someone to explain how we worked it out (if it wasn't made clear in the original answering post).

Aim
What I would like to do in this discussion is to find out an expression for the freefall velocity v of a hamster at any time t. This discussion is open to all forum members as it will encompass a range of different Physics and Mathematical levels, from KS3 Physics/Maths (ages 11-14) up to degree level engineering. To assist those doing KS3/GCSE/A-Level Physics and Maths, I strongly suggest we limit answers to 3 sig fig where appropriate (it is recommended you use more in calculations then round the final answer, as this increases the accuracy of your answer).

Key Points
We will need to work out a few variables on the way to our final expression, ones that immediately spring to mind are:
  • Mass and weight of the average hamster
  • Volume and cross-sectional sirface area of the average hamster
  • Freefall acceleration of the hamster with simple air resistance (up to terminal velocity)
  • Freefall acceleration of the hamster through any fluid (with any density and viscosity, up to terminal velocity)
  • Freefall acceleration of the hamster including drag coefficient of the hamster (optional)
  • Velocity of the hamster as a function of time (derived from the above acceleration expressions)

More may be added as we progress, these were just the first few I thought of.

Data Required
Obviously, we're going to need some raw data in order to start this off.
  • Hamster data (mass, area, volume)
  • Gravitational acceleration constants
  • Fluid resistance constants (including viscosities)
  • Example drag coefficients (optional)

Physics Involved
To start people off, we will consider the basic Physics of a hamster in freefall. The hamster will fall due to its weight - the gravitational attraction it experiences due to the pull of the Earth's mass on its mass. Put simply, F=ma and W=mg (we shall simplify g to be -9.81m/s^2 for this discussion), so it falls with an acceleration of -9.81m/s^2 downwards. I shall define the vertical displacement to be positive when moving upwards, so anything moving downwards has a negative velocity and displacement. Therefore, g is negative, and is -9.81m/s^2.

Ignoring the effects of air resistance, its velocity will increase by -9.81m/s^s as long as it is in freefall. We can find the velocity as a function of time, and assuming the hamster started at rest the velocity will be:

v(t) = u + at (u = 0m/s; a = -9.81m/s^2)

v(t) = -9.81 * t

After 1s, v is -9.81m/s. After 2s, v is -19.62m/s (-19.6m/s to 3SF).



Feel free to continue this as you see fit, the topics we (as a group) can work on are listed above so I encourage all budding Physicists/Mathematicians/Engineers to have a go if they think they can. There are a few experienced Physicists and engineers amongst us forum regs (I myself teach Physics from ages 11-18), and I'm sure we will all be happy to occasionally cast an eye over this thread and sort out any major mistakes that crop up and answer questions that appear.

Finally, have fun! This is meant to be a light-hearted group problem solving exercise, that places important scientific concepts in a readily accessible way - who doesn't dream of pets in freefall? And remember, Physicists always like to prove theoretical results in an experiment, so I suggest Safire locks her hamster up rather sharpish! :twisted:

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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Arbor plena simia on Mon Jan 25, 2010 10:28 pm

Looks good. I'll have a proper look tomorrow and try and redeem post in the other thread.

Might I suggest we break the hamster into 2 parts. Well the 2 parts that will be subject to the air when falling; the fur and the flesh. Since both are going to have different properties, and knowing small furry animals they usually seem to have more hair than one might expect. Albeit I suppose this comes under "Freefall acceleration of the hamster including drag coefficient of the hamster (optional)".
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Safire on Tue Jan 26, 2010 11:11 am

lol ^^ I do love how you guys have taken such a keen interest in my freefalling hamster!
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Odgor on Tue Jan 26, 2010 12:17 pm

.

Last edited by Odgor on Wed Jul 08, 2015 5:05 pm, edited 1 time in total.

