The Kingda Ka: A New Kind of Roller Coaster

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Objective

Students determine the maximum height a roller coaster achieves based upon the starting kinetic energy.

Big Idea

In a closed system energy is always conserved, although it can change from one form to another.

Context

In previous lessons (Skate Park Energy and Skate Park Energy Revisited), students applied conservation of energy to a traditional roller coaster where the coaster is slowly pulled to the top of a large hill and all of the starting energy is gravitational potential. In this lesson, students again apply conservation of energy to a roller coaster, but this time it is the Kingda Ka, which launches the coaster down a horizontal track. The students determine the starting velocity required to get the roller coaster over the huge vertical hill. I play a few Youtube videos that show the roller coaster in action. One of the videos shows a "roll back" where the coaster does not have enough starting kinetic energy to make it over the hill. 

Students apply NGSS Science Practice 3: Planning and carrying out investigations and Science Practice 4 Analyzing and interpreting data as they are presented with a similar problem of energy conservation but with a twist. They also reason abstractly and quantitatively, which is CCSS Math Practice 2 and NGSS Science Practice 5: Using mathematics and computational thinking and Science Practice 2: Developing and using models are both a part of this lesson. This is in the context of the topic of energy which applies NGSS performance standard HS-PS3-2: Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects). 

If a class is able to do a more advanced problem, I include friction as a part of the calculation which involves NGSS HS-PS3-1: Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

Socrative Quiz on Energy Calculations

15 minutes

I start the lesson with a short formative assessment to measure student understanding of energy conservation and calculations involving kinetic and potential energy. I use this data to provide small group instruction during the lesson. As students come into class, displayed on the board is the instruction to go to my Socrative "room" and take the Energy Miniquiz. Most of my students have their own smart phones that they can use for this quiz. For the one student who does not have a smart phone, I discretely hand them my own phone already navigated to the page with the quiz ready to go. Students can also use a laptop, chrome book or tablet to take the quiz as long as they can access the internet through our school WiFi. 

The assessment is a "pop-quiz" and is a twelve question quiz whose purpose is to inform me of student understanding on energy conservation and the application of kinetic and potential energy formulas. This quiz is set so that Socrative.com reveals student's names and their responses as they answer them (only I can see the results). I know within the first few minutes of class if there are misunderstandings that need to be addressed.  If more than 7 or 8 students make mistakes on a single problem then I do some sample problems with the whole class.

If there are a few students who would benefit from more instruction, I do Small Group Instruction. This is a three step strategy to help struggling learners. First, I collect data. In this case I give the Energy Miniquiz formative assessment. Then I analyze that data to identify students who need additional help. Energy Mini-quiz Data is sorted to show which students had the lowest score. I notice with these students that many of them struggled with the calculations on the mini-quiz. While the rest of the class does an activity, I pull those few students aside and give them direct instruction on their area of need.

Kingda Ka Roller Coaster Calculation

25 minutes

As students take the miniquiz, I open the kingda ka with friction power point. If I feel a class struggles mathematically, I may use the kingda ka no friction which is easier to solve but still applies conservation of energy calculations.

When all of the students are done with the quiz, I introduce the Kingda Ka with the first slide of the presentation. This is a different kind of roller coaster. Instead of climbing a hill to start, this coaster launches the cars, giving them a large horizontal velocity first. After a few seconds, the launch mechanism no longer accelerates the coaster and conservation of energy determines the rest of the trip. I play a short YouTube video that gives a 1st person view of the coaster (students love it!)

Slide two shows the students task, which I ask each student to do in his or her notebook. Students are to determine the required launch velocity to make the coaster clear over the first hill. Students must use conservation of energy to determine the starting velocity based on the needed potential and kinetic energies to get the coaster over the first hill (plus energy lost due to friction if using the first power point). Overall, it is not a difficult problem, but it challenges student thinking because of the reverse nature of the roller coaster's starting energy. It also opens their thinking to different coaster designs which they can have for the upcoming roller coaster project

While the class works on this task, I do small group instruction where I call up the students who need extra instruction based on their performance on the miniquiz. I try to group students together based on the problems they get wrong. This requires 5-10 minutes of time. After I have given the instruction to this group, they return to their seats and I circle the class to ensure students are on task with the King Da Ka assignment.

Closure

10 minutes

I finish the class by reviewing the Kingda Ka calculation. I present the solution that is part of the power point. The solution I present solves the problem by keeping the variables in place while I solve for the starting velocity. I instruct students to write this solution in their notebooks if they didn't solve it this way. Now many students may have multiple ways to apply the solution to this problem.

Next I show what happens if the roller coaster does not have enough energy to make it over the hill. It is called "roll back" and I play another Youtube video showing this (links are also in the power point). Students gasp in terror as they see the coaster momentarily stop at the top of the hill! The class finishes off with a quick calculation of the power required to get the Kingda Ka its starting velocity.