Weekly 4: Communicating Mathematics

Three.....Two....ONE....

These were the last three words our elephant heard before he took the fall to the first floor.  He put all of his trust in the hands of four mathematicians.  Now, judging from our performance, who knows if he would trust us again.  

From looking at Galileo's Thought Experiment, Galileo wanted to explore what is now gravitational pull on an object.  He wanted to know what exactly what would happen if two objects with different weight were dropped at the same height, which would reach the ground first.  Picturing this in his head, he could only do so much.  Today, we know that the gravitational pull is equal on both of these objects, so they will hit at the same time.  However, this was not the information available at the time.  The only way to support or disprove this prediction was to gather data.  This was our task as a class.  We wanted to put ourselves into the mindset of Galileo.  After selecting from an array of action figures, we were told to predict how many rubber bands would be needed to keep our elephant off the ground.  As a group, we needed to take into consideration that the weight of the object.  How would that affect the rubber bands?  Would it?  There were many ideas that were bounced around:

• What is the stretch capacity of a single rubber band?
• How much will be taken up by knotting the rubber bands together?
• Will each rubber band stretch to their fullest?
• Which ones would bear the most weight from the elephant?
• Are we trying to just keep off the ground or are we trying to be the closest?
• How accurate can our measurements be from one rubber band to two bands to ten?

These were questions that we had to find answers to.  To start, we measured one rubber band resting and then two, and three.  Then, we measured how the distance increased in rubber band stretch when the elephant was dropped.  

This is the distance the ten rubber bands stretched
when the elephant was hung.  This is not the maximum
distance the rubber bands can stretch because this
does not indicate peak distance.

We took the distance and created a ratio with the number of rubber bands used.  As the number of rubber bands increased, the decimals got bigger and bigger.  In order for us to make our prediction, we wanted to be on the safe side.  We took the smallest decimal and used that number to find out how many rubber bands we needed to go just shy of the 505cm to the ground.  When we found those calculations, we found that we would need 16.69 rubber bands.  Again, playing it safe, we put 16 rubber bands on the bungee.  We thought that our prediction was relatively reserved, but we had no idea to what degree.  After the first drop, we were under a meter from the ground.  Those were not the results we wanted to see, so we did a few more calculations.  Our second try used more of a trial and error method.  We knew that adding two more bands would give the elephant a significant further drop.    By adding two, the elephant was close.  Close was not good enough for us so we added another.  This drop proved to be too much.  Our friend went smashing trunk first into the ground.  We did not have to be bungee experts to know that we had gone too far.  Thankfully, death was not the result, but it did give us enough information to calculate the difference.  

Looking at our results, there were a few things that I noticed:

• Weight did affect the result of the drop.  Our elephant was one of the heaviest objects that could have been used and we had the least amount of rubber bands.  Barbie dolls had around 25 and we started out with 16.
• It is hard to predict how much each rubber band is going to stretch and which ones stretch the most.  I think that this hindered our calculations.  
• Guess and check is probably the most successful way to find results.  Once we went from 16 to 18 and then to 19, we could see which was best.  Thankfully, there are not real bungee jumpers involved because the calculations need to be as accurate as they can be. 
• Repeated trials is important too.  There are a lot of factors that should not be overlooked.  The way the object is dropped can change and the way the rubber bands fall could affect the results.