A Little Nerd Math

A couple of weeks ago, I read a post over at Padded Cell Confessions. I've been reading Maggie's posts for a while and she's always quite entertaining. It seems that she and her husband had been having a discussion on how many guinea pigs it would take to haul a person in a cart. 

Well...I'm one of those oddballs that thinks about strange things when I really should be sleeping. So...of course I was contemplating Maggie's guinea pig situation. I decided that I needed to solve the problem using math and physics. 

Now...keep in mind that it's been double digit years since I've taken either physics or math...so bear with me. I had originally posted the following comment on Maggie's post:

"I am in agreement with the more than 100 comment. I think they're pretty wimpy. Most of the ones I've seen don't do much more than lay around and stare at things."

Well...it turns out that guinea pigs are a lot stronger and faster than I gave them credit for.  However, they also apparently have really crummy back structure. One website suggested that you can train your guinea pig, but that you shouldn't train it to "play dead" as the shift in weight can cause damage to the spine. So...the mathematical answer is probably just a bunch of hooey, as there are really a lot of other factors at play. As my brother stated, they would probably run in different directions. You'd have to hook them up reindeer style.

But...let's take a look at my math and go from there...

For the sake of this argument, the guinea pigs will be pulling three different shopping carts, on concrete. The first cart will contain a 70 lb. child, the second a 130 lb. woman, and the third a 185lb. man. An average shopping cart weighs 40 lb.

So...the basic physics formula at work here is: force = mass * acceleration. If you figure out how much force each guinea pig can generate as well as how much force would be needed to move the cart, then you should be able to figure out how many guinea pigs you need.

The average male guinea pig weighs 3 pounds, females weigh an average of 2 pounds. So I figured on a mix and put the average weight at 2.5 pounds. Of course, everything needs to be completed in metric, so this is equivalent to 1.14 kilograms. Tada! Mass solved.

The tricky part is the acceleration. And this, honestly, is where I may have gone wrong. If we have any guinea pig experts out there who know the average acceleration rate of a guinea pig, I'd be happy to redo the math...but this is how I figured out my estimated acceleration:

According to the interwebs, the average domesticated guinea pig can run at a rate of 19.5 mph for long distances. However, apparently they have clocked "wild" guinea pigs at a rate of 41.16 mph (for up to 8-15 sec). I took these two numbers to guesstimate that a guinea pig could reach a speed of 30 mph in 15 seconds. This gives an acceleration rate (using change in velocity over change in time) of 2 mph/sec. Convert this to metric again, and you get 0.894 meters/second/second (no...i don't know how to get superscript on here...let it go).

Using this rate of acceleration and the mass calculated earlier, this means that every guinea pig should be able to generate a force of 1.019 Newtons.

Now...obviously, pulling a shopping cart with smooth wheels on a smooth surface will be easier than pulling say a wooden wheeled cart on sand. So...we need to use a coefficient to accommodate for the different friction present in the situation. Since we're dealing with wheels, we're using a rolling resistance coefficient for hard rubber wheels on concrete...a value of 0.01.

Using this coefficient, as well as the force of gravity holding each object to the ground, I calculated the force required to move these objects from rest. Based on that answer, I then divided by the force calculated for a guinea pig. Obviously, partial guinea pigs will not be helpful here (unless we're dealing with zombie guinea pigs), so I rounded up from the devised answer.

So...according to this math, it will take 5 guinea pigs to pull a child, 8 guinea pigs to pull a woman, and 10 guinea pigs to pull the adult male.

Honestly, I'm still not sure I agree with this. But...the other answer I came up with doing it a different way required over 1500 guinea pigs...which seemed rather excessive. So, I'm waiting on that guinea pig expert. Does anyone know how fast a guinea pig can accelerate or much weight a single guinea pig can pull? I don't feel like performing this experiment in real life. (Though I'm sure there is probably some fraternity somewhere that has tried it.)