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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby MittinsKittens on Tue Jan 26, 2010 1:19 pm

I'm glad I got people thinking, Probably the best thing I've done for UKCS so far.
Also, I really hope you're not going to start buying hamsters by the boxload to start testing this all out...Although if your cruel enough to do so, we got a WHOLE topic for naming them, might as well use it since some-one didn't want it :D
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby quaduski on Tue Jan 26, 2010 6:29 pm

the answer is still 65.86 no matter how many threads you start. - and clara is a nice name
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Bobbobthebob on Wed Jan 27, 2010 12:04 am

How used to freefall do we assume this hamster is? Not only will we potentially need to model hamster tumbling and therefore multiple variables to denote the initial posture at the very least, but we may need to model hamster behaviour itself! It might be easier if we assume the hamster maintains a stable belly down posture? Then of course we have integumentary issues...
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby paddyohale on Wed Jan 27, 2010 12:22 am

Assume the hamster follows the most aerodynamic shape during freefall - the aspect with the smallest surface area, so probably face-down. Who knows, Safire might be training daredevil hamsters for a display team!

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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Pieclock on Wed Jan 27, 2010 12:37 am

Hamster Data ;

Weight:

* Adult Male 80 - 100 gm
* Adult Female 80 - 100 gm
* Newborn 2 gm
* Lenth 20-25cm


This will depend though on pre / apré meals, and wether there is food stored in its pouches at the time of weighing, Apparently a hamster can eat (15gm+) + drink (20ml+) a day, but it again depends how greedy the hamster is.

The mass is hard to measure as it really depends on the breed of hamster, and the thickness of fur, the above data is for a syrian hamster.

I guess you could use the following drugs to put it in a trance ;

Anesthesia Methods: ketamine, methoxyflurane, pentobarbital

or

Euthansia Methods: OD sodium pentobarbital, C02

but then again this could affect the mechanics of the freefal, as if it is in a state where it is seeing the walls as carrots then its neck could be facing upwards, or the legs could be in the air effecting the way it falls due to the weight balance of the hamster and the gravity.

A russian hamster however would be weighing more like 28-56.7g and a max of 10cm in length

A dwarf hamster however would be weighing between 20-25g and between 4 to 5cm in length

So to further the developments on this, can we have a set breed of hamsters that we would use as test subjects, or are you wishing to compare the data between them?

I have a trampoline i could probably drop the hamsters onto, and use light gates to measure them if i can get hold of some to determine the acceleration and speed that they fall.


Another point i was thinking of, if we are using gravity as a set value, then that would be saying the whole experiment is in a vacuum, i know hamsters are cheap and all, but using them in a vacuum means that you will only get 1 result per hamster as there will be no oxygen, thus making a mean value from 5 tests null.

Last edited by Pieclock on Wed Jan 27, 2010 1:01 am, edited 1 time in total.

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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Templar+ on Wed Jan 27, 2010 12:47 am

bunch of sick b******.
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Pieclock on Wed Jan 27, 2010 12:58 am

Templar+ wrote:bunch of sick b******.

Not really sick,

Think about how many theories / mathematical equations have been tested out before on animals ;

guinea pigs
dogs
rats
mice
monkeys

it feels a bit rude to leave out the hamster, and they are cheap enough to go to the shop and buy a bundle of, guinea pigs are kindof expensive now a days, and hamsters are easiest to clean out / feed, plus big enough to hold / find if they run away as training them takes a bit of time, and mice are just too small.


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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Kruzin on Wed Jan 27, 2010 10:40 am

Hamsters are hardly the most 'ergonomic' of the small rodents. Have you considered a vole?


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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Arbor plena simia on Wed Jan 27, 2010 11:43 am

paddyohale wrote:Assume the hamster follows the most aerodynamic shape during freefall - the aspect with the smallest surface area, so probably face-down.
Wouldn't the most aerodynamic and also natural falling position of a hamster be bottom first, creating a sort of tear shape?
For this we need to know the mass distribution within the hamster, since the heaviest part will be the bit pointing down.

