Transcript Capturing the Elusive Parabola

The Humble Rubber Band
is your Friend
It will help you:
to warm yourself when you are cold.
to cool yourself when you are hot.
to ward off dangerous attackers.
to protect yourself from lethal ozone levels.
to insulate yourself from increasing gasoline prices.
to hold things together.
How does it do all of these wonderful things?
The Hysteresis Loop
Properties of the Rubber Band
 It takes more energy to stretch than you get back
when you let go.
 The energy inside the hysteresis loop is converted
to heat.
 Both the top curve and the bottom curve can be
accurately modelled using a cubic function.
 Rubber is made up of long chains of molecules.
 When the rubber band is at rest, the molecules are
tangled, and entropy is high.
 When the rubber band is stretched, the molecules
straighten somewhat, and entropy is decreased.
When the rubber band is released, the molecules
tangle again, and entropy is increased.
 When entropy is lowered, the band gives out heat.
When entropy is increased, the rubber band takes in
heat.
The Negative Coefficient of Expansion
 If you heat the rubber band, it will contract.
 If you cool the rubber band, it will expand.
 You can demonstrate these effects using a
rubber band, a weight, and a heat gun.
From Theory to Practice
 If your lip is cold, stretch the rubber band, and
apply it to your lip.
 If your lip is hot, stretch the rubber band, wave it
around in the air, let it contract, and apply it to your
lip.
Warding Off Attackers
You can use your fingers and the rubber band to make a “gun” to shoot
dangerous attackers. However, you may find that the band does not travel
very far due to air resistance.
 To stabilize the flight of the band, you must impart a “spin” to it when
firing.
 Hold your hands such that the tops face each other, and your index
fingers point down. Suspend the band between your index fingers.
 Twist your hands around such that your index fingers point up. In doing
so, you will twist the band such that one side is under more tension than
the other.
 When you fire the band, it will spin, similar to a frisbee with a hollow
centre.
 This will add stability to the flight, decreasing air resistance, and greatly
increasing the range and accuracy.
 Fun Fact: if you could get rid of air resistance entirely, you could shoot
the band over a kilometer.
Lethal Levels of Ozone
 Ozone will quickly oxidize a
rubber band.
 Oxidation makes the band brittle,
and it breaks under tension.
 Suspend a weight or bucket of
water from the ceiling using a
rubber band.
If high levels of ozone should
occur, the band will break, alerting
you to the danger.
Beat the High Cost of Gasoline
 Combine the energy you can
store in a rubber band with
Newton’s Third Law of Motion.
 Construct the apparatus shown,
and attach it to the top of your car.
 When you wish to travel, cut the
string.
World’s Largest Rubber Band Ball
 Built by John Bain of
Wilmington, Delaware.
 Contains 850,000 rubber
bands.
 Height: 1.5 m.
 Mass: 1418 kg.
The End