Roller Coaster Design Training: The Snake

You have been commissioned to be a roller coaster designer and as part of your training you will look at some roller coasters that do not work and your task is to figure out why they do not work and design a solution to the coaster's problem, using what you have learned about physics.

Warm Up: Potential and Kinetic Energy

Practice telling the difference between potential energy and kinetic energy. You can have your students come up with examples, or you can write some down on slips of paper and have them sort them into the correct categories. Have them include this in their notebooks along with their own definitions of potential and kinetic energy.

Demonstration 1: Potential and Kinetic Energy Toy

James made this little spool toy that demonstrates potential vs. kinetic energy.

To make this toy, you will need: 

a thread spool

a small rubber band

a toothpick

a dowel or the like

tape

a washer

Feed a rubber-band through the center of a wooden spool. Stick a toothpick through the loop the rubber-band makes at the end of the spool. 

Tape down the loop of the rubber-band that sticks out of the end of the spool. 

 Break off the ends of the toothpick so that the spool can roll freely.

On the other end of the spool, place the loop through a washer.

 Put a dowel on top of the washer, feeding it through the rubber-band loop. 

 Now turn the pencil around and around, tightening the rubber-band. 

When the rubber-band is very tight, put your device on the floor and let go. 

Or, you can hold the spool and watch the dowel act as a helicopter blade.

When did the potential energy enter the toy? When did the potential energy transfer into kinetic energy?

Demonstration 2: The Balls

You will need a hard floor that is clear of anything that could be broken by a bouncing ball.

Drop a basketball and then a tennis ball on the floor, noticing how high they bounce.

Now, holding the basketball in front of you, take the tennis ball and put it on top of the basketball so they are touching. Now drop the balls together on the floor, making sure that the tennis ball is still touching the basketball when the basketball hits the floor. If you were able to do this properly, the basketball should not have bounced as high as it did when you let go of the ball by itself. This was because most of the basketball's energy was transferred to the tennis ball. This shows the principle that things with more mass have more energy, at a given speed. This is why the tennis ball had so much more energy than when it was dropped by itself.

At what point is potential energy illustrated in this demonstration? At what point is kinetic energy illustrated?

Demonstration 3: The Energy Can

Before you begin problem solving, let's review some scientific facts that might help you. You will need:

an empty coffee can (1-lb. and 5'' diameter w/plastic lid)

Fishing sinker (1 oz.)

Hammer

1-2 Long Rubber-bands (6'')

2 paper-clips

nail

With a hammer and nail, punch one hole through the bottom of the can and one in the center of the plastic lid. 

Thread the paper-clip onto one end of the rubber-band. Then thread the other end of the rubber-band through the hole in the bottom of your can. The clip should be on the outside of the can.

Slide the sinker onto the middle of the rubber-band.

Thread the free end of the rubber-band through the hole in the lid.

Attach the paper-clip to the rubber-band on the plastic lid so the band won't slip into the can.

Place the plastic lid tightly onto the end of the can.
Now you can explore potential and kinetic energy with this toy. Keep in mind the mathematical formula:

Potential Energy + Kinetic Energy = Total Energy

Can you predict where the potential energy is going to be the highest? Where is the kinetic energy going to be the highest?

Once you have made your predictions, push the Energy Can slowly across a smooth floor, and watch it travel until it stops by itself. Now, push it rapidly across the floor and watch it until it stops.

What did the Energy Can do when pushed slowly?

What did the Energy Can do when pushed rapidly?

How is the behavior of the Energy Can different from an ordinary can?

What conclusions can you make? 

Why do you think the Energy Can acts differently from an ordinary can? 

Where was potential energy the highest? Why?

Where was the kinetic energy the highest? Why?

Where is the potential energy the highest on a roller coaster?

Where is the kinetic energy the highest on a roller coaster?

As the Energy Can travels, some of its kinetic energy is changed to thermal (heat) energy in the form of friction. The thermal energy is waster kinetic energy. It does not help the Energy Can move so the can slows down. The potential energy was highest at the point where the Energy Can stopped moving away from you after the first push because that is where the most energy was stored inside it. Later trips lose more and more kinetic energy to friction, so it cannot build up as much potential energy. 

The same thing happens with a roller coaster. As the coaster train is towed by electrical energy to the top of the first hill, the train gathers potential energy. The top of the first hill is where the train has the most potential energy. As the train travels to the bottom of the first hill, this potential energy is converted to kinetic energy. The bottom of the first hill is where the kinetic energy is the highest. The total potential and kinetic energy can never be more that what the electrical energy gave the train. In addition, friction converts some of the kinetic energy into thermal energy instead of movement, wasting some of the kinetic energy. 

The Law of Conservation of Energy states that energy cannot be created or destroyed, only changed in form. How does this apply to the Energy Can or roller coasters? As we learned in Newton's First Law of Motion, the roller coaster cars will continue to move until another force, in this case friction (wheels on the track and the coaster's brakes), acts upon them.

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Fixing the Snake

The first roller coaster you are to work with is called the Snake because of all its hills and valleys look like a snake. The first hill is 160 feet tall, giving a thrilling first drop. Riders hurtle through the first tunnel at 61 mph. The designed decided to make the second hill even taller because coaster enthusiasts really love a terrific second drop. It is 200 feet high. The problem is that the cars won't go over the second hill. They make it part way and slide back and forth, finally stopping in the tunnel between the first and second hills. Can you discover anything that will help get this coaster up and running again? Write your solution in your notebook. Include in your explanation the facts you have learned (or reviewed) in this lesson.