Templar+ wrote:bunch of sick b******
This is all purely hypothetical of course, I doubt anyone would actually put this into practice. But even so, the point of this ultimately stemmed from the fact that no matter the height, a hamster will survive a fall.
Which brings me onto another point; my original argument in the old thread was that cats can survive a fall from over 7 sorties as they have a non fatal terminal velocity and have time to twist into a safe landing position. Do we therefore want the hamster to have a safe landing position, if so we need to know how long it takes for a hamster to be falling from mass first to paws first. Again, this will depend upon the viscosity of the fluid through which it is descending, but I assume this is going to be air else we really are sick :roll:.
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Pieclock on Wed Jan 27, 2010 11:49 am

When a hamster falls it sort of goes into a flying squirrel type shape, where the legs go outwards to slow the velocity, coming in just before landing (not sure how it manages it as the hamster doesnt look down when it is falling)

Although looking for article on this ;

"Occasionally a hamster may break a limb or its tail from a fall, even whilst in its cage. Often the accident that resulted in the broken limb occurs in the evening or night and is not witnessed but the following morning the hamster may be limping or have a bent tail."

So im guessing they can hurt themselves, probably if they fall funny though


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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby meyenburg on Wed Jan 27, 2010 1:27 pm

This thread is like, totally pointless.
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Frying Dutchman on Wed Jan 27, 2010 5:29 pm

This is why UKCS is UKCS.

but no discussion about lemmings?
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Mr Tortoise on Wed Jan 27, 2010 6:57 pm

I think the orientation of the hamster clearly deserves more though.


Hamsters are clarly cunning ceratures that have a sense of self preservation and a sense of humor (as clearly seen in the many high speed wheel videos).

You cannot treat a hamster like a lemming (who clearly seeks as great a terminal velocity as poissible due to its disatisfaction with its home and family. Hell if any creature is emo the existential angst of the lemming has to qualify it). A hamster is likley to try and increase its surface area in order to prolong the experience and more importantly give it more time to chew on whatever it is eating.

You also have to take into account that it will behave somewhat like a parachute ... due to its flabby body mass but also its cheek puches ... which leads to another reason why it cant free fall wit the least surface area ... lets be blunt itd turn into a tube.

Unfortauntley the parachute wind break will at some point become hard to maintain due to its velocity increasing causing the air flow to become chaotic - the question then becomes is the drag fromthe chaotic fluid dynamics greater than the drag from its innate tendancy to becom a parachute?


Personally i think i may have to do some experiements over the weekend to investigate the effects of various lengths of hamster hair aginst the bmi of the hanster


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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Arbor plena simia on Wed Jan 27, 2010 8:06 pm

Mr Tortoise wrote:lemmings
Frying Dutchman wrote:lemmings
Lemmings don't commit suicide. It was merely a misinterpretation by some naturalist who saw Norwegian lemmings migrating. In order to migrate they had to cross a river, which considering their size seemed like suicide. This popular belief in mass lemming suicide was then cemented with the release of the Lemmings game.
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Frying Dutchman on Wed Jan 27, 2010 8:10 pm

Lemmings still fall of heights, so why no discussion about lemmings? :3
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Re: "The Mechanics Of Hamsters In Freefall" - Discussion

Postby Bobbobthebob on Thu Jan 28, 2010 1:08 am

Arbor plena simia wrote:Wouldn't the most aerodynamic and also natural falling position of a hamster be bottom first, creating a sort of tear shape?
For this we need to know the mass distribution within the hamster, since the heaviest part will be the bit pointing down.

Not necessarily. Depending on the shape of the hamster's posterior, unless it's symmetrical we would expect a certain amount of lateral force acting upon the hamster pushing him off a vertical tear drop shape. Which also leads us to ask whether or not we're calculating the absolute speed or simply in the z direction, as an angled posterior would generate some lateral movement. This also all assumes that the hamster will be rigidly maintaining a shape that has a stable freefall position to settle into. If he remains limp, not only might the hamster be an inhernetly unstable aerodynamic object but, at certain velocities, we can expect his limbs to enter harmonic frequencies, increasing the amplitude of limb flappage and thus the overall drag too. As a hamster's limbs have more than one joint we can expect multiple modes of vibration to plan for.

On a separate note, any thoughts on modelling the change in atmospheric pressure with altitude? He may well reach incredible speeds if we release him 20 miles above the earth's surface. In which case we need to find the hamster coefficient of thermal expansion as during re-entry we can expect an increase in heat which will in turn increase his surface area and drag. I suggest careful measurements while subjecting hamsters to blowtorches. All in the name of science. Of course. :P